Home

TMCM Labs and Software - HWS Department of Mathematics and

1. SUB starburst lineCount Creates a bunch of lines radiating out from a center point The number of lines is given by the parameter The lines have random lengths and point in random directions Because of a limitation on the Fork command lineCount can t be more than 100 fork lineCount There are now lineCount turtles face random 360 Each turtle faces in a random direction forward random 5 Each turtle goes forward by a random amount All the turtles di before th subroutine returns END SUB PenUp MoveTo 5 5 PenDown Starburst 50 PenUp MoveTo 5 5 PenDown blue StarBurst 50 here is a special variable that you an use to tell the turtles created in fork statement apart The name of he variable is ForkNumber Each the turtles created by a Fork N ommand has a different ForkNumber he values are 1 2 N Fh ey Or DO Fork 2 PenUp IF ForkNumber 1 THEN MoveTo 5 5 One turtle does this http math hws edu TMCM java xTurtle samples Tutorial8_multitasking txt 1 of 2 3 26 2000 12 50 37 PM http math hws edu TMCM java xTurtle samples Tutorial8_multitasking txt green ELSE MoveTo 5 5 The other turtle does this yellow END IF PenDown Fork 60 Both turtles split there are now 120 turtles Face 6 Forknumber Because they have
2. val length width Compute a value RI Gd H URN val Specify the value to be returned by the function END FUNCTION DECLARE answer answer Area 5 7 Call the function Area with parameter values 5 and 7 PenUp MoveTo 7 7 Pendown green DrawText A 5 by 7 rectangle has area answer http math hws edu TMCM java xTurtle samples Tutorial6_subroutines txt 2 of 2 3 26 2000 12 50 36 PM http math hws edu TMCM java xTurtle samples Tutorial7_recursion txt xTurtle Tutorial Example 7 Recursion A recutsive subroutine or function is one that calls itself or that calls another routine that calls it back and so on You can do recursion in xTurtle This file demos two standard examples the recursive factorial function and a recursive tree drawing subroutine For a positive integer N factorial N is defined to be N factorial N 1 as long as N gt 1 If N lt 1 then the answer is given directly as 1 This definition can b xpressed easily ina function that calls itself recursively FUNCTION factorial N IF N gt 1 THEN return N factorial N 1 ELSE return 1 END IF END FUNCTION DECLARE N F N 1 PenUp MoveTo 10 9 PenDown black LOOP EXIT IF N gt 9 F factorial N DrawText factorial N F N N 1 END LOOP A binary tree m
3. including DrawText are examples of output from the computer to the user This file gives examples of several other I O commands in xTurtle TellUser Hello World D This command pops up a box displaying the specified tring to the user The ser must click ona he program can continue ECLARE amount AskUser What is the amount his also pops up a box isplaying the string number That number s stored as the value of he specified variable tro FHQaH in the variable amount amount amount 1 07 Uses the value typed in S u displayed OK button before t here is also an input box here the user can type in amount In this example the number typed by the user is stored by the user in a computation The computed value is then stored as the new value of amount TellUser The amount is now amount Just as in DrawText strings can include variables This D YesOrNo Are you happy command displays a string containing the new value of amount ECLARE resp Displays the string and resp gets a response from the user With this command the user can only answer yes or no If the user says yes the value of the variable is set to 1 if the user says no the value is set to 0 http math hws edu TMCM java xTurtle samples T utorial3_io txt 1 of 2
4. s to the answer shift lod N2 Multiply N2 by 2 by shifting it left shl jmz done If N2 is zero we are done http math hws edu TMCM java xComputer samples Labels txt 1 of 2 3 26 2000 12 50 28 PM http math hws edu TMCM java xComputer samples Labels txt sto N2 jmp loop Proceed to the next iteration doAdd lod N2 This section adds N2 to ANS before add ANS doing the preceding shift operation sto ANS jmp shift done hilt Halts the program 20 This says that when the program is loaded the 7 following item is to be at location 20 Thus N1 will be 20 N2 will be 21 and ANS will be 22 Nis 13 The number 13 is stored in a location named N1 N2 56 56 is in a location named N2 These are the numbers that will be multiplied change them to any values you like ANS 0 ANS is the name for a memory location that will hold the product of N1 and N2 when 4 the program ends http math hws edu TMCM java xComputer samples Labels txt 2 of 2 3 26 2000 12 50 28 PM http math hws edu TMCM java xComputer samples Three_N_Plus_One txt Example 4 3N 1 sequences This file doesn t illustrate anything in particular about the xComputer It s just that really like the 3N 1 problem Starting for N is sequence from any positive integer N the 3N 1 sequenc computed as follows If N is 1 then stop the is complete Otherwise if N is even then divide
5. you will be able to save and load files For example you could create sample files to use with the applets on your own Web pages There are three applications One simply makes the applets available without loading any sample files Another loads the applets with the sample data files used in the labs worksheets from http math hws edu TMCM java The third application loads the applets with the sample files and tutorial examples from the applet information pages at the same address The idea for the latter two applications is that you could read the Web material in a Web browser at the same time that you run the applets using the applications This will let you use files with the applets When an applet is run in a Web browser it probably won t be able to save and load files If you ve downloaded the labs and tutorials for use on your own computer you can view them in a Web browser but in that case the applets in the Web browser will be even more limited They probably won t even be able to load the sample files that are used in the labs and tutorials All the sample files are included in this archive They have names that end with txt and they are really just plain text files that you can read with a text editor if you want I know it s messy to have all these files in one directory but I couldn t find a way to get the applets to work reliably with the sample files u
6. Machine language consists of binary numbers but it would be almost impossible for people to program if they had to write programs directly in binary Instead programmers use assembly language or high level language The programs they write in these languages are translated by assemblers and compilers into machine language You ll use a high level language called xTurtle in later labs In this lab and the next you ll use assembly language Assembly language is closely related to machine language but has several features that make it much easier to use You ve already seen that assembly language uses meaningful instruction names such as ADD C instead of numerical instruction codes In this lab you ll see how memory locations and data values can also be referred to by name rather than by number Such names are called labels You ll also learn about a few new machine language instructions which use indirect addressing The material in this lab is based on Chapter 3 of The Most Complex Machine Labels are introduced in the postscript to that chapter This lab includes the following sections Labels and the Assembler e Loops and Decisions e Indirect Addressing e Dancing Bits e Exercises Start by clicking this button to launch the xComputer applet in its own window Sorry your browser doesn t do Java For a full list of labs and applets see the index page http math hws edu TMCM java labs xComputerLab2 html 1 of 8 3 2
7. Some of th can be cre However t are runnin the Save mentioned try runnin To be used by an applet uits you gn center gt ar uncher version user clicks a separate window DataRepsLaunc For example co let archive x launcher versions of the applets only a button appears on the Web the button the applet is opened The names for the launcher versions her class tmcem xLogicCircuitsLauncher class to use the launcher version of uld use the lt applet gt tag iogicCircuits zip code tmem xLogicCircuitsLauncher class width 18 et gt e applet ated using his button g the appl button g above O g the appl 0 ts can the wW e E Ey et height 30 gt load sample input files Such files Save button of one of the applets ill generally not be functional when you in a Web browser If you want to use the application version of the applets if you have the Java Development Kit with the appletviewer command a sample input file should be in the same directory as the HTML source file for the Web page that contains the applet The names of the sample input files must be specified as params in the lt applet gt tag For example the xLogicCircuits applet can read one sample file The file is specified in a param named LOAD For example if you want xLogicCircuits to load a sample file named SampleCir
8. This is the transformation which moves x y z to x Ay y z Lines that were perpendicular to the xz plane are tilted or skewed to the left or right e ySkew A This is the transformation which moves x y z to x y AXx z xyShear A B This is the transformation which moves x y z to x Az y Bz z Lines perpendicular to the xy plane are skewed I have not included a complete set of skew shear transformations because I don t expect them to be used much Note that although xModels is a 3 dimensional graphics program you can restrict yourself to two dimensions if you want The names and semantics of the transformations were chosen so that all the two dimensional transformations are available with reasonable names This explains the otherwise odd rotate A about B C for example It is important to understand what a list of transformation does to an object All the transformations are applied to the object before it is displayed So square scale 2 5 is just a way of specifying a 2 by 5 rectangle and circle translate 5 is just a way of specifying a circle centered at the point 5 0 You don t actually see the object moving or changing shape For that you have to use an animation and specify a range of values for the http math hws edu TMCM java xModels info html 7 of 9 3 26 2000 12 50 33 PM xModels Info transformation In that case each frame of the animation gets its own transformation to specify the shape or posit
9. We often think of the machines as working with binary numbers made up of O s and 1 s or with words made up of x s y s and z s But remember that the meaning of a symbol has no effect on any calculation performed by a Turing machine all the machine does is follow its rules At the very top of the xTuringMachine applet is a pop up menu that you can use to select from among the machines that the applet knows about The applet is set up to load several sample machines when it starts up Later you ll see how to construct new machines from scratch You ll work with the first of these sample machines ChangeO1toXY to help you learn how to use the applet Just below the pop up menu is the Turing machine itself and its tape The Turing machine itself moves back and forth along the tape The number that the machine displays is its currents state which can change as it computes The tape is an infinite sequence of cells Each cell contains a symbol possibly blank Below the machine on the left is a set of controls Use the Run and Step buttons to control the computation of the machine If you click on the Step button the Turing machine will perform one step in its computation If you click on Run the machine will compute until you stop it or until it enters the halt state You can control the speed of a running machine with the Speed pop up menu which is just above the run button You might want to stick with the Step bu
10. e ADD X Add the number in memory location X to the AC e ADD C X Add the number X to the AC e ADD I X Let Y be the contents of memory location X and add the number in location Y to the AC e SUB X Subtract the number in memory location X from the AC e SUB C X Subtract the number X from the AC e SUB I X Let Y be the contents of memory location X and subtract the number in location Y from the AC e AND X Bitwise AND the number in memory location X with the AC e AND C X Bitwise AND the number X with the AC e AND I X Let Y be the contents of memory location X and bitwise AND the number in location Y with the AC OR X Bitwise OR the number in memory location X with the AC OR C X Bitwise OR the number X with the AC OR I X Let Y be the contents of memory location X and bitwise OR the number in location Y with the AC NOT Apply a bitwise NOT to the AC INC Add 1 to the AC DEC Subtract 1 from the AC SHL Shift the AC left one bit SHR Shift the AC right one bit LOD X Load the number in location X into the AC LOD C X Load the number X into the AC LOD I X Let Y be the contents of memory location X and load the number from http math hws edu TMCM java xComputer info html 7 of 8 3 26 2000 12 50 30 PM xComputer Info location Y into the AC e STO X Store the value in AC into memory location X e STO I X Let Y be the contents of memory location X and store the valu
11. http math hws edu TMCM java xTurtle info html 3 of 13 3 26 2000 12 50 17 PM xTurtle Info Combined words like endif and endfunction are redundant since they can all be written equivalently as two words For example end if Probably it was a mistake to include these combinations in the language but there they are I will not mention them again instead I will always use two separate words Variable names subroutine names and function names are collectively known as identifiers You can make up your own names for the variables and routines that you declare as long as you don t use reserved words and as long as you don t try to reuse a name in the same program Identifiers must begin with a letter They can contain letters digits from 0 to 9 and the underscore character _ They cannot contain spaces or other white space They can be of any length Variables and Expressions Before a variable can be used it must be declared This is done using a variable declaration which consists of the reserved word declare followed by the names of one or more variables that are being declared Variables in the list should be separated by commas For example DECLARE InterestRate DECLARE x y row column Variable declarations cannot be nested inside other statements such as loops They can occur in subroutines and functions where they are used to create local variables as discussed below In xTurtle the value of a varia
12. 3 turn 120 forward 3 Statements to define turn 120 what the subroutine forward 3 does turn 120 END SUB Marks the end of the subroutine Defining this subroutine has not actually drawn anything When the subroutine is called by using its name as a statement the commands inside the subroutine ar xeuted Triangle Call the subroutine to draw a triangle SUB Square length Define a subroutine that has a parameter called length A value for the parameter will be supplied when the subroutine is called forward length turn 90 forward length Statements to define turn 90 what the subroutine forward length does turn 90 forward length turn 90 END SUB Marks the end of the subroutine PenUp MoveTo 6 6 PenDown blue Square 5 Draw a 5 by 5 square PenUp MoveTo 5 5 PenDown Square 3 Draw a 3 by 3 square PenUp MoveTo 4 4 PenDown Square 1 Draw a 1 by 1 square http math hws edu TMCM java xTurtle samples Tutorial6_subroutines txt 1 of 2 3 26 2000 12 50 36 PM http math hws edu TMCM java xTurtle samples Tutorial6_subroutines txt FUNCTION Area length width Begin definition of a function named Area with two parameters named length and width DECLARE val This is a local variable for use inside this function only
13. 3 26 2000 12 50 32 PM The xSortLab Applet The Log Every time a sort completes successfully statistics about that sort are written to a log For a visual sort the number of copies and the number of comparisons are recorded For a timed sort all the statistics that are displayed in the Timed Sort panel are written to the log You can view this log by selecting the Log option from the pop up menu at the top of the applet The Log panel has buttons for clearing the log and for saving it to a file However it is likely that your browser will not permit you to save the log Unfortunately the applet has no provision for printing the log at this time You might try using copy and paste to copy the data from the log to another program from which you can copy or print it David Eck eck hws edu August 1997 http math hws edu TMCM java xSortLab index html 3 of 3 3 26 2000 12 50 32 PM xModels Intro The xModels Graphics Applet The applet at the bottom of this page assuming that you have a Java enabled browser let s you write scene descriptions in a simple language The applet can display still images and animations described in this language Images are displayed as wireframe models The point is to learn something about geometric modeling and geometric transformations which are important in computer graphics The applet was written by David Eck for use with his introductory computer science textbook The Most Complex Machi
14. 5 stairs 7 turn 30 EXIT IF heading 0 END LOOP What picture is drawn by one execution of the loop in this program Why You will only get the correct picture if your solution to Exercise 5 meets the fourth requirement imposed on the program in that exercise What picture is drawn by the program as a whole Why Exercise 7 Here are some questions about the subroutine you wrote for Exercise 6 e Why does the single line SUB stairs NumberOfStairs replace the first two lines of the program from Exercise 5 Why does it make sense for the variable NumberOfStairs in the program to become a parameter in the subroutine http math hws edu TMCM java labs xTurtleLab2 html 5 of 7 3 26 2000 12 50 19 PM xTurtle Lab 2 Inthe subroutine why don t you ask the user for the number of steps to draw Why is it better to use a parameter e The variable count in the program from Exercise 5 becomes a local variable in the subroutine Why Why is it a local variable instead of a parameter e What did you learn from Exercise 6 about subroutines and their use in complex programs Exercise 8 Explain carefully why running the sample program SpiralsSubroutine does not produce any output or have any visible effect What exactly does the program do when it is executed What is the point of it if it doesn t do anything Exercise 9 Write a program that will draw pictures like the following where the number of bumps is input by the use
15. Enter a lod 17 instruction into memory location zero and reset the PC to zero Set the display style to Control Wires Then use the Step button to step through the fetch and execute cycle as the lod instruction is executed Write down what happens during each step Carefully explain the purpose of each step in the execute phase of the cycle steps 4 and later What differences do you find between the execution of a lod c instruction and the execution of a lod instruction How can the differences be explained in terms of what the instructions do Exercise 5 Use the Step button to trace the execution of an add c instruction and of an add instruction See Exercise 4 for detailed instructions about how to do this Record the control wires that are on during each step in the execute part of the fetch and execute cycle that is for steps number 4 and later and carefully explain the purpose of each of those steps What differences do you observe between these two instructions How can the differences be explained in terms of what the instructions do Exercise 6 Carefully explain why the first three steps of the fetch and execute cycle are always the same and why they have nothing to do with the contents of the instruction register Exercise 7 Modify the first counting program used in this lab so that it will count just from one to sixteen stopping when it reaches sixteen The program is repeated below To do this each time through the loo
16. N by 2 Otherwise if N is odd multiply N by three and add 1 The question is whether this sequence terminates for ALL starting values N The answer is not known at this time his program comput T s 3N 1 sequences for various values fe starting from Ss 1 For each sequence it counts in the sequenc The values are successive memory locations the number of terms tored in memory in Run this at Fastest speed and watch it in graphics mode to see the random looking series of sequence lengths that are generated Or watch locations 42 43 and 44 labeled by num N and ct which are where all the computational action takes place lod c 1 Let num 1 Num is the starting sto num j value for the current sequenc lod c 100 100 is location in memory where sto loc i first answer is to be stored loopl lod num Loopl computes one sequence begin by sto N initializing N to the starting value h for the sequence lod c 1 Ct keeps track of the number of terms sto ct in the sequence start counting at 1 loop2 lod N Loop2 computes one term in the sequence dec Test if N 1 by subtracting 1 from it and jJmz next testing if the answer is 0 If so this sequence is complete jump to next to get ready for the next sequenc and c 1 Compute bitwise logical AND of 1 with N 1 jmz odd If the answer is 0 N is odd
17. The JMN instruction is similar except that it checks whether the number in the accumulator is negative Another conditional jump instruction JMF tests the value in the Flag register It is described in one of the exercises at the end of the lab There are two sample programs for you to look at that make effective use of loops and decisions Each of these programs is used in one of the exercises at the end of the lab The sample program ThreeNPlusOne txt computes a 3N 1 sequence This is a problem that you will see several times in these labs Given a positive integer N the program applies the rule If N is even then replace N by N 2 if N is odd then replace it by 3N 1 It applies this rule over and over until the number N becomes equal to 1 For example if the starting value of N is 7 then the program generates the sequence of values 7 22 11 34 17 52 26 13 and so on Run the ThreeNPlusOne txt program To see the numbers as they are generated watch memory location number 17 which contains the successive values of N starting with 7 You will probably want to bump the speed up to Fast You can run the program again with any other starting value of N Modify the value of N in the assembly language program and then reload it into memory with the Translate button You could also change the number in location 17 directly and then run the program If you do this don t forget to click the Set PC 0 button to http math
18. The computer stores the zeros even though you don t ordinarily include leading zeros when you write a number Base ten Integer A binary number can be interpreted as a normal positive integer 0 1 2 3 4 written in the base ten Base ten is the usual way of writing numbers using the digits O through 9 See Section 1 1 of The Most Complex Machine With 32 bits you can represent 232 different numbers Usually you want to use both positive and negative numbers The scheme for representing negative numbers is a bit strange It is explained in Subsection 2 2 3 of the text Using 32 bits the integers from 2147483648 to 2147483647 can be represented Hexadecimal It is difficult for humans to read long strings of zeros and ones Hexadecimal numbers are a kind of shorthand for writing such strings A hexadecimal number is written using the sixteen hexadecimal digits 0 1 2 3 4 5 6 7 8 9 A B C D E and F Each hexadecimal digit stands for four bits So 0 represents 0000 1 represents 0001 2 represents 0010 E represents 1110 and F represents 1111 We could also say that the hexadecimal digit A stands for the base ten number 10 ten B stands for 11 eleven C stands for 12 D for 13 E for 14 and F for 15 A hexadecimal number is really just a number written in the base sixteen just as ordinary integers are in the base ten and binary numbers are in the base two You should be able to translate between hexadecimal
19. There are http math hws edu TMCM java labs xSortLabLab html 8 of 11 3 26 2000 12 50 22 PM xSortLab Lab actually many different logarithm functions and you can use any of them as long as you are consistent If you use a differernt logarithm function you ll just get a different value for K The log function on your calculator is almost surely the common or base 10 logarithm and that s the one that I will use in this lab You don t need to know anything about logarithms except that when N is large N log N is much smaller than N2 This means that for large values of N an N log N algorithm will run much faster than an N2 algorithm Based on this you can probably guess which of the five algorithms are N algorithms and which are N log N algorithms Of course you can use the measurements you made in the previous section of the lab to compute an approximate value for K If T is the time it takes to sort an array of size N then an approximate value for K is given by the formula K T N log N You will do some calculations of this kind in the exercises below Exercises Exercise 1 Each phase of Insertion Sort inserts an item into its correct location in a sorted list Describe in detail how this insertion is accomplished Try to give an algorithm an unambiguous step by step procedure for inserting a new item into a sorted list You can get the information you need by running the xSortLab applet and seeing how it pe
20. To get a square that is five times as large as the default you have to scale it by a factor of five This is done by saying square scale 5 Try typing the following scene description into the empty text area The render the scene and see what you get square square scale 5 You should see two squares of different sizes By the way if you make some sort of mistake in the program an error message will be displayed above the text area You can click on the message if you like to make it go away Now using transformations is not the most obvious way of doing things but it turns out to be remarkably powerful and even after some experience intuitive In addition to the scaling transformation the geometric transformations that you can use are translation and rotation Scaling changes an object s size Translation moves it Rotation pivots it about the point 0 0 or about some other specified point It is important to understand that you don t actually see the object moving The applet applies the transformations to determine the size position and orientation of the object before it adds the object to the scene You only see it http math hws edu TMCM java labs xModelsLab1 html 3 of 10 3 26 2000 12 50 25 PM xModels Lab 1 in its final position Later you ll see how to make an animation in which objects do seem to move but even then each individual frame of the animation is constructed as described here You ve seen that the t
21. a loop you should call PrimeTest to see whether p is prime If p is prime then add it to the list In any case you should then add 1 to p and jump back to the start of the loop to test the next value of p Making a list of primes means storing primes in consecutive memory locations Use a location named list to point to the end of the list That is the value of 1ist is the location where you want to store the next prime that you find Let s say that you want the list of primes to begin at location 50 At the beginning of the program you should store a 50 in 1ist When you find a prime number you can add it to the end of the list with a STO I list command Then you should add 1 to the value of list to get ready for the next number http math hws edu TMCM java labs xComputerLab3 html 6 of 7 3 26 2000 12 50 11 PM xComputerLab 3 If you run your program at high speed you can watch it store the numbers 2 3 5 7 11 13 and so on in memory You might want to watch the program in graphics mode so that you can watch the activity in the main program and in the two subroutines Exercise 8 Write a short essay discussing how subroutines can make it easier to design and write complex programs Your answer should show that you understand that they can do more than save you typing In your essay use some of the work you did in this lab for examples This is one of a series of labs written to be used with The Most Complex Machine A Survey
22. animation and play it backwards The last option Once Through makes the computer stop when it reaches the end of the animation After you have played with the Pinwheel animation for a bit it s time to learn how to write a scene description of your own Basic Objects and Basic Transformations To begin working with scene descriptions click on the New Program button or select New from the pop up menu at the top of the applet In this section you will work with single images Animating an image will be a simple extension of this To add an object to a scene you just have to add the name of the object to the scene description Every time you use the name you get a new copy of the object If you give only the name of the object it will appear at a default size position and orientation If you want it to have a different size position or orientation you have to apply one or more transformations to the object This is done simply by listing the transformations after the object name For example the word square will add a square to the scene It will be a small square one unit wide and one unit high in the center of the scene The entire image always includes a 20 by 20 unit region with x coordinates from 10 to 10 and y coordinates from 10 to 10 Since the image might not be exactly square it can extend farther than this in one direction or the other To get a bigger or smaller square you can apply a scale transformation
23. archive that can be downloaded at the top of the page However for convenience you can also download the source code separately using one of the following links http math hws edu TMCM java download tmcm_source_code zip for Windows http math hws edu TMCM java download tmcm_source_code tar gz for Linux UNIX You can view the README file from this archive Note that this code was written for version 1 0 of Java and uses many features that should not appear in modern Java code It was not written with the intent of publishing it and it has almost no comments I have made the source code available because a number of people have requested it For Users of MacOS 9 or Earlier If are still running MacOS 9 or earlier on an old PowerMac computer you cannot and will never be able to use versions of Java newer than version 1 1 The changes that were made to this web site in June 2004 are irrelevant to you You might want to use the following Macintosh format archives of the old version of this site The complete Web site from March 2000 http math hws edu TMCM java download tmcm java web site sit hgx for Macintosh The Labs and Tutorials examples in a single archive from March 2000 http math hws edu TMCM java download tmcm java apps sit hgx for Macintosh The Java source code files from March 2000 http math hws edu TMCM java download tmcm java source sit hqx for Macintosh David Eck eck hws edu
24. e What real number has the same binary representation as the hexadecimal number 4228AE14 e What real number has the same binary representation as the four letter word Fred e What binary number represents the base 10 number 3 Exercise 8 Enter the following base 10 integers into the DataReps applet 1 2 4 8 16 32 64 Describe the corresponding pixel representation of these numbers The pixel representation is displayed in the center of the applet What pattern do you see Why does this pattern occur What can you say about the binary representation of these numbers Exercise 9 Enter a four letter word such as TIME into the DataReps applet Select ASCII Text as the input type type the word into the applets input box and press return Consider the pixel representation of the word which is displayed in the center of the applet Play with the pixels in the third column of pixels from the left Turn them on and off by clicking on them and observe what happens to each letter in the word What happens What does this tell you about the ASCII coding of letters What is the meaning of the third bit in that encoding Exercise 10 This final exercise is meant to be a longer essay question You should try to show your understanding of the way data is represented in a computer and an appreciation for the fact that meaning depends on context and convention It would be legal to input 1000 into the Data Representation Applet as ei
25. forward 5 turn 120 forward 5 forward 7 turn 90 forward 5 back 10 Color Unless you tell it to do otherwise the turtle will draw everything in red However you can tell it to change its drawing color to any other color The turtle understands the following basic color commands red blue green cyan magenta yellow black white and gray After it executes one of these commands it will draw in the specified color until it comes to http math hws edu TMCM java labs xTurtleLab1 html 3 of 10 3 26 2000 12 50 15 PM xTurtle Lab 1 another color change command For example the following sequence of commands will draw a triangle with each side in a different color green forward 5 turn 120 blue forward 5 turn 120 cyan forward 5 turn 120 Besides these basic color commands there are two commands that can be used to specify any drawing color that the computer is capable of displaying The commands are rgb x y z and hsb x y z where x y and z are parameters that can have any value in the range 0 0 to 1 0 To understand these commands you need to know something about color But you can safely skip the details if you want Any color can be specified as some combination of the primary colors red green and blue In the command rgb x y z the parameters x y and z specify the amount of red green and blue in the color For example a value of zero for x indicates that the color is to contain no red at all and a
26. is turned on This causes the number stored in the PC which is the location of the instruction that is to be fetched to be copied into the ADDR register where it sets up the main memory for reading from that location The purposes of most of the wires are clear from their names The seven wires at the top of the list starting with Select Add are connected to the ALU The ALU can perform several different calculations The Select wires are used to tell it which calculation it should do The Assembly Language of xComputer An assembly language program is simply a way of specifying a sequence of 16 bit binary numbers to be stored in the computer s memory As such it can include any of the data items described above Assembly language instructions numbers in the range 32768 to 65536 hexadecimal numbers up to four digits preceded by binary numbers up to 16 bits preceded by B or b and ASCII characters one or two characters preceded by a single left quote mark The legal instructions are listed below An instruction consists of a two or three character code such as LOD OR and HLT Since upper and lower case letters are not distinguished these could also be written as lod or and hlt In some cases this instruction code can be followed by an addressing mode indicated by C for constant addressing mode and by I for indirect addressing mode The addressing mode indicates how the data for the instruction is to be u
27. jump to location odd to handle that case lod N Otherwise N is even divide N by 2 by shr j shifting it right and putting the sto N result back into N Then jump to jmp count j count where this term in the sequence A is counted odd lod N If N is odd multiply it by 3 by adding it add N it to itself twice Then add T jmf error j If any of these additions produces a add N result greater than 65535 the FLAG jmf error j register is set This indicates an add c 1 error Number too large for this jmf error j computer Jump to error if the sto N FLAG is set http math hws edu TMCM java xComputer samples Three_N_Plus_One txt 1 of 2 3 26 2000 12 50 29 PM http math hws edu TMCM java xComputer samples Three_N_Plus_One txt count lod ct Count this term in the sequence by inc incrementing the value of ct sto ct jmp loop2 Return to start of loop2 to do the next term in the sequence next lod ct The 3N 1 sequence for the current starting sto i loc value num is complete Store the lod loc number of terms in the sequence in the inc location given by the value of loc sto loc gt then add 1 to loc lod num Also add 1 to num to give the starting ince value for the next sequenc sto num jmp loopl Jump to loopl to do the next sequenc error lod c 0 A term in the current sequence has dec exceeded 65535 Store 1 computed sto c
28. lt value gt is a constant variable or formula specifying the value to be returned Here are two sample functions FUNCTION NextN num FUNCTION UpdateAmount amount IF num 2 round n 2 THEN IMPORT Rate return num 2 DECLARE Interest ELSE Interest amount Rate return 3 num 1 DECLARE newAmount END IF newAmount amount Interest END FUNCTION return newAmount END FUNCTION User defined functions are used in the same way as built in functions such as sin x Functions can have ref parameters they can be recursive and they can be predeclared Multitasking In parallel processing several processes are going on at the same time Multitasking is a way of simulating parallel processing by giving a little bit of execution time to one process then a little bit to another process and so on Multitasking can be done in xTurtle by using the fork statement Fork is a subroutine that takes a single parameter specifying the number of processes to be created This number must be between 1 and 100 Conceptually the command fork N splits a turtle into N different turtles Each of the turtles then proceeds to execute the following statements independently Any variables that exist before the fork are shared by all http math hws edu TMCM java xTurtle info html 11 of 13 3 26 2000 12 50 17 PM xTurtle Info the turtles However if a variable declaration statement occurs after the fork each turtle will create its own copy of the
29. math hws edu TMCM java labs xSortLabLab html 7 of 11 3 26 2000 12 50 22 PM xSortLab Lab N2 and N log N In the previous section of the lab you measured the computation times for the five sorting algorithms on arrays of different sizes You probably noticed that QuickSort and Merge Sort are much faster than the other three algorithms except for very small arrays This final section of the lab gives a more rigorous mathematical form to this observation Some sorting algorithms exhibit what is called running time on the order of N squared They are also called more briefly N2 algorithms The N here is the number of items being sorted To say that an algorithm is of the order of N means that the running time of the algorithm for an array of N items is given approximately by K N2 where K is some constant number The approximation tends to become more exact as N gets bigger Different algorithms have different values for K Furthermore if the same algorithm is run on different computers each computer will give a different value of K Saying that K is a constant means that for a given algorithm running on a given computer there is one value of K that will work for any array size N Bubble Sort is an example of an N algorithm You should be able to use the data you collected in the previous section of the lab to calculate a K value for Bubble Sort running on your computer For example suppose that it took 8 205 seconds to sort 5 arrays
30. not be used outside the fil to the is contained in the directory named tmcm for the applets belong to the package named kages tmcm directory espond 1 and also effect that a class sh r is defined unle il wh name of the class agrees with the name of The development system that it is defined wrote the applets didn t enforce this rul cause a problem if you try to compil but it s OK as long you compil in a directory at the same time The warning messages are not time right order the file wh d the oul ss used w e This co the files one at e all the files or compile them in th errors and N u will not stop the files from being compiled The code can be compiled wit the JDK classes that are defined in its sub packages the tmcm directory and you to compile all the files in you would say javac tmem or javac tmem For convenience all the classes in a shell script nam is will also builda class files script files themselves the tmcm Note for Macintosh users been able to make it work Java Development Kit the tmcm package or one of you must be in to the file or files you want to compile the package tmcm xSortLab xSortLab java xSortLab java Theoretically to compile the files using Apple s SDK for Java The applets were original h the javac command fr
31. the actual range of visible values can be larger in one direction The turtle can move outside the visible region and will just keep drawing happily even though you can t see what it s doing The command home moves the turtle back to the center of the screen Below the graphics area is an input box where you can type in commands for the turtle When you press return the turtle will carry out the commands or tell you that there was an error in your input Clicking on the button named Do It is equivalent to pressing return If an error message is displayed you can make it go away by clicking on it It will also go away the next time you press return or click the Do It button There are no restrictions on what you can type in the command input box You can even put a whole subroutine definition there However for anything that takes more than a few words you ll want to write a program If you want to create a new program click on the New http math hws edu TMCM java xTurtle info html 1 of 13 3 26 2000 12 50 17 PM xTurtle Info Program button at the top right corner of the applet The graphics area will be replaced by a text input area where you can type your program To run the program just click on the Run Program command If the program is correct it will be compiled and executed If there is an error you ll get an error message Again you can make the error message go away if you want by clicking on it If there is an
32. the number of arrays and the total computation time in the three boxes at the top The applet will calculate the computation time per array and the value of T N N It will do the calculation when you click the Compute button and whenever you press return while typing in one of the boxes Sorry your browser doesn t do Java Exercise 8 QuickSort is an N log N sorting algorithm You should be able to use data you collected in this lab to compute the value of K in the equation T K N log N for QuickSort running on your computer Make a table just like you did for Exercise 7 but use the value of T N log N instead of T N N You can use the above applet to do the calculation Based on the data in your table what is your best guess for the actual value of K Explain your reasoning Exercise 9 Is Insertion Sort an N2 or an N log N algorithm You can probably guess but how can you be sure From the data you collected in the lab compute both T N N and http math hws edu TMCM java labs xSortLabLab html 10 of 11 8 26 2000 12 50 22 PM xSortLab Lab T N log N for various values of the array size N Based on the answers you should be able to tell whether Insertion Sort is an N2 or an N log N algorithm Which is it Explain your reasoning Do the same thing for Merge Sort Exercise 10 In Exercise 7 you determined the value of K for selection sort in the equation T K N2 Now that you know the value of K you can use the e
33. they were when the drawing begins This is a postcondition for the program as a whole Start your program with the following three lines DECLARE NumberOfSteps AskUser How many steps NumberOfSteps DECLARE count The variable named count should be used as a counting variable in a loop to count the number of steps that have been drawn You should think about preconditions and postconditions as you write the program Include comments in your program that discuss specific preconditions and postconditions for various parts of the program and explain how they were used or could have been used in developing the program It is a bit easier to write the program if you start drawing the steps at the top of the staircase Exercise 6 Convert the program you wrote for Exercise 5 into a subroutine Start by removing the first two lines of the program which were given to you in Exercise 5 Replace them with SUB stairs NumberOfSteps Add the line END SUB at the end of your program These two steps turn your staircase drawing program into a staircase drawing subroutine After running the modified program you will be able to use commands like stairs 5 to draw a staircase with five steps and turn 30 stairs 4 to draw a tilted staircase with four steps To make a more interesting picture add the following lines at the end of your modified program after the definition of the subroutine and then run the program LOOP stairs 3 stairs
34. units and up 6 units from its original position This will show in the image as a small red circle centered at the point 6 6 circle scale 5 translate 6 6 Transformations can be combined The circle is FIRST scaled by a factor of 5 and then the resulting object is moved 6 units to the left and 6 units up The result is a circle of diameter 5 centered at the point 6 6 The drawing color is esti red for this circle blue Color changes to blue for following objects square scale 5 Start with a square rotate 30 rotate it 30 degrees about the origin translate 6 6 then move it 6 units over and 6 down Note that you don t have to list all the http math hws edu TMCM java xModels samples Tutorial1_Basics txt 1 of 2 3 26 2000 12 50 37 PM http math hws edu TMCM java xModels samples Tutorial1_Basics txt transformations on one line square scale 6 2 A scale command can also have two or translate 5 5 three parameters scale 2 6 magnifies 7 by a factor of 6 horizontally and 2 vertically Scaling a square in this way gives a rectangle green cube scale 4 translate 5 0 A 1 by 1 by 1 cube is magnified by a factor of 4 and translated 5 units to the right cone scale 4 translate 5 0 The cone shows up 5 units to the left of its default position at the origin magenta A bright purple ish color cylinder sca
35. want to display an actual character you have to write it as in the program The TellUser command pops up a box to display its string The user must click on an OK button to dismiss this box and the program waits for the user to do so The display is not changed There is also a command for displaying a string in the graphics display area This DrawText command writes the string at the current turtle position in the current drawing color The string is drawn even if the turtle s pen is currently up After drawing the string the turtle moves to a point just below its original position so that the output of successive DrawText commands will line up neatly one under the other DrawText has one parameter specifying the string to be drawn For example DrawText Hello World There are commands for doing input AskUser and YesOrNo Each of these input commands has two parameters The first parameter is a string to be displayed to the user This string is meant to prompt the user for a response The second parameter is the name of a variable where the user s response is to be stored For AskUser the use can type in any real number as a response For YesOrNo the user is given the choice of responding yes or no If the user says yes the value 1 is stored in the variable if the user says no the value 0 is stored For both of these commands the computer pops up a box to display the string and get the user s response The program waits until
36. 1000000000 in binary The number 1000000000 has nine zeros and so is equivalent to 29 or 512 in base 10 Based on your answer compute approximately how long the machine would take to count from 0 to 1000000000000000 that is from 0 to 215 Explain how you computed your answer and why the method that you used is valid Exercise 7 Construct a Turing machine to do the following Assume that the tape contains a binary number and that the machine is started on the right hand end of the number The machine should write a string of s where the number of s is given by the binary number that was initially on the tape For example if the number on the tape was 10110 which is 22 http math hws edu TMCM java labs xTuringMachineLab html 8 of 9 3 26 2000 12 50 12 PM xTuringMachine Lab in binary then the machine should halt with a string of twenty two s on the tape In order to construct this machine you will have to understand something of how the sample machine MultiplyByAdding works In that machine the problem was to repeat the addition operation a specified number if times In this exercise the problem is to repeat the operation add a to the string a specified number of times Exercise 8 Construct a Turing machine to do the following Assume that the machine is started on a tape that contains nothing but a sequence of x s and y s The machine must work for any such sequence The machine is started on the left end of this se
37. 3 26 2000 12 50 35 PM http math hws edu TMCM java xTurtle samples Tutorial3_io txt TellUser The recorded answer is resp http math hws edu TMCM java xTurtle samples T utorial3_io txt 2 of 2 3 26 2000 12 50 35 PM http math hws edu TMCM java xTurtle samples Tutorial4_loop txt xTurtle Tutorial Example 4 A loop is used to repeat a seq of statements over and over method must be provided to exi the loop In xTurtle the beginning of a is marked with LOOP and the e is marked with END LOOP LOOP forward 4 back 4 line to cente 5 degree maybe loop start of a loop draw a return turn 5 rotate EXIT IF heading 0 END LOOP marks end of In the preceding loop the repeated statements draw a line radiating out froma center point and then rota the turtle Each time through the loop the computer asks itself Is heading 0 If the answe is yes then the loop ends and the computer goes on to the next statement followin the loop If the answer is no the computer continues to execute the loop The heading is the direction that the turtle is facing PenUp MoveTo 2 5 6 PenDown DECLARE count gray count 0 LOOP forward 5 turn 45 count EXIT END LOOP In this loop the computer adds 1 to count each time it goes through the loop After it does this 8 times the value of
38. 45 and 55 When you use a number range in a segmented animation you must specify a number for each of the key frames For example you could use the number range 1 3 5 2 in an animation with three segments and four key frames Note that the number of colons is http math hws edu TMCM java labs xModelsLab1 html 6 of 10 3 26 2000 12 50 25 PM xModels Lab 1 always equal to the number of segments The number range 1 3 5 2 specifies a value of 1 for the first key frame 3 for the second 5 for the third and 2 for the fourth and final key frame You can leave out some of the numbers in the middle of a number range as long as you don t leave out the colons For example the number range 1 2 provides a value of 1 for the first frame and a value of 2 for the last frame The computer interpolates smoothly between these two values for all the intermediate frames For example here is an animation that shows a small square moving along the inside edges of a big square You might want to type this in or cut and paste it in and see how it works animate 15 15 15 15 square scale 12 red square scale 2 translate 5 5 5 5 5 5 5 5 5 5 Defined Objects and Structured Complexity It s a long way from simple geometric shapes to complex scenes As usual this complexity is handled by tackling it level by level with reasonable jumps in complexity from one level to the next In the xModels applet new objects can be defined on o
39. Followed visited link LC Background Background image overrides this color Color Schemes Netscape Default Colors z If you don t want to use the default browser colors which can vary from browser to browser select a color scheme from the pop up menu or click on Use custom colors and click on any of the five color boxes to change that color Each page has five associated colors one for the page background one for regular text and three different colors that are used to display links You can select the colors for your page from the Color Scheme pop up menu Alternatively you can set each color individually Now make some changes to the text If you have a page heading on the first line of text hilite it and then select Heading 1 from the pop up menu at the left end of the toolbar Center the heading by selecting centered text from the pop up menu at the right end You might also use the color pop up menu in the toolbar to change the color of the heading You can make similar changes to any text on your page Dividing lines can help to organize a page Add one to your page by clicking on the H Line button Once the line appears on your page you can drag its edges to change its size and you can right click on it to get a pop up dialog with various options To make a hypertext link on your page use the Link button in the toolbar You will get a dialog box where you can type in the URL of the page to
40. In the next phase of the sort the lists of length two are merged to form lists of length four Then lists of length four are merged into lists of length eight This continues until all the items have been merged into one long sorted list In the picture below lists of length four are being merged into lists of length eight The two lists that are being merged are in the top row enclosed inside a pair of green boxes The merged list that is being formed is in the bottom row surrounded by a bigger green box In the picture items 3 and 7 have just been compared Since item 7 was smaller it has been moved to the bottom list i atam r m g Me te da is ila 16 QuickSort is the most complicated of the available sorting methods The main idea in QuickSort is an operation called QuickSortStep which works like this Remove one item from the list Then divide the remaining items into two parts items bigger than the removed item and items smaller than the removed items Move all the smaller items to the beginning http math hws edu TMCM java labs xSortLabLab html 5 of 11 3 26 2000 12 50 22 PM xSortLab Lab of the list and all the bigger items to the end leaving a gap in the middle The item that was removed at the beginning is placed in the gap Since all the items to the left are smaller and all the items to the right are bigger the item that was placed into the gap is in its correct final position In the xSortLab applet the i
41. In the picture the items have already been swapped Top message gives high level goal oriented information about What the applet is doing Use the Step and Go buttons in the xSortLab Applet to execute Bubble Sort Check the Fast checkbox when you want to speed things up This option might also help you to get the broader picture of how the algorithm operates You should try stepping slowly through the algorithm with the Step button reading each message in detail It will also be useful for you to watch the algorithm run itself at Fast speed At this speed the applet only displays the upper message which tells you what it is trying to accomplish in each major phase of the algorithm In Bubble Sort each major phase moves one item into its final position at the end of the list The learn how the Bubble Sort algorithm works you will have to pay attention to what you see and think about it You have control over the applet Use your best judgement about how to proceed In the exercises at the end of the lab you will be asked to apply Bubble Sort by hand You should make sure you understand it well enough to do this http math hws edu TMCM java labs xSortLabLab html 3 of 11 3 26 2000 12 50 22 PM xSortLab Lab Other Sorting Algorithms You can go on to learn about the four other sorting algorithms or as many of them as you care to look at The five sorting algorithms can be divided into two groups Bubble Sort Selectio
42. PenUp and PenDown used to raise and lower the turtle s pen If the pen is up it does not draw anything This affects all the movement commands described above HideTurtle and ShowTurtle HideTurtle makes the turtle invisible ShowTurtle makes it visible again It continues to draw while it is invisible provided its pen is down If the applet s No Turtle checkbox is checked the turtle will not be seen no matter what is done with HideTurtle and ShowTurtle e Halt Halts the program e Commands for changing the drawing color to one of eleven named colors red green blue cyan yellow magenta black darkGray gray lightGray and white rgb x y z Changes the drawing color using an RGB color specification The parameters x y and z must be in the range 0 0 to 1 0 They specify the amount of red green and blue respectively in the desired color A value of 1 0 represents the maximum possible amount of a color For example rgb 0 0 0 is black rgb 1 1 1 is white and rgb 1 0 5 0 5 is pink hsb x y z Changes the drawing color using an HSB specification The parameters x y and z must be in the range 0 0 to 1 0 They specify the hue saturation and brightness respectively of the desired color Setting y and z equal to gives bright saturated colors As x ranges from 0 to 1 the resulting hues cover the entire spectrum Input Output http math hws edu TMCM java xTurtle info html 6 of 13 3 26 2000 12 50 17 P
43. You ll be using the xLogicCircuits applet in this lab Start by clicking the button to launch the applet in its own window Sorry your browser doesn t do Java For a full list of labs and applets see the index page http math hws edu TMCM java labs xLogicCircuitsLab2 html 1 of 9 3 26 2000 12 50 07 PM xLogicCircuits Lab 2 Circuits that Remember You ve seen that a circuit that does not have any feedback loops simply takes the values from its inputs and computes an output value based on those inputs Changing the values on the input wires will change the output values after just a very short delay for the signal to pass through the circuit Such circuits have no memory The output is computed based on the current inputs and anything that happened to the circuit in the past has no effect In this lab we are interested in circuits that have some memory of what happened to them in the past That is the output of the circuit is not based solely on the current inputs It can also depend on inputs that were given to the circuit in the past Memory circuits include feedback loops A feedback loop occurs when the output from a gate is connected back to an input of the same gate possibly through one or more other gates Such a loop allows previous inputs to affect current outputs This is exactly what we need for memory circuits The xLogicCircuits applet is set up to load several examples You should see three sample circuits on
44. alternatives based on whether a condition is true or false Here is an example DECLARE N x N randomiInt 3 Nis 1 2 or 3 AskUser Guess a number x IF x N THEN TellUser That s right ELSE TellUser Sorry the number was N The first TellUser statement is executed if x N is true The second is executed if x N is false You can have umber of statements between and ELSE or between ELSE END IF The END IF at end is required to mark end of the IF statement ELSE part of the IF statement tional 5 zZ 5 ooo ahs lt n O ue There is another version of the IF statement that chooses among more than two alternatives It uses OR IF to make additional tests The conditions in the IF and OR IF parts are tested in order If one is found that is true than the corresponding statements are executed The IF statement then ends without testing the other conditions If an ELSE part is present it is executed in the case wher all the conditions are false Here is an example that does a random walk LOOP begin a loop statements can be nested so I can put an IF statement inside this loop http math hws edu TMCM java xTurtle samples Tutorial5_if txt 1 of 2 3 26 2000 12 50 36 PM
45. and other components onto a circuit board and drawing connections between them You can turn the inputs of your circuits on and off to see how the circuits behave xComputer An implementation of the model computer developed in Chapter 3 You can write assembly language programs for that computer and watch as the computer executes them step by step xTuringMachine Lets you create Turing machines and watch as they move back and forth along a tape reading and modifying its contents Turing machines are covered in Chapter 4 xTurtle Lets you write and execute programs written in the xTurtle programming language which is used as an example in Chapters 6 7 and 10 xSortLab Lets you watch several sorting algorithms in action and measure their performance This applet is related to material on the analysis of algorithms that is covered in Chapter 9 xModels http math hws edu TMCM java index html 3 of 4 6 25 2004 11 48 41 AM TMCM Labs and Software Does geometric modeling and computer animation as discussed in Chapter 11 You can write scene descriptions and then render the resulting images or animations as wireframe models David Eck eck hws edu Labs last updated 28 May 1998 Page design updated 23 March 2000 Software updated June 2004 http math hws edu TMCM java index html 4 of 4 6 25 2004 11 48 41 AM TMCM Java Downloading and Info TMCM Labs and Applets Downloading and Information Page Thi
46. arrow labeled Max is pointing to item number 2 since that is the largest item that the computer has seen so far during this phase of the sort The magenta colored boxes indicate that the computer has just compared items 2 and 7 The next step will be for it to compare items 2 and 8 10 11 12 13 14 15 16 1 Pax In Insertion Sort the basic idea is to take a sorted list and to insert a new item into its proper position in the list The length of the sorted list grows by one every time a new item is inserted You can start with a list containing just one item Then you can insert the remaining items one at a time into the list At the end of this process all the items have been sorted In the picture below the items that are enclosed in a green box have been sorted into increasing size Each major phase of the sort inserts one new item into this list and increases the size of the box by one The problem is to determine where in the list the new item should be inserted You can use the applet to see how it all works http math hws edu TMCM java labs xSortLabLab html 4 of 11 3 26 2000 12 50 22 PM xSortLab Lab Le ee eS ea ae Temp Merge Sort uses the idea of merging two sorted lists into one longer sorted list To start think of single items as being sorted lists of length one In the first phase of the sort these lists of length one are paired off and are merged to form sorted lists of length two
47. be translated into machine language and put into xComputer s main memory When the applet is in programming mode there is a Translate button at the bottom of the applet that will attempt to do this If an error is found in the program an error message will be displayed You can rid of this message by clicking on it if you like If the program contains no errors it will be put into xComputer s memory and the applet will switch to the main computer screen You can then run the program or step through it as described below Short programs can also be entered directly into memory from the Control area of the xComputer screen Information that you want to put into memory instructions or data can be entered into the text input box labeled data When you press return or click the Data to Memory button the data is stored in memory The location in memory where it is stored is specified by a number in the addr text input box You can only enter data for one memory location at a time Each time you enter data the number in the addr box is automatically incremented by one This lets you store information into successive memory locations simply by typing values and pressing return after each one The question remains exactly what sort of thing can you enter into main memory The first thing you need to understand is that what is really in each memory location is a 16 bit binary number Any other form of information must be represented in
48. completely meaningless to the machine from our human point of view we can assign a kind of meaning to each state In state 0 this machine is moving to the right searching for an x In state 1 it has found one x and needs to check the next square to see whether there is another x there In state 1 after checking the next square it halts if it finds an x there and returns to state 0 if not One might say that the state number counts the number of x s in a row that the machine has encountered In state 0 it has encountered zero x s in a row in state 1 it has encountered one x in a row You will need to understand this in order to do one of the exercises at the end of the lab You will also need to know about editing the rule table This is covered in the next section of the lab The complete table of rules for the FindDoubleX machine looks like this x x k other same x x other same The entries other under Reading and same under Write need some explanation The word other is used here to indicate a default rule This rule is used when the machine is in the state specified in the In State column and no other rule applies For example suppose that the FindDoubleX machine is in state 0 If it happens to be reading an x it will follow the first rule in the table which tells it to write an x move right and change to state 1 However if it is in state 0 and reads any other symbol then it will apply the second rule in the tab
49. compute Note If the scroll bars on this text area are not active it s a bug in your browser Try resizing the window forward 5 Move turtle forward 5 units drawing a line as it goes turn 90 Rotate turtle 90 degrees counterclockwise green Change drawing color to green Color names include red green blue cyan magenta yellow black gray forward 2 Move forward 2 back 4 Move backwards 4 The net result of the preceding commands is to draw a red and green T shape Red is the default drawing color PenUp When pen is up turtle doesn t draw anything as it moves MoveTo 5 3 Move directly to the point with coordinates 5 3 PenDown Start drawing again rgb 1 0 5 0 5 Changes drawing color to the color with red green blue components given by 1 0 5 0 5 This will be sort of pink face 0 Set turtle s heading to 0 degrees meaning face to the right circle 3 Draw a circle of radius 3 The circle is drawn to the left of the turtle s current position PenUp MoveTo 3 7 Move again PenDown Magenta Change drawing color to magenta http math hws edu TMCM java xTurtle samples Tutorial1_basics txt 1 of 2 3 26 2000 12 50 34 PM http math hws edu TMCM java xTurtle samples Tutorial1_basics txt Arc 2 90 Draw a 90 degree arc of a radius 2 circle forward 3 Arc 2 90 forward 3 A
50. d 0 into the AC re the 0 into location 26 value in location 25 is an address of some memory location Get the value from that address and pu indicates what the value int end of the lis to location 12 the number in t it into the AC The i is called indirect addressing he AC is zero indicating t of numbers then jump where the program will halt location 26 the sum of the previous numbers to the AC which contains the next number from the list the number from the AC into location 26 http math hws edu TMCM java xComputer samples TheBasics txt 1 of 2 3 26 2000 12 50 28 PM http math hws edu TMCM java xComputer samples TheBasics txt lod 25 inc sto jmp hit 30 25 This items are to be stored in memory starting AT Load th Add one Put the locat next Jump to from star This is comp loca e number from location 25 into the AC to the number in the AC number from AC into location 25 so ion 25 now contains th number in the list location 4 to get th the list NOTE e location of the e next number Locations are numbered ting from zero a halt instruction tion number 12 which tells the uter to stop execution It is in is a special command that says that the following number 30 location These numbers will be in memory st
51. define some subroutines However once the subroutines are defined you can use them as commands just as you would use any of xTurtle s built in commands As an example type the following commands into the text input box below the xTurtle drawing area pressing return after you enter each command multiArc 5 40 turn 40 multiforward 3 multicircle 2 Also try some other commands If you want to make a more complicated picture go back to the SymmetrySubs program and add your commands at the end of that program after the definitions of all the subroutines For example add the following commands to the end of the program and then hit the Run Program button LOOP multiforward 0 5 face randomInt 360 EXIT IF 1 2 END LOOP You will have to end the program with the Stop button The statement exit if 1 2 in this program is a fancy way of saying Never exit In the previous part of the lab you used several subroutines as black boxes without having to understand what went on inside the box But you should remember that not having to know what s inside is only part of the black box story When you write a subroutine yourself you are working inside the box While you are writing the subroutine you can concentrate on making it perform the specific task it is designed to do without worrying for the moment exactly what role it will play in a complete program From the point of view of a programmer trying to desig
52. different values for ForkNumber the turtles face in different directions Forward 4 Every turtle does this http math hws edu TMCM java xTurtle samples Tutorial8_multitasking txt 2 of 2 3 26 2000 12 50 37 PM The xSortLab Applet The xSortLab Applet SorTING a list of items that is arranging the items into increasing or decreasing order is acommon operation It is also the most common example in the analysis of algorithms which is the study of computational procedures and of the amount of time and memory that they require The xSortLab applet knows five different sorting methods It has a visual sorting mode where you can watch as sixteen bars are sorted into increasing order And it has a timed mode where you can measure the time it takes to sort a large number of items The applet is easy to use but you probably won t quite get the point of it unless you already know something about sorting More information about the applet can be found below This applet was originally written by David Eck for use with his introductory computer science textbook The Most Complex Machine However it can also be used on its own For a list of other applets and for lab worksheets that use the applets see the index page Sorry Your browser doesn t do Java Visual Sort Mode The xSortLab applet can display three different panels a panel for Visual Sort a panel for Timed Sort and a Log panel There is a p
53. displays 1024 memory locations numbered from 0 to 1023 Each location contains a 16 bit binary number that can be interpreted either as data or as a machine language instruction The Registers section of the applet shows eight registers that are components in the xComputer s Central Processing Unit The registers are explained below Finally the Controls are for interacting with and controlling the xComputer The applet has another mode in which it displays a text input area where you can write and edit assembly language programs Information about the assembly language of xComputer is http math hws edu TMCM java xComputer info html 1 of 8 3 26 2000 12 50 30 PM xComputer Info given below To start a new assembly language program just click on the New Program button in the Control area of the applet Alternatively choose New from the pop up menu at the very top of the applet There is also a Load File button that can be used to load a program that has been previously saved to a file however you can only do this if your browser permits applets to access files Programs that have been created or loaded are listed in the pop up menu at the top of the applet You can view any program by selecting it from this menu You can return to main computer screen by selecting Computer from this menu Suppose that you are looking at an assembly language program in programming mode Before xComputer can do anything with that program it must
54. edu TMCM java labs DataRepsLab html 5 of 9 3 26 2000 12 50 04 PM Introductory Lab This applet lets you type in a data value You can select the type of data you want to enter by clicking on one of the five radio buttons Just type your data into the input box at the top of the applet and press return You can also click on the 8 by 4 grid of big pixels at the center of the applet The applet takes the data you enter and it converts that data into a 32 bit binary number It has to do this in order to store it It then takes that same binary number and interprets it in six different ways The six interpretations are a binary number an integer a hexadecimal number a real number a string of four characters and an eight by four grid of pixels You should remember that you see the same string of thirty two bits interpreted in different ways You should also remember that the same bit patterns could also be interpreted in an endless variety of additional ways as a bar of music or the chemical ingredients in a bar of soap or your tab at your favorite bar or Here is a short explanation of each of the six data displays You should try entering various types of values in the applet to see how they are represented as binary numbers Binary This is the most direct display of the 32 bit binary number showing a zero or one to represent each individual bit The displayed binary number shows the full 32 bits including any leading zeros
55. error the computer will move the blinking cursor to the position in the program where it noticed the error The browser should scroll the text if necessary to show the cursor Unfortunately not all browsers do this Once the program has finished executing you can run it again by clicking the Run Program button again Before running a program the computer always clears the screen and restores the turtle to its initial state at the point 0 0 facing right with pen down and drawing color set to red If you ve just run a program that defines subroutines or variables you can use them in any commands that you type into the command input box However they will be cleared out of memory if you run another program At the top left corner of the applet is a pop up menu that you can use to switch among the graphics display and any of the programs that the applet knows about This includes programs you write but it can also include programs that the applet loads automatically when it starts up If you know about lt applet gt tags Applet parameters can be used to specify URLs of programs to be loaded when the applet starts up However I don t want to go into the details here This pop up menu includes an entry for the graphics display It also includes a special item called New Selecting New is equivalent to clicking the New Program button Finally here is some information about each of the other buttons and other widgets that appe
56. even though they are the same number mathematically I will not describe the representation of real numbers in detail ASCII Text Characters can be encoded using ASCII code Each possible character is assigned a code that is one byte that is eight bits long With 32 bits you can represents 4 characters in ASCII code Not every possible byte represents an ordinary printable character The applet shows other bytes in the form lt n gt where n is the base ten number corresponding to the byte For example the byte 00000111 which is equivalent to 7 in base ten is shown as lt 7 gt Pixels At the center of the applet you will see an 8 by 4 grid of little squares Each of these thirty two squares corresponds to one byte in the binary number You should think of these squares as being very big pixels Each pixel can be either black or white One bit specifies the color of one pixel 0 for white or 1 for black This is how two color graphical images can be represented by binary numbers Again see Section 1 1 of the text In the applet you can change the color of a pixel by clicking on it David Eck eck hws edu June 1997 http math hws edu TMCM java DataReps index html 2 of 2 3 26 2000 12 50 26 PM xLogicCircuits Intro The xLogicCircuits Applet The applet on this page lets you build simulated logic circuits from AND OR and NOT gates and see how they behave This is not a serious circuit design tool It s an educatio
57. first step in this process is to build logic gates which are circuits that compute basic logical operations such as AND OR and NOT In fact once AND OR and NOT gates are available a computer could be assembled entirely from such gates In this lab you will work with simulated circuits made up of AND OR and NOT gates You will be able to build such circuits and see how they operate And you will see how simpler circuits can be combined to produce more complex circuits This lab covers some of the same material as Chapter 2 in The Most Complex Machine The lab is self contained but many of the ideas covered here are covered in more depth in the text and it would be useful for you to read Chapter 2 before doing the lab This lab includes the following sections e Logic and Circuits Building Circuits Complex Circuits and Subcircuits Circuits and Arithmetic e Exercises The lab uses an applet called xLogicCircuits Start the lab by clicking this button to launch the xLogicCircuits applet in its own window Sorry your browser doesn t do Java For a full list of labs and applets see the index page Logic and Circuits A logic gate is a simple circuit with one or two inputs and one output The inputs and outputs can be either ON or OFF and the value of a gate s output is completely determined by the values of its inputs with the proviso that when one of the inputs is changed it takes some small amount of time for
58. for the background Exercise 2 This exercise builds on the nested squares that you created for Exercise 1 Turn your scene description into an animation in which each of the five squares rotates about its center The squares should rotate at different speeds Some of them should rotate clockwise and some should rotate counterclockwise The speed of rotation has to do with the range of angles through which the object rotates over the course of the animation Exercise 3 The first scene you looked at in this lab was the Pinwheel example The scene description for this example contains no comments Explain what each line in this scene description does Exercise 4 Carefully explain the difference between square scale 5 2 rotate 45 and square rotate 45 scale 5 2 What image is produced by each command Why are they different How does the computer carry out each command Exercise 5 Use two polygons to make a large letter A like this http math hws edu TMCM java labs xModelsLab1 html 8 of 10 3 26 2000 12 50 25 PM xModels Lab 1 The triangle inside the top of the A is one polygon All the other lines form another larger polygon This exercise builds on the Pinwheel example Use the definition of the pinwheel object form that example Make a double_pinwheel object consisting of a long rectangular bar with a rotating pinwheel at each end Use your double_pinwheel object in an animation that shows a double pinwheel rotating
59. from a subroutine at any point by using a RETURN statement which consists simply of the word return RETURN statements can only occur in subroutines When the computer executes a RETURN statement it exits immediately from the subroutine A subroutine can call itself This is called recursion It is also possible for one subroutine to call another which in turn calls the first subroutine Longer loops of subroutine calls are possible This is called mutual recursion Because subroutines must be declared before they are used a special syntax is required to make mutually recursive subroutines possible One of the subroutines must be predeclared This is done by giving the reserved word predeclare followed by the subroutine heading The rest of the subroutine is omitted Predeclaring a subroutine allows it to be called by other subroutines A full definition of the predeclared subroutine must be given later in the program The full definition includes another copy of the subroutine header User defined Functions A function is very similar to a subroutine except that it computes and returns a value A function in xTurtle is defined in the same way as a subroutine with the word function substituted for the word sub The only other difference in the definition is that a function must include a RETURN statement that specifies the value to be returned by the subroutine A RETURN statement in a function takes the form return lt value gt where
60. if you back up but this doesn t happen Things will however look more squashed in the z direction Objects that actually lie in the xy plane will look exactly the same no matter how the viewing distance is set The xModels applet which you launched above is set up to load several sample programs When it first starts up it should be displaying a program called Flaps Click on the RENDER button to see what this animation looks like The object in the animation is made from eight rectangles but the rectangles have been rotated out of the xy plane so that the object as whole is three dimensional To understand the scene description you ll have to read the next section of the lab However you might want to try adding a viewDistance command to the scene description Try several different distance settings In particular you should try viewDistance 5 which places the viewing point inside the object Try to understand what you see Three Dimensional Objects and Transformations The basic building blocs of three dimensional models in the xModels applet still include line circle square and polygon which start out as two dimensional objects in the xy plane but which can be translated or rotated out of that plane You saw an example of this in the Flaps program above There are also a few three dimensional basic objects in xModels A cube is a one by one by one unit cube centered at the point 0 0 0 A cone is a cone that just fit
61. in the bottom right cell when you press the tab key then a new row of cells will be added to the table As you must by now be able to guess you can set the table s properties by right clicking on the table The pop up menu that appears when you do this also contains commands for adding a row or adding a column to the table If you select Table Info from this menu you will get a dialog box with three panels one for setting Table Properties one for setting Row Properties and one for setting Cell Properties You can use the Row Properties panel for example to set the background color for an entire row Have some fun playing with all the options As a finishing touch you might want to add an email link to your page The URL for such an email link contains an email address Someone who views the page can send an email message to that address by clicking on the link assuming of course that they have properly configured their browser for email Here for example is an email link to me Send me mail The URL for this link is mailto eck hws edu where eck hws edu is my email address Substitute your own email address in your own email link http math hws edu TMCM java labs WebPublishingLab html 6 of 7 3 26 2000 12 50 13 PM Web Publishing with Netscape Composer HTML Email Now that you have learned something about creating HTML pages you might be interested to know that if you use Netscape Communicator for email then you c
62. inside complex objects that is between and have no effect past the closing The default drawing color is black Objects There are six predefined objects in xModels line square circle cube cone and cylinder These objects are sized so that each object just fits inside a 1 by 1 by 1 cube centered at the origin The line object stretches along the x axis from 0 5 0 to 0 5 0 The square object has vertices at 0 5 0 5 0 5 0 5 0 5 0 5 and 0 5 0 5 The circle has center 0 0 and radius 0 5 The cone is oriented to point upwards along the y axis The cylinder also has a vertical orientation To include one of these objects just list its name in the scene description Usually the name will be followed by a transformation that affects the size position and orientation of the object There are also four commands for creating an object out of a list of points These commands are polygon polygon_3d lathe and extrude The polygon command takes a list of parameters that specify a sequence of x y points The polygon consists of these points joined by lines Note that there must be an even number of parameters since there are two parameters per point For example the following command creates a triangle polygon 0 0 4 0 2 2 It s legal to have a polygon command with just two points In that case it specifies a line The polygon 3d is similar except that it takes a list of x y z points The lathe command takes a
63. is a small modification if you do it right You don t have to modify the definitions of the flap or the paddles object Exercise 3 Define an object that consists of a large cube ten units on a side with a circle on each of its six faces Each circle should be a different color You will have to work to get all the circles properly oriented and positioned You ll need some commands along the lines of circle scale 8 xrotate 90 ytranslate 5 Make an animation that shows the entire object rotating as a whole Exercise 4 Consider the following four animations The command viewDistance infinity indicates projection from a very large effectively infinite distance This is also called parallel projection 1 animate 60 viewDistance 20 Note This is the default value cube scale 10 yrotate 0 360 2 animate 60 viewDistance 100 cube scale 10 yrotate 0 360 3 animate 60 viewDistance infinity cube scale 10 yrotate 0 360 http math hws edu TMCM java labs xModelsLab2 html 5 of 7 3 26 2000 12 50 26 PM xModels Lab 2 4 animate 60 viewDistance 5 cube scale 10 yrotate 0 360 Explain what is happening in each animation and why each animation looks the way it does Explain the differences among them Exercise 5 Use lathing to create a goblet shape like this one Exercise 6 The sample program Wagon which was also used in the previous lab shows a simple two dimensional wagon Convert it into a three dimension
64. lab On a separate web page I ve provided a set of six sample programs that use xTurtle multitasking to draw some interesting tilings of the plane These are pictures that would be more difficult to draw without multitasking If you like pretty pictures you might want to take a look Scheduling The operating system of a multitasking computer is in charge of scheduling all the processes That is it determines which process gets to run next and how long it will be permitted to run The CPU under the control of the operating system will execute one process for a while then switch to another then to another and so forth In xTurtle the scheduling is done by the xTurtle applet but the objective is to simulate the way things are done in an actual multitasking computer system When you watch the execution of the ParallelSnowflake txt or Circles txt sample program you ll see that the processes do not all run at exactly the same speed As the system switches its attention from one process to another there is some randomness in the amount of time that is spent on each process The xTurtle program is set up to run this way by default since it s the way real multitasking systems work However the xTurtle applet has an option to run all the processes at exactly the same rate of speed To turn this option on click on the Lock Step checkbox in the bottom right corner of the xTurtle window When this box is checked all the turtles on the
65. ll be using the Timed Sort mode The applet can perform five different sorting algorithms Bubble Sort Selection Sort Insertion Sort Merge Sort and QuickSort When it fist starts up it is set to use Bubble Sort There is a pop up menu near the upper right corner of the applet that you can use to select the sorting method that you want to work with Below the pop up menu are three buttons and a checkbox that can be used to control the applet Click on the Go button to let the applet perform the sort automatically without further intervention from you Click on the Step button to perform just one step in the sort The Start Again button lets you start a new sort with a randomly arranged set of bars The applet will also start a new sort if you select a new sorting method from the pop up menu All the sorting algorithms that you will look at use two basic operations compare two items to see which is largest and copy an item from one place to another Sorting consists of these two operations performed over and over plus some bookkeeping such as keeping track of which step in the sort the computer is currently performing Sometimes the program has to exchange or swap two items It takes three copy operations to perform a swap First copy the first item to a special location called Temp Second copy the second item into the first location And third copy the item from Temp into the first location As the xSortLab applet perf
66. location after the JMP Loop instruction If there were additional items after Count they would be stored in locations 13 14 and so on until the next directive This program is one of the sample programs loaded by the xComputer applet that you launched above Select the program SimpleCounter txt from the pop up menu at the top of the xComputer window Load it into xComputer s memory by clicking on the Translate button Once it is loaded you can use the Run Step or Cycle button to execute the program If you need more information about using the xComputer applet please see the previous lab Loops and Decisions Complex programs can be constructed using loops decisions and subroutines All of these things become easier to use when labels are available Subroutines will be introduced in the next lab In this lab you will work with loops and decisions Loops of course are implemented with jump commands when the computer jumps back to a previous location in the program Decisions are implemented with conditional jump instructions such as JMZ and JMN When the computer executes one of theses instructions it decides whether or not to jump based on the current circumstances When the computer encounters the instruction JMZ Loc it checks the accumulator register If the number in the accumulator is zero then the computer jumps to location Loc Otherwise the computer simply proceeds on to the next statement following the JMZ
67. loop it should add 1 to Count When the program ends the value in Count is the number of times the program has gone through the loop This is also the number of steps that were computed in the sequence How many steps are there in the sequence that begins with N 7 How about N 27 Be sure to add comments to your program to explain how Count is being used Exercise 4 The assembly language instruction SHR shifts the number in the Accumulator one bit to the right That is each bit in the binary number is moved over one bit position to the right The leftmost bit position which would be left empty is filled in with a zero The rightmost bit which has no other place to go is placed into the Flag register A JMF instruction can be used to test the contents of the Flag register Suppose XXX is a label If the Flag register contains a one then JMF XXX causes a jump to location XXX If the Flag register contains a zero then JMF XXX has no effect Write a program that counts the number of 1 s in a binary number When the program begins the number should be stored in a memory location labeled Num There should also be a memory location named Count for counting the number of 1 s in Num The program begins by storing a zero in Count It then goes into a loop that shifts Num one bit to the right If the number that http math hws edu TMCM java labs xComputerLab2 html 6 of 8 3 26 2000 12 50 10 PM xComputer Lab 2 falls off the end into the Flag
68. machines are covered in Chapter 4 of The Most Complex Machine Although the lab is mostly self contained it would be useful for you to have some familiarity with Turing machines before beginning the lab Especially important is the idea that a Turing machine is described by a table of rules that specify what action the machine will take for each combination of state and scanned symbol The action takes the form of writing a new or the same symbol to the current square moving either left or right on the tape and entering a new or the same state This lab includes the following sections e Using the Applet A More Interesting Machine Making New Machines Binary Arithmetic Exercises In this lab you will work with an applet called xTuringMachine Start by clicking this button to launch the applet in its own window Sorry your browser doesn t do Java For a full list of labs and applets see the index page http math hws edu TMCM java labs xTuringMachineLab html 1 of 9 3 26 2000 12 50 12 PM xTuringMachine Lab Using the Applet The xTuringMachine applet can simulate Turing machines with up to twenty five states The states are numbered from 0 to 24 There is also the special halt state which is denoted by h The Turing machines in this applet are restricted to using the following symbols the letters x y and z the binary digits 0 and 1 the dollar sign and the blank space often written as
69. most general form with all three parameters it specifies motion in all three directions With one parameter it specifies movement in the x direction only and with two parameters it specifies movement in the x direction and y direction only There is a command ztranslate for moving an object in the z direction only For example square ztranslate 5 represents a square that has been moved 5 units forward out of the screen You already saw the analogous commands xtranslate and ytranslate in the previous lab Scaling and translation are pretty much the same in three dimensions as in two but rotation in three dimensions is another matter In two dimensions an object is rotated about a point A three dimensional object must be rotated about a line like a top spinning about its axis In xModels there are three rotations commands for rotation about the x axis the y axis and the z axis respectively The commands are called xrotate yrotate and zrotate The zrotate command is actually the same as the plain old rotate It is easiest to understand rotation in three dimensions by looking at examples Enter the following simple scene description into a new program in xModels and render it animate 60 square scale 10 yrotate 0 360 You will see a square rotating about its vertical axis Note that the edge of the square that is farther from you looks shorter as it should Try the same scene with the square changed to a cube Try using xrotate an
70. number It can be built using four copies of 1 Bit Mem Your circuit should have four DATA IN wires and four DATA OUT wires However it should have only one LOAD DATA control wire You want to load data from the DATA IN wires into all the 1 Bit Mem circuits at the same time This will be done by turning the single LOAD DATA wire on and off Exercise 4 This continues Exercise 3 Explain in detail how you would store the binary number 1011 in the four bit memory that you constructed for Exercise 3 Also explain carefully what it means to say that this value is stored in the memory Exercise 5 This exercise uses the four bit memory that you built for Exercise 3 One of the examples in this lab was a 2 Bit RAM circuit that can store two one bit numbers It stores one number in each of two locations and an ADDRESS wire is used to determine which of the two locations is in use Suppose that you want to store a four bit number in each of two locations The circuit would be very similar to the 2 Bit RAM but it would have four Inputs and four Outputs It would still have just one LOAD DATA control wire and one ADDRESS wire to select between the two locations For this exercise you should build such a circuit You can start with your four bit memory Use it to build a Guarded 4 Bit Mem modeled on the Guarded 1 Bit Mem from the 2 Bit RAM circuit Then use two copies of the Guarded 4 Bit Mem to construct a RAM with two locations Test your c
71. numbers to specify the red blue and green components of a color The numbers must be in the range zero to one For example rgb 0 7 0 7 1 0 represents a light blue color There is also an hsb command that lets you specify the hue saturation and brightness levels of a color but I won t discuss the details here For example here is a scene description for an image scene that contains several objects of different colors red square scale 2 translate 5 5 cyan circle scale 5 2 rotate 30 rgb 0 4 0 2 0 2 square scale 3 rotate 30 translate 5 5 blue polygon 0 0 0 5 3 4 translate 7 7 magenta line scale 5 rotate 45 translate 5 5 You can give your scene a background color with the background command The word background must be followed by the color you want to use for a background For example background gray Or background rgb 1 0 0 8 0 8 The background command should occur at most once in a scene It will have the same effect no matter where it occurs You ll find a copy of the above scene description with a pink background in the sample program SimpleObjects You can select this example from the pop up menu at the top of the applet You should render the scene to see what it looks like You should also spend some time making modifications to the scene Try changing the color of the objects or the background Try changing the numbers for the transformations Add some new objects and new transformations You should try to und
72. of labs and applets see the index page Black Boxes You are familiar with the idea of a subroutine as a black box When you use predefined subroutines such as forward and moveTo you don t need to know exactly how they work All you need to understand is how to use them and what they will do User defined subroutines can also be used as black boxes provided that someone else has written them for you The xTurtle applet that you launched for use in this lab is set up to load a sample program called SymmetrySubs This program contains the definitions of six subroutines for drawing symmetric pictures These subroutines are meant to be used in the same way as the usual drawing subroutines such as forward and circle For example one of the subroutines defined in SymmetrySubs is multiForward This subroutine is similar to the built in forward command except that instead of just drawing one line it draws eight lines in a symmetrical pattern The SymmetrySubs program defines the following six subroutines each of which draws a symmetric pattern multiForward multiBack multiMoveTo multiMove multiCircle and multiArc To see how this works select the SymmetrySubs program from the pop up menu at the top of the xTurtle applet and use the Run Program button to run the program Nothing http math hws edu TMCM java labs xTurtleLab3 html 1 of 6 3 26 2000 12 50 20 PM xTurtle Lab 3 appears on the screen since all the program does is
73. of size 1000 Here N the array size is 1000 Let T be the time it took to sort one array of size 1000 T can be computed by dividing the total time 8 205 by the number of arrays 5 This gives T 1 641 seconds Now T is supposed to be given approximately by the formula T K N 2 We know that N is 1000 and T is 1 641 so the equation becomes 1 641 K 10002 You can solve this for K to get K 1 641 10002 0 000001641 More generally a value for K can be calculated from the formula K T N N Of course this is only supposed to be an approximation But if you repeat the experiment several times with different array sizes and calculate a value for K from each experiment you should get values of K that are fairly close to one another If this does not happen then the algorithm you are looking at is probably not an N2 algorithm Remember though that there is room for some experimental error because of the difficulty of measuring compute time Also keep in mind that the values calculated for K tend to get more accurate as N increases A very small value of N might give a poor approximation for K Not every sorting algorithm is an N2 algorithm Some of them are N log N algorithms This means that the running time of the algorithm is given approximately by K N log N where N is the size of the array and K is a constant The function log N is the logarithm of N You can compute this function using the log button on your calculator
74. of the display PC register The program counter is a 10 bit register that contains the address in memory of the next program instruction that is scheduled to be executed The PC is ordinarily incremented by 1 during each fetch and execute cycle Its value can be also be changed by the execution of a jump instruction which tells the computer to jump to a different location in the program and continue execution from there IR register The instruction register is a 16 bit register that holds a program instruction while it is being executed This is where an instruction is put when it is fetched from memory COUNT register This is a 4 bit register that counts off the steps in each fetch and execute cycle At the beginning of each step its value is incremented by one The last step of the cycle resets this register to zero so that the next cycle can begin AC register The accumulator is a 16 bit register that holds a number that is being used in the current calculation When a number is loaded from memory it is put in the AC When a number is added it is added to the value currently in the AC and the result is put back into the AC Etc FLAG register This is a 1 bit register that can give extra information about a calculation For example when two 16 bit numbers are added the final carry into the 17 th column is stored in the FLAG register When a shift operation is performed on the AC the extra bit that is shifted off the end is pl
75. out you ll need to do some detective work after the program ends Look at what has happened to the program in the computer s memory Try to be as explicit and complete with your explanation as possible This is not an easy question Hint something you did in Exercise 1 turns out to be relevant here This is one of a series of labs written to be used with The Most Complex Machine A Survey of Computers and Computing an introductory computer science textbook by David Eck For the most part the labs are also useful on their own and they can be freely used and distributed for private non commercial purposes However they should not be used as a formal part of a course unless The Most Complex Machine is also adopted for use in that course David Eck eck hws edu Summer 1997 http math hws edu TMCM java labs xComputerLab1 html 10 of 10 3 26 2000 12 50 09 PM xComputer Lab 2 Labs for The Most Complex Machine xComputer Lab 2 Assembly Language Programming THE MACHINE LANGUAGE FOR xComputer consists of thirty one different instructions Each instruction performs a very simple task Nevertheless very complex programs can be built up from these instructions The previous lab introduced the xComputer applet and the basic xComputer machine language instructions In this lab you will learn more about programming the xComputer Hopefully you ll begin to appreciate how complex programs can be composed from very simple instructions
76. represents To run a program click the appears in the applet below the program The program will be translated into assembly language and the computer screen will reappear program probably appears in can change the language It is that lly stored in memory Translate button that with the program in its memory The the form of numbers but you way the contents of memory are displayed by selecting a view style from the pop up menu that is above the scrol lling memory display Once the program is in memory you can run it by clicking Ww Run W selecting the speed at which the program runs Alternatively on the you can use the button There is a Speed pop up menu for Step or Cycle button to move through the execution of the program manually If you want to run the program a second time you should first click on the Set PC 0 button The PC tells the computer where to be set Each of what it lod c 30 sto 25 lod c 0 sto 26 lod i 25 jmz 12 add 26 sto 26 t to zero to poin the following ins does f Lo st Loa Sto The Add Put to find its next instruction It has t to the start of the program tructions has a comment that says ad the constant 30 into the AC register ore the value 30 from AC into location 25
77. rules without worrying about the action specified in each rule You can then edit the action parts of all the rules in the table There are lots of things in the xTuringMachine applet that you can edit You can use the arrow keys and the tab key to move among the various editable items Often this is quicker than using the mouse http math hws edu TMCM java labs xTuringMachineLab html 5 of 9 3 26 2000 12 50 12 PM xTuringMachine Lab You will notice that sometimes the Make Rule button changes into a Replace button This will happen whenever the first two items in the Rule Maker match the first two items in an existing rule If you click on the Replace button the rule in the Rule Maker will replace the rule in the table Before you do the exercises at the end of the lab you should get some practice at creating and editing a table of rules Here is a table of rules for a Turing machine that Nudges a string of x s y s and z s one square to the left The machine must be started on the leftmost symbol in the string and it will only work if there are a couple of blank squares surrounding the string co E amp FN cK A Tm FO FFT hu e na orm Oo fF E F amp F WU N 0 o o 1 Z 3 A 5 6 6 other You should make a copy of this machine by adding each of the above rules to the applet s rule table Begin by selecting New from the pop up menu at the top of the applet if you haven t done so a
78. same object simply by listing them all after the object s name in the order in which they are to be applied For example square scale 3 rotate 30 translate 5 5 specifies a square that is first magnified by a factor of 3 then rotated through 30 degrees then translated 5 units horizontally and 5 units vertically The order in which the transformations are applied can make a difference Switching the order can produce a very different picture There are other basic objects besides squares A circle is a circle of diameter one centered at 0 0 A line is a line of length one that extends from the point 0 5 0 to 0 5 0 A polygon can be specified by listing its vertices For example polygon 0 0 0 5 3 4 specifies a triangle with vertices at the points 0 0 0 5 and 3 4 These few simple shapes are all that you have to work with To make things a little more interesting you can add color to your scenes The default drawing color is black You can use a color change command to change the drawing color The drawing color that you specify remains in effect until it is changed by another color change command That is it does not just apply to the next object The color change commands include the names for the standard colors red green blue cyan magenta http math hws edu TMCM java labs xModelsLab1 html 4 of 10 3 26 2000 12 50 25 PM xModels Lab 1 yellow black white and gray There is an rgb command that uses three
79. state or use the mouse to click on the state in the palette Editing the tape is similar Click on any cell to hilite it The palette displays the symbols that the cell can contain You can type a symbol or click on it in the palette When you do this the hilite will move to the next cell on the tape This makes it easy to type a string of symbols onto the tape Symbols oO 1 x y z blank The input palette for symbols hk to 2 Fo a i ie 1S ir 1s 3 3s States 5 2 4 amp 8 10 12 d4 is ig 20 23 34 The input palette for states Try making a new input tape for the ChangeO01toXY machine Move the machine to the beginning of the input Make sure that the machine is in state 0 Then run the machine on http math hws edu TMCM java labs xTuringMachineLab html 3 of 9 3 26 2000 12 50 12 PM xTuringMachine Lab your new input A More Interesting Machine As another example select the sample machine FindDoubleX from the pop up menu at the top of the applet The purpose of this machine is to move to the right along its tape until it finds two x s in a row it then halts on the leftmost of those two x s The machine you looked at in the previous section had only a single numbered state state 0 The FindDoubleX machine has two states number 0 and number 1 As this machine runs you will see it changing between these two states Try it Use the Step button to step through the computation Although its states are
80. that was on the board previously is iconified and moved to the pallette unless it is empty in which case it is discarded There is only one circuit on the board at any given time You can edit the circuit while it is on the circuit board and the changes you make will be permanent even after you http math hws edu TMCM java xLogicCircuits index html 2 of 4 3 26 2000 12 50 27 PM xLogicCircuits Intro re iconify the circuit If the circuit on the board containes a subcircuit you can enlarge that circuit to see what is inside it This does not remove the main circuit from the board it just lets you see an enlarged part of it When you shrink the subcircuit back down to its original size the main circuit is still there For an example Enlarge the 4 Bit Adder sample circuit from the pallette You ll see that it contains four copies of a subcircuit called Adder If you hilite one of the Adder circuits and Enlarge it you can see what s inside it You ll also see a big red message Enlarged from 4 Bit Adder to remind you that what you are looking at is a part of a larger circuit It is important to understand that when you drag a subcircuit onto the circuit board what you get is a copy of the circuit from the pallette If you edit the original circuit on the pallette it doesn t affect any copies that have been made If you edit one of the copies it doesn t affect the other copies Note in particular that it s easy to get two ci
81. the center of projection through the point x y z and finding the x y point where it intersects the xy plane Objects behind the projection point are not displayed The viewDistance command must be followed by a parameter that specifies the z coordinate of the projection point The parameter can be any positive number If the scene is an animation the parameter can be a number range The parameter can also be the word infinity which specifies projection from infinity A program can contain at most one viewDistance command If none is specified a default value of 20 is used The viewDistance command does not have to come at the beginning of the program However it applies to the entire scene in any case The background command is used to specified the background color for the scene This command must be followed by a color specification The color can be specified by one of the specific color words listed below It can also be given using the rgb or hsb color command Since rgb and hsb can use number ranges as parameters the background color can change from one frame of an animation to the next The default background color is white The background command does not have to appear at the beginning of the program The define is used to give a name to an object Once a named object has been defined it can be used in the same way as any of the built in objects including in the definitions of other named objects The define must be followed by the nam
82. the circuit board Each of these is a simple circuit containing a feedback loop You should turn on the power and experiment with these circuits The first circuit consists of a NOT gate with its output connected back to its input What happens to this circuit when you turn on the power This is not what I would call a memory circuit It shows that not every circuit that contains a feedback loop can properly be called a memory circuit In fact building memory circuits is a pretty touchy affair However even this simple example of a feedback loop turns out to be useful and interesting as you ll see in some of the exercises at the end of the lab The second example on the circuit board is an OR gate whose output is fed back to one of its inputs Input P Output The other input to the OR gate is under your control As soon as you turn this input on the feedback loop turns on and the output of the circuit comes on After that you can turn the input off and on as much as you want The output stays on until you turn off the power to the circuit The circuit remembers that its input has been turned on sometime in the past This is interesting but it would be nice to have a way of turning the circuit off The third example on the circuit board shows how this can be done http math hws edu TMCM java labs xLogicCircuitsLab2 html 2 of 9 3 26 2000 12 50 07 PM xLogicCircuits Lab 2 Turn it ON Output Turn it OFF This circ
83. themselves as they are loaded into the IR And you can observe that the value in memory location 12 changes from 1 to 2 to 3 to 4 and so on This program will run forever if you let it You will be working with this little program throughout most of the remainder of the lab Your objective is to understand how xComputer operates and to appreciate the fetch and execute cycle Controlling Speed and Memory Display Style As you let the counting program run you can try varying the speed at which the computer executes instructions by changing the setting on the speed pop up menu located just below the Run button The lower speeds allow you to watch what is happening in more detail The higher speeds allow the computer to get more done At the very highest speed the registers are not displayed so that the computer can run as quickly as possible without updating the register display all the time When you have had enough of this stop the program and experiment with the memory display style pop up menu which is located just above the scrolling memory display This menu allows you to select how you would like to view the contents of main memory There is also a similar pop up menu for setting the register display style Of course the actual contents of memory are binary numbers but a binary number can mean many things depending on how it is interpreted When the applet first starts up it is set to display the contents of memory as ordinary de
84. think of it as dragging a pen that draws as the turtle moves The command PenUp tells the turtle to raise the pen While the pen is raised the turtle will move without drawing anything The command PenDown tells the turtle to lower the pen again Just below the drawing area of the applet are a text input box and a button labeled Do It You can type commands for the turtle in the text input box When you press return or click on the Do It button the turtle will carry out the command or commands that you typed You can type in several commands at once or you can type in one command at a time pressing return after each command Note also that after a command is executed the contents of the text input box are hilited so that as soon as you start typing the previous command will be erased and replaced with what you type And finally note that you can change the speed at which the turtle follows a sequence of commands by changing the setting of the Speed pop up menu which is one of the controls located to the right of the drawing area The speed is initially set to Fast As an exercise you should try to make the turtle draw two separate parallel lines like this If you make a mistake you can use the command clear to clear the screen and the command home to return the turtle to its original position and orientation at the center of the screen facing right The turtle can execute a number of other commands in addition to f
85. tinus Note To change the size and shape of a subcircuit click the circuit to hilite it When a circuit is hilited it is surrounded by a rectangle with a little square handle in each corner You can click and drag one of these handles to adjust the size of the circuit All you have to do is construct the rest of the circuit so that the control wires can control whether the answer from the 4 Bit Adder or the answer from the 4 Bit Minus gets through to the Outputs of the ALU One way to do this is to use four copies of the Select circuit that you built for Exercise 9 This is one of a series of labs written to be used with The Most Complex Machine A Survey of Computers and Computing an introductory computer science textbook by David Eck For the most part the labs are also useful on their own and they can be freely used and distributed for private non commercial purposes However they should not be used as a formal part of a course unless The Most Complex Machine is also adopted for use in that course David Eck eck hws edu Summer 1997 http math hws edu TMCM java labs xLogicCircuitsLab1 html 10 of 10 3 26 2000 12 50 06 PM xLogicCircuits Lab 2 Labs for The Most Complex Machine xLogicCircuits Lab 2 Memory Circuits Tuts LAB CONTINUES THE STUDY OF CIRCUITS built from logic gates which was begun in the previous lab That lab showed how circuits can be built to perform arithmetic and logical computations wit
86. to draw the steps since when you are writing the program you don t know how many steps there will be Each execution of the loop will draw one of the staircase s steps Before drawing each step the turtle must be facing in the right direction this is a precondition After drawing the step the turtle has changed direction this is a postcondition You have to include commands that will provide splicing from the actual postcondition to the desired precondition After the loop you will still have to draw the two long sides of the staircase To get them into the correct positions and orientations you will have to think about the postconditions that hold after the loop has been executed and how they match up with the preconditions for drawing the lines Exercise 5 at the end of the lab asks you to write this program Subroutines A subroutine is more or less a small program made into a black box and given a name Some subroutines such as forward and PenUp are predefined others are written by a programmer as part of a larger program Subroutines are an essential tool for organizing complex tasks Most subroutines have parameters such as the 9 in forward 9 or the 30 in turn 30 Parameters allow subroutines to receive information from the rest of the program or to send information back Suppose that we want to turn the staircase program described above into a subroutine Then it would no longer make sense to get the input from the user sinc
87. turtles do several completely different tasks When you run this program two processes are created with a fork command Both processes execute an IF statement of the form IF ForkNumber 1 THEN do one thing ELSE do something else END IF http math hws edu TMCM java labs xTurtleLab4 html 2 of 7 3 26 2000 12 50 23 PM xTurtleLab 4 The first turtle with a ForkNumber of 1 does one task while the second turtle with a ForkNumber of 2 does another completely different task You are asked to do something similar in Exercise 3 at the end of the lab Two other sample programs ParallelSnowflake txt and Circles txt show that a program can contain more than one fork command In these programs the first fork command creates several processes Each of these processes then goes on to execute a second fork command When this happens each process splits into several processes You can see this clearly when you run ParallelSnowflake txt which creates 216 processes with a sequence of three fork 6 commands The Circles txt sample program illustrates another important fact It shows how a declare statement works when it occurs after a fork Every process will execute the declare statement separately so that every process will have its own copy of the variable Thus the variable can be assigned different values in different processes You will need to understand the Circles txt program in order to do exercise 4 at the end of the
88. values for forkNumber allow the different processes to do different things Note that it is certainly possible to have two or more forks in a row A process only remembers the fork number from the most recent fork command that it has executed Grab Statement After a fork command has been executed the processes that it creates can communicate by setting or checking the values of shared variables variables that were declared before the fork command This form of communication has the problem of mutual exclusion making sure that only one process at a time has access to the shared variable It is up to the programmer to enforce mutual exclusion In xTurtle this can be done using the grab statement which takes the form GRAB lt variable gt THEN any statements except fork exit return END GRAB The lt variable gt in a GRAB statement must be a global variable If you want to use a GRAB statement inside a subroutine you will have to use an imported global variable The point here is that only one process at a time is allowed to grab a given variable If a process tries to grab a variable and another process has already grabbed it then the second process has to wait until the first process exits from its GRAB statement There is a variation of the grab statement that has an ELSE part I have never found it actually useful It has the form GRAB lt variable gt THEN some statements http math hws edu TMCM java xTurtl
89. which you want to link You can also enter the text of the link that you want to appear on the page Alternatively you could hilite the link text before clicking the http math hws edu TMCM java labs WebPublishingLab html 4 of 7 3 26 2000 12 50 13 PM Web Publishing with Netscape Composer Link button Remember that an easy way to get the URL for a page is to go to that page in the Netscape browser and then Cut and Paste the URL from the Location box at the top of the browser window Once the link is created on the page you can right click on it to get a pop up dialog with various options You should play with the basic tools mentioned in this section until you get your page into reasonable shape As a final step you will probably want to run a spell checker on your page by clicking on the Spelling button in the toolbar You will then be ready to publish your page Publishing Your Page To publish a page that you have created in Netscape Composer click on the Publish button in the toolbar This will bring up a dialog box that looks something like this Publish file 7 Untitled Page Title Welcome to my page e g My Web Page HTML Filename index html e g mypage htm HTTF or FTF Location to publish to tte escher hws edu export home username waw User name Jusemamel Use Default Location Password J Save password The Location and Username should already be filled in with the configuration inform
90. with twenty one s on the tape If it is started on a string that contains just one it should halt with three s on the tape Here is one way that the machine might operate Change one of the s to an x then go to the end of the string and write two more x s Go back and process the next in the same way Continue until all the s have been processed Then change all the x s to s Exercise 5 Construct a Turing machine to do the following Assume that the machine is started on a tape that contains nothing but a string of s The machine is started on the left end of this string The purpose of the machine is to divide the length of the string by 3 Throw away any extra fractional part so that 17 divided by 3 would be 5 For example if the machine is started on a string of twenty one s it should halt with seven s on the tape If it is started with ten s on the tape it should halt with three s on the tape And if it is started with five s on the tape then it should halt with one on the tape Exercise 6 Modify the sample machine Increment so that instead of halting after it adds one to its input it enters into state 0 All you have to do is change the New State in one rule from h to 0 With this modification you have a counting machine It will continue to add one to the number on the tape over and over as long as you let it Run the counting machine at Fastest speed and time how long it takes to count from 0 up to
91. xLogicCircuits applet should have loaded several subcircuits for the pallette One of these circuits is called Two or More Open this circut now The circuit has three inputs It turns its output ON whenever at least two of its inputs are ON Try it Click on the inputs to turn them ON and OFF and don t forget to turn the Power on first As a simple exercise in building circuits from subcircuits use the Two or More circuit as part of a At Most One circuit You want to build a circuit with three inputs that will turn on its output whenever zero or one of its inputs is on Notice that this is just the opposite behavior from the Two or More circuit That is At Most One is ON whenever Two or More is not ON This logical description shows that the At Most One circuit can be built from a NOT gate and a copy of the Two or More circuit Begin by re Iconifying the Two or More circuit then drag a NOT gate and a copy of Two or More onto the empty circuit board Add Inputs Outputs and wires as appropriate then test your circuit to make sure that it works If you like you can give it a name and turn it into an icon Next open the 4 Bit Adder sample circuit You ll see that it contains several copies of a subcircuit called Adder It s possible to look inside one of these circuits Just click on the adder circuit to hilite it and then click the Enlarge button This does not remove the main circuit from the board it just lets
92. zero Exercise 11 You have probably already discovered that the computer can display error messages if you try to run a program that contains an error Errors that the computer can find before actually running the program are called syntax errors The following program contains several syntax errors Find each error and explain what is wrong in each case You can type in the program and let the computer find the errors DECLARE length length 8 LOOP forward length turn 90 http math hws edu TMCM java labs xTurtleLab1 html 9 of 10 3 26 2000 12 50 15 PM xTurtle Lab 1 length length 1 EXIT IF length equals 0 END LOOP Some errors can only be found when a program is running For example what error occurs when the following program is run Type it in and find out DECLARE sum count sum 0 count 0 LOOP sum sum 1 count count count 1 EXIT IF count 10 END LOOP DrawText The sum is sum There is a third and much worse type of error which occurs when the program gives an incorrect result but the computer gives you no warning of the fact that the answer is wrong Give an example of such an error Explain why the computer cannot detect such wrong answer errors Exercise 12 This exercise assumes that you are familiar with the xComputer model computer which is used in some other labs Write a short essay comparing the assembly language of xComputer with the high level programming language
93. 0 The command mountain x y c should move the turtle along a jagged path from its current position to the point x y The amount of jaggedness is specified by the complexity c If the third parameter c is zero then mountain x y c simply draws a straight line from the current position to x y If c gt 0 then mountain x y c will choose a random point x1 y1 somewhere between the current position and x y It will draw a mountain of complexity c 1 to the point x1 y1 and from there it will draw a second mountain curve of complexity c 1 to the point x y The trick is to choose the intermediate point x1 y1 This can be done by finding the midpoint between the current position and x y and then moving the y coordinate of that midpoint up or down by a random amount This computation can be done as follows recalling that the current position of the turtle is given as xcoord ycoord xl xcoord x 2 yl ycoord y 2 yl t yl random 0 5 xcoord x Try to put all this together into a definition of mountain x y complexity Remember to declare x1 and y1 at the beginning of your subroutine This is one of a series of labs written to be used with The Most Complex Machine A Survey of Computers and Computing an introductory computer science textbook by David Eck For the most part the labs are also useful on their own and they can be freely used and distributed for private non commercial purposes However th
94. 3 26 2000 12 50 15 PM xTurtle Lab 1 There are two commands for output sending information from the computer to the user and one command for input getting information from the user into the computer All of these commands use strings A string is sequences of characters enclosed in quotes such as Hello The command DrawText Hello will print the string He11o in the drawing area at the current turtle position Note that the quotes are not of the string that is displayed The quotes are just there in the program to tell the computer that this is a string The command TellUser Hello will display tt Hello in a little green colored box in the center of the display area There will also be a button labeled OK The user reads the string and then clicks on the OK button to get rid of the box The TellUser command has no permanent effect on the picture in the drawing area Finally there is the more complicated input command AskUser This command allows the user to enter a number the number entered by the user will be stored in a variable The variable must of course be declared before it can be used in this command For example assuming that a variable named betAmount has been declared the command AskUser How much do you want to bet betAmount will display a box containing the string How much do you want to bet along with a text input box where the user can enter a response The number entered by the user
95. 6 18 3 6 9 12 15 18 21 24 27 4 8 12 16 20 24 28 32 36 5 10 15 20 25 30 35 40 43 6 12 18 24 30 36 42 48 54 7 14 21 28 35 42 49 56 63 8 16 24 32 40 48 56 64 72 9 18 27 36 45 54 63 72 81 The entry in row number row and column number col is row col Your program will be similar in outline to the sample program Circles txt You ll need to use the DrawText command to write each number on the screen Recall that if num is a variable then the command DrawText num will output the value of num at the current turtle position Exercise 5 A recursive subroutine for drawing binary trees was covered in xTurtle Lab 3 Binary trees can also be drawn using multitasking Each fork in the tree is represented by a fork command in the program Here is a recursive subroutine that uses multitasking to draw a binary tree SUB tree size complexity IF complexity gt 0 THEN forward size 2 fork 2 IF ForkNumber 1 THEN turn 45 ELSE turn 45 END IF tree size 2 complexity 1 END IF END SUB Implement this subroutine in a program that draws binary trees Then modify the subroutine to add some color and an element of randomness For example instead of being always equal to two the number of branches could be random Instead of just dividing the size by 2 you could multiply it by a random amount Try to make your program draw bushes that bear at least some resemblance to real bushes Exercise 6 Modify the sample program Synch
96. 6 2000 12 50 10 PM xComputer Lab 2 Labels and the Assembler The previous lab introduced the xComputer applet and the most basic aspects of xComputer s assembly language Here is an example repeated from that lab This program simply counts forever by adding 1 to location 12 over and over in an infinite loop LOD C 1 STO 12 LOD 12 INC STO 12 JMP 2 The numbers 12 and 2 in this program are addresses of memory locations While this short program is not terribly difficult to understand it can be extremely tedious and error prone to keep track of the large number of numerical addresses that would be used by a complex program For this reason assembly language allows you to give names to memory locations so that you can refer to the locations with meaningful names rather than meaningless numbers Names used in this way are called labels To give a name to a memory location in an assembly language program all you have to do is put the name followed by a colon before the contents of the memory location For example the line Loop LOD 12 in a program would give the name Loop to the memory location that contains the LOD 12 instruction Elsewhere in the program you can use the word Loop to refer to that location instead of using the numerical address For example you could jump to that location with the command JMP Loop Memory locations can be use to hold either instructions or data Labels are useful in both situations If
97. 7 at Hobart and William Smith Colleges The entire lab assumes that you are working with Netscape Communicator version 4 0 or presumably later which includes a component called Netscape Composer for creating Web pages The use of HTML in email as described in the last section of the lab is possible in Netscape Communicator for Windows but might not be available in versions of Netscape that run on other platforms Other details will be different on other platforms as well The only exercise for this lab is to produce a Web page Your page should include headlines lists links colors graphics and at least one table You might want to create a personal home page with information about yourself You might make a page with information on some selected topic Or you might want to be more creative maybe a work of Web based art The lab includes the following sections e What is HTML Netscape Configuration Making Your First Page Publishing Your Page Adding Some Frills HTML Email What is HTML The pages that are displayed by a Web browser program such as Netscape are written in a special language called HTML or HyperText Markup Language The word hypertext refers to documents that can contain links to other documents the use of such links is the most distinctive feature of HTML and of the Web An HTML document is a plain text file It contains the text that you see on the page along with special commands called tags that t
98. A wire and leaves its DATA OUT wire turned OFF The 1 Bit Decode is used to make sure that exactly one of the two locations is selected at any given time The ADDRESS wire is used as input to the Decode circuit The Decode circuit has two outputs When the ADDRESS wire is OFF the Decode circuit turns its lower output ON and this in turn selects one of the Guarded 1 Bit Mem circuits When the ADDRESS wire is ON the Decode circuit turns its upper output ON and this in turn selects the other Guarded 1 Bit Mem circuit Thus the Decode circuit decodes the ADDRESS to decide which location to select Finally the OR gate is necessary so that both locations will be able to send their output to the DATA OUT wire of the RAM You can t connect two wires to one output Using the OR gate allows either of the Guarded 1 Bit Mem circuits to turn on the output Exercises Exercise 1 A clock in a computer is a component that ticks by turning its output wire on and off This regular ticking can be used as a signal by other components in the computer Open the sample circuit Clock in the applet that you launched above This example is a clock that will start ticking by turning its output on and off as soon as you turn the power off However you can stop the ticking by turning on the clock s control wire at the top of the circuit Turning this control wire off will restart the clock Write a few paragraphs explaining exactly how this circuit works Wh
99. CM java labs xTurtleTilingExamples html 3 26 2000 12 50 24 PM xModels Lab 1 Labs for The Most Complex Machine xModels Lab 1 Two D Graphics and Animation ImMaAGEs ARE OFTEN CREATED ON COMPUTERS in a two step process First a geometric model of a scene is created then the scene is rendered using realistic coloring and lighting effects In this lab and the next you will use an applet called xModels which deals with the model construction stage of image creation This lab covers two dimensional scenes while the next lab moves on to the problem of working with three dimensional objects Complex geometric models are built up out of simpler components which are scaled rotated and positioned in the scene using geometric transformations Simple geometric shapes like circles and lines are used as a starting point in the modeling process These shapes can be combined to form more complex figures that can then be combined to form even more complex scenes Scenes constructed from objects in this way can be used in a natural way to produce animations An animation is just a sequence of frames in which objects move slightly from one frame to the next When the frames are quickly displayed one after the other the viewer perceives objects in motion In this lab you will use the xModels applet to create two dimensional geometric models and simple animations In the process you will learn about various two dimensional geometrical transformation
100. Circuit outputs are on the right edge of the circuit e Data inputs are on the left edge of the circuit e Control inputs are on the top and bottom edges of the circuit In the simple memory circuit discussed above it is not really clear to me whether the two input wires are data inputs or control inputs For this reason and also because it will fit better into the design of other circuits we will use a modified version of this memory circuit for the rest of the lab The basic memory circuit that we will use is in the example called 1 Bit Mem You ll find this circuit in the scrolling pallette in the xLogicCircuits applet Remember that you can use the circuits in the pallette as building blocks in other circuits simply by dragging them onto the circuit board You can also see inside any iconified circuit just click on the circuit to hilite it and then click the Enlarge button The one bit memory circuit can store one bit either zero or one You won t need to understand the inside of this circuit but it important that you understand how it is used The circuit has one data input one control input and one output I refer to these as DATA IN LOAD DATA and DATA OUT http math hws edu TMCM java labs xLogicCircuitsLab2 html 3 of 9 3 26 2000 12 50 07 PM xLogicCircuits Lab 2 Control input LOAD DAT A Turn this on and off to store Data input DATA IN a value in the memory Specifies which value Zero or one is to be st
101. IT EXECUTES A PROGRAM one step at a time fetching each instruction from memory and executing it before going on to the next instruction In many cases though a problem can be broken down into sub problems that could be solved at the same time In parallel processing several CPUs work simultaneously on a problem each one solving a different sub problem This is one of the major techniques for speeding up the execution of programs Even when only one processor is available it is sometimes natural to break down a program into parts that can be executed simultaneously Multitasking can be applied to divide the single processor s time among the various parts of the program The program won t be executed any more quickly but the use of parallel processing abstractions might make the program easier to write In this lab you will use the multitasking capabilities of the xTurtle programming language In this language it is possible to split or fork a process into several processes that will all execute simultaneously and independently Each process will have its own turtle visible on the screen so you can actually see what is going on Although you will be seeing only simulated parallel processing it would be at least theoretically possible for each process to run on its own CPU The background material for this lab is covered in Sections 10 1 and 10 2 of The Most Complex Machine It would be useful but not essential for you to read that mate
102. June 2004 http math hws edu TMCM java DownloadingAndInfo html 3 of 3 6 25 2004 11 48 57 AM Introductory Lab Labs for The Most Complex Machine Introductory Lab The Web Java and DataReps THIS IS THE FIRST in a set of lab worksheets meant to be used with the introductory computer science textbook The Most Complex Machine The lab worksheets are written for use on the World Wide Web and they make use of software written in the form of applets Applets are computer programs written in a new programming language called Java All this is explained in the lab which acts as an introduction to the Web and an orientation to the way applets will be used in the rest of the lab As part of the lab you will use an applet called DataReps to help you learn about how different types of data can be represented using binary numbers This material is related to Section 1 1 of the text For a full list of labs and applets see the index page This lab includes the following sections e The World Wide Web URL s and All That e e Searching the Web e Java and Applets e e Data Representations Exercises The World Wide Web The Internet consists of millions of computers around the world linked together by a network so that they and their users can communicate and interact In the last few years the Internet has become a common part of everyday life for many people The Internet provides a number of useful services includin
103. M xTurtle Info The input output commands in xTurtle are pretty rudimentary However it is possible to display messages to the user and to read numbers input by the user There are four built in subroutines for doing such input and output These subroutines are special in that they use strings A string is a sequence of characters to be displayed to the user A string cannot include an end of line For example the command TellUser Hello World will display the characters Hello World to the user Note that in the program the string is enclosed in double quotes but that the quote characters are not part of the string that is displayed to the user There are rules for converting the string in the program to the string to be displayed to the user To display a quote character to the user you have to use two quote characters in the string in the program For example TellUser I said Stop will display I said Stop The value of a variable can be included in the displayed string To do this you have to include a character followed by the variable name in the string in the program This works for declared variables as well as for the predefined read only variables For example TellUser The turtle is at xcoord ycoord will tell the user the current position of the turtle That is when the string is displayed the value of xcoord will be substituted for xcoord in the string and similarly for ycoord If you
104. M java xModels samples Tutorial5_PolygonsEtc txt Here for example is a 3D E cyan extrude 2 The number of copies 0 0 0 5 3 5 3 4 1 4 1 3 The list of points Lp di Qh Leh Lyd Beck 33 0 O40 translate 7 5 9 5 0 And here is an example that rotates so you can see it better magenta extrude 5 2 2 0 2 2 2 Extrude 5 copies of an inverted v yrotate 30 30 translate 3 6 5 http math hws edu TMCM java xModels samples Tutorial5_PolygonsEtc txt 2 of 2 3 26 2000 12 50 38 PM http math hws edu TMCM java xModels samples Tutorial6_Segments txt Tutorial 6 An anim animat contain 51 fram the fin an anim animate 9 define fl square Segments ation can have e 30 50 s 31 frames es segments ation with four segments 0 90 90 90 ap scale 5 3 xtranslate 5 define paddles hsb 0 Gives a color by hue flap yrotate 0 0 0 0 360 hsb 0 125 11 flap yrotate 0 45 45 45 360 hsb 0 25 11 flap yrotate 0 90 90 90 360 hsb 0 375 11 flap yrotate 0 135 135 135 360 hsb 0 5 1 flap yrotate 0 180 180 180 360 hsb 0 625 1 1 flap yrotate 0 225 225 225 360 hsb 0 75 11 flap yrotate 0 270 270 270 360 hsb 0 875 1 1 flap yrotate 0 305 305 305 360 background black paddles yrotate 0 0 360 720 720 xrotate 15 lt 15 15 375 375 The ent during third segment x axis about the x axis t
105. ModelsLab2 html 1 of 7 3 26 2000 12 50 26 PM xModels Lab 2 of the screen Larger positive values are closer to you Points behind the screen have negative z values Any point in three dimensions has three coordinates giving its position with respect to the x y and z axes In the previous lab you worked with two dimensional objects that lay entirely in the xy plane In this lab we add a z coordinate and you can work with objects that lie anywhere in xyz space The image that you see on the screen is obtained by projecting the three dimensional objects onto the two dimensional computer screen By default objects appear as they would from the point 0 0 20 which is on the z axis 20 units in front of the screen Any objects or parts of objects that are behind this point are not shown at all The number 20 is called the viewing distance You can set a different viewing distance for a scene by using the viewDistance command in your scene description For example the command viewDistance 50 sets the viewing distance to 50 This means that the objects are projected onto the xy plane from the point 0 0 50 The viewDistance can only occur once in a scene description and it will have the same effect no matter where it occurs This description of viewing distance is somewhat misleading since xModels will display the same region of the xy plane no matter what the viewing distance You might expect to see a larger region of the xy plane
106. Num is the label of a location that is used to hold data then it would make sense to use Num in data manipulation commands such as LOD Num STO Num and ADD Num Labels for instructions on the other hand are mostly used in jump commands Here is a version of the counting program that uses labels The name Loop is used for the instruction that begins the loop and Count is used for the location that contains the value of the counter LOD C 1 Set Count equal to 1 STO Count Loop LOD Count Add 1 to Count INC STO Count JMP Loop Jump back to start of loop 12 Count data Location to be used for counting This example introduces two other features of xComputer s assembly language and data The word data is used as a place holder for a memory location that is going to be used by the http math hws edu TMCM java labs xComputerLab2 html 2 of 8 3 26 2000 12 50 10 PM xComputer Lab 2 program to contain a data value When the assembler translates the program into machine language and loads it into memory it replaces data with a zero Actually you could just use a 0 in the program but data is more descriptive of your intentions The line 12 is not translated into machine language It is a directive to the assembler telling the computer to store the next item in location 12 In this case it means that the Count will be stored in location 12 Without the 12 it would be stored in location 6 the next sequential
107. SUB T Recall that LOD C XXX tells the computer to load the number XXX into the accumulator LOD XXX on the other hand tells the computer to copy the contents of memory location XXX into the accumulator This is known as direct addressing In the LOD I XXX instruction XXX is the address of a memory location but not of the memory location containing the data Instead memory location XXX contains another address and that address specifies the location whose contents are to be loaded into the accumulator For example if location 17 contains the number 42 then LOD I 17 will load the contents of memory location 42 into the accumulator Admittedly this is confusing but it turns out to be just what we need to do list processing In fact in that context its not all that confusing after all Consider the following program outline set up LOD ListStart Load Loc with the starting A location of the list STO Loc Loop LOD I Loc Process the number http math hws edu TMCM java labs xComputerLab2 html 4 of 8 3 26 2000 12 50 10 PM xComputer Lab 2 LOD Loc Add 1 to Loc INC STO Loc JMP Loop Return to the start of the loop Loc data Location of next number to be processed ListStart 183 List of data to be processed 72 902 164 The first time LOD I Loc is executed it loads 183 the first number in the list into the accumulator since the value of Loc is ListStart After processing the 183 the program ad
108. TMCM Java PFD version Labs and Applets for The Most Complex Machine March 2000 Software updated June 2004 This PDF file contains material from the web site at http math hws edu TMCM java The PDF version can be read and printed using Adobe Acrobat Reader It is provided mainly to allow easy printing of material from the web site Most of the original Web pages that are reproduced here contained Java applets In this PDF version the places where the applets should appear are marked with a note stating that Java is not available David Eck Department of Mathematics and Computer Science Hobart and William Smith Colleges Geneva NY 14456 USA Email eck hws edu WWW http math hws edu eck http math hws edu TMCM java pdf_cover html 6 25 2004 11 48 26 AM TMCM Labs and Software boom anng Labs and Applets for THEMOST rew The Most Complex Machine David Eck May 1998 March 2000 and June 2004 On THIS PAGE YOU LL FIND a set of lab worksheets and Java applets that are meant to help people learn about computer science They were written for use with my introductory computer science textbook but they can also be used independently of that text The labs and applets are free for personal use In addition the applets can be freely used for non commercial purposes including courses that do not use my textbook I ask that teachers use the labs as an official part of a course only if they adopt my tex
109. X you should be able to unpack a TAR GZ archive named archive tar gz with the command tar zxf archive tar gz or with the two commands gunzip archive tar gz followed by tar xf archive tar gz This requires that you have gzip software installed Download the Entire Web Site Use one of the following links to download a complete archive of the TMCM Labs and Applets Web site You are welcome to post an unmodified copy of this material on your own Web site You can also use it on your own computer However when you use the applets on your own computer the applets on the web pages in this archive will probably not be able to read the example files that they are supposed to read This is a security feature of applets but it can be annoying at times To deal with this problem you might also want to download the Lab and Tutorial Examples archives below http math hws edu TMCM java download tmcm java web site zip for Windows http math hws edu TMCM java download tmcm java web site tar gz for Linux UNIX You can take a look at the README file for this archive The README file explains in detail how to use the applets on your own web pages and how to run the applets as stand alone applications http math hws edu TMCM java DownloadingAndInfo html 1 of 3 6 25 2004 11 48 57 AM TMCM Java Downloading and Info Applet Jar Files Software The seven applets are packaged as jar files These files can be run as standalone applications
110. about its center Here are two frames from such an animation The sample scene description called Bounce contains an animation in which a red circle seems to bounce back and forth between two edges on a square Try it Add a second circle bouncing between the other two edges The second circle should be blue This can be done by adding two short simple lines at the end scene description one for the color and one for the ball Think about geometric transformations Once you have the two bouncing circles inside the square make the square and the two circles into a single object by putting them into a define command Make an animation in which the combination object rotates and changes size Write an essay comparing object definitions in xModels with subroutine http math hws edu TMCM java labs xModelsLab1 html 9 of 10 3 26 2000 12 50 25 PM xModels Lab 1 definitions in a programming language such as xTurtle How are they similar and how are the different Among other things you should discuss the fact that object definitions in xModels do not have parameters What are the consequences of this Exercise 9 Write an essay discussing how objects created by the define command can be used to create complex scenes Why is the ability to define objects so important to dealing with complexity Keep in mind that once an object has been defined it can be used as a component in another more complex object Your essay should discuss
111. aced into the FLAG register X and Y registers These are 16 bit registers that hold numbers that are to be used in a calculation For example when two numbers are to be added they are placed into X edu TMCM java xComputer info html 4 of 8 3 26 2000 12 50 30 PM xComputer Info and Y The Y register is also used as a temporary storage place in a few cases The X and Y registers are connected to the inputs of an Arithmetic Logic Unit or ALU which does all the arithmetic and logical calculations in the computer The outputs of the ALU are connected to the AC and to the FLAG register The ALU is not shown in the xComputer applet The components of the computer including the main memory the registers the clock and the ALU are controlled by turning wires on and off These wires are connected to various components of the computer and they control the operation of those components It is these control wires that make the steps of the fetch and execute cycle happen You can see a list of the control wires in xComputer by selecting the Control Wire option from the memory display pop up menu The wires that are currently turned on are shown in red As a program is executed the wires that are on change during each step of each fetch and execute cycle You can watch how they change in order to learn how each step is accomplished For example in step 1 of each fetch and execute cycle the control wire named Load ADDR from_PC
112. achines can do any computation that can be done by any computer What is your reaction to this claim Do you believe it What evidence is there to support this claim What reasons might someone have for doubting it Write a short essay discussing your answers to these questions Exercise 12 Write a short essay comparing Turing machines as computational devices with the model computer xComputer that you worked with in previous labs This is one of a series of labs written to be used with The Most Complex Machine A Survey of Computers and Computing an introductory computer science textbook by David Eck For the most part the labs are also useful on their own and they can be freely used and distributed for private non commercial purposes However they should not be used as a formal part of a course unless The Most Complex Machine is also adopted for use in that course David Eck eck hws edu Summer 1997 http math hws edu TMCM java labs xTuringMachineLab html 9 of 9 3 26 2000 12 50 12 PM Web Publishing with Netscape Composer Labs for The Most Complex Machine Web Publishing Lab Creating Web Pages with Netscape Composer Tuts LAB IS A BREAK FROM THE USUAL run of Java applets and exercises You ve used Web pages in the previous labs In this lab you ll learn something about how Web pages are created and you will publish a page of your own on the Web Note Parts of this lab are specific to students in CPSC 100 Fall 199
113. address wires they can be set to any of the eight combinations OFF OFF OFF OFF OFF ON OFF ON OFF OFF ON ON ON OFF OFF ON OFF ON ON ON OFF and ON ON ON These combinations represent the binary numbers 000 001 010 011 100 101 110 and 111 In ordinary decimal notation they represent 0 1 2 3 4 5 6 and 7 So a RAM with three ADDRESS wires can have eight locations numbered 0 through 7 Twenty ADDRESS wires are enough to specify over a million locations and thirty ADDRESS wires can specify over a billion You should spend some time understanding how to use the 2 Bit RAM and how it works Each of the two locations in the RAM is a Guarded 1 Bit Mem circuit This circuit is similar to the basic 1 Bit Mem circuit that you looked at above but it has an addition control input called the GUARD http math hws edu TMCM java labs xLogicCircuitsLab2 html 6 of 9 3 26 2000 12 50 07 PM xLogicCircuits Lab 2 DAT A IN LOAD DATA and DATA OUT wires have the same functions as in the basic 1 Bit Mem Guarded 1 Bit Hem When this GUARD control wire is OFF the output is OFF and the LOAD DATA wire has no effect The GUARD must be ON to store or read data When the GUARD of a location is ON that location is selected When it is selected it outputs its stored value on its DATA OUT wire and its LOAD DATA wire can be used to store a new value in it When the GUARD is OFF the Guarded 1 Bit Mem is inert It ignores its LOAD DAT
114. ain program Exercise 6 The sample file PrimesAndRemainders txt defines two subroutines One of the subroutines can be used to find the remainder when one integer is divided into another The other subroutine can be used to determine whether a number is prime The file does not contain a main program If you want to use one or both of the subroutines you can add a main program at the beginning of the file You should read the comments on the two subroutines to find out how to use them Then write two programs that use the subroutines The first program should use the Remainder subroutine to compute the remainder when 609 is divided by 81 The second program should use the PrimeTest subroutine to determine whether or not 51 is prime Note that you do not have to understand how the subroutines work You just need to know how to call them and pass the proper parameters to them Exercise 7 This exercise like the previous one involves writing a main program for the PrimesAndRemainders txt example However this exercise is much more challenging Write a main program that makes a list of prime numbers The program should use the PrimeTest subroutine to test whether each of the numbers 2 3 4 5 6 and so on is prime Each number that is found to be prime should be added to a list You can write a program that runs in an infinite loop Woe Use a location named p to store the number that you are checking Start by storing a 2 in p In
115. al other pairs of numbers to add Note that as the machine adds the second number to the first it replaces O s and 1 s with x s and y s When it finishes it erases the second number from the tape and changes all the x s and y s back to 0 s and 1 s The final sample machine MultiplyByAdding multiplies two binary numbers It does not do this by the usual multiplication algorithm Two numbers can be multiplied by repeatedly adding the first number to itself The second number tells how many times the addition is to be performed The MultiplyByAdding machine works in this way Each time it adds the first number to itself it subtracts one from the second number When the second number reaches zero the process is finished At that point the machine erases the two original input numbers The number remaining on the tape at the end of this process is the product of the two inputs You won t have to understand this machine in detail but it s interesting to see how a relatively complex computation can be performed by a Turing machine Exercises Exercise 1 Create a Turing machine that will move to the right until it finds a Then it will erase everything on the tape between that and the next to the right It will halt when it gets to the second The s themselves should not be erased You can do this with a fairly simple machine that uses only two states 0 and 1 Note that if the machine is started http math hws edu TMCM java labs xTur
116. al wagon Use four wheels Use a cube instead of a square as the starting point for the body of the wagon Try out your wagon in an animation with the command wagon xtranslate 10 10 yrotate 60 xrotate 15 You should see a wagon that looks like it s driving away from you up a hill Exercise 7 The picture below shows a radio telescope from several different viewpoints This telescope is made of two pieces The base is a cone You can use a cone object or you can make it by lathing a single line segment The dish of the telescope is not a cone since it s cross section is curved You can make the dish by lathing a curve consisting of several line segments connecting 0 0 to 4 2 The dish has to be rotated and translated into position after it is created Define a telescope object as described Then make an animation that shows three telescopes rotating back as forth sweeping the skies for signs of new galaxies or extraterrestrial life http math hws edu TMCM java labs xModelsLab2 html 6 of 7 3 26 2000 12 50 26 PM xModels Lab 2 Exercise 8 Use the xModels applet to make a three dimensional image not an animation of your choice Your scene description should include at least one object definition You might for example try to make a house a sailboat a robot or a space station Exercise 9 Use the xModels applet to make an animation of your choice Try to be creative and or aesthetic Exercise 10 Write an essay discussing
117. al was covered in the previous lab and is not repeated here This lab includes the following sections e Inthe Direction of Z e Three Dimensional Objects and Transformations e Lathing and Extrusion e Exercises Start by clicking this button to launch the xModels applet in its own window Sorry your browser doesn t do Java For a full list of labs and applets see the index page In the Direction of Z Geometric models can be constructed in three dimensions as well as in two Even for three dimensional models of course the image still has to be displayed on a two dimensional computer screen but the model of the scene exists at least in our imagination and the computer s memory in three dimensions Once you understand the basic ideas of geometric modeling in two dimensions the step up to three dimensions is not so hard Just remember that in addition to the x and y coordinates that you are used to there is also a z coordinate Think of z as measuring distance in front of the computer screen or if z is negative behind it The x axis is a horizontal line on the computer screen The y axis is a vertical line on the screen The x and y axes intersect at a point called the origin which is at the center of xModels display area The z axis is a line perpendicular to the screen Like the other two axes the z axis goes through the origin The positive direction of the z axis points at you out http math hws edu TMCM java labs x
118. am MultiplyTwoNumbers txt Make sure to include comments in your program http math hws edu TMCM java labs xComputerLab3 html 5 of 7 3 26 2000 12 50 11 PM xComputerLab 3 Exercise 4 Read the Reality Check section above Why can t you express the jump to subroutine and return from subroutine operations in the language of xComputer What do these instructions need to do that can t be expressed in that language What sort of modifications would have to be made to xComputer to add them to xComputer s machine language Exercise 5 The sample program ListSumSubroutine txt uses a subroutine to add up a list of numbers Suppose you would like to multiply the numbers instead To do this copy the multiplication subroutine from the Multiply TwoNumbers txt sample program and paste it onto the end of ListSumSubroutine txt Modify the List Sum subroutine so that instead of adding two numbers it uses the Multiply subroutine to multiply You have to replace the instruction add Sum with several instructions that set up a call to the Multiply subroutine And you ll need to make up a return address label for the subroutine to jump back to Once you ve made this modification the program will compute the product 1 2 3 4 5 6 7 instead of the sum 1 2 3 4 5 6 7 You might want to change the name of the subroutine from ListSum to ListMul and change the name of the memory location Sum to Product This will require that you also change the names in the m
119. an send and receive email messages written in HTML When you compose an email message in one of Netscape s email windows you can use the full range of HTML composition tools You can also drag images and links onto your page just as can when you are creating a Web page When you send the message you have the option of sending it in HTML format only or in a combination form that includes both HTML and plain text versions of the message If the recipient of the message reads it with Netscape they will see the message just as you created it with colors active links graphics and whatever else you put on the page Unfortunately recipients who don t use Netscape will only see the plain text version or the nasty HTML source code Before you can experiment with using Netscape for Email you will have to configure it I have a page on using Netscape Email if you are interested David Eck eck hws edu October 1997 http math hws edu TMCM java labs WebPublishingLab html 7 of 7 3 26 2000 12 50 13 PM xTurtle Lab 1 Labs for The Most Complex Machine xTurtle Lab 1 Introduction to Programming THIS LAB is an introduction to a high level programming language called xTurtle This language was created to be used with The Most Complex Machine but it is in the mainstream of high level languages along with Pascal Ada and C It incorporates some ideas common to all these languages such as variables assignment statements loops if sta
120. and since it just rotates everything around the z axis which points out of the screen towards the user This rectangle starts at the top of the screen and rotates around the x axis blue cube scale 2 translate 12 12 2 2 6 6 A small blue cube moves from 12 2 6 to 12 2 6 green cylinder scale 5 rotate 0 360 about line 1 1 0 The cylinder rotates about the line that extends from 0 0 0 to 1 1 0 The rotate about line command lets you rotate objects about lines other than the coordinate axes http math hws edu TMCM java xModels samples Tutorial3_3D txt 3 26 2000 12 50 38 PM http math hws edu TMCM java xModels samples Tutorial4_ ComplexObjects txt xModels Tutorial 4 Complex Objects he real power of xModels what there is of it comes from act that it is a hierarchical modeling language You an combine several objects into one complex object hich can then be treated as a unit Transformations pplied to a complex object apply to the object asa hole A complex object can even include other complex objects It is also possible to define a name to represent a complex object Then the name can be used in the scene just as if it were one of the predefined objects such as square and cone o f amA animate 60 This will be a 60 frame animation A complex object begins with a and ends with Jj square sca
121. and binary by hand But of course you could use the applet instead Real Number Real numbers are numbers that can contain decimal points like 3 14159 or 234 5 or 12 0 They can also be written using scientific notation For example 2 15e12 is a way of writing 2 15 times 10 2 The representation used in computers for real numbers is very complicated And it allows some strange possibilities such as INF http math hws edu TMCM java labs DataRepsLab html 6 of 9 3 26 2000 12 50 04 PM Introductory Lab and INF which stand for infinity and minus infinity There are also NAN s NAN stands for not a number NAN s are used to represent the results of illegal operations such as taking a square root of a negative number Note that the integer 17 and the real number 17 have completely different representations in the computer even though they are the same number mathematically All in all it s probably best not to worry about the internal representation of real numbers I include this data type here for completeness since real numbers are so important ASCII Text Characters can be encoded using ASCII code as explained in Section 1 1 of the text Each possible character is assigned a code that is one byte that is eight bits long With 32 bits you can represents 4 characters in ASCII code Not every possible byte represents an ordinary printable character The applet shows other bytes in the form lt n gt where n is the base
122. and for doing lathing is lathe lathe 8 0 5 1 1 3 0 1 1 0 5 The first parameter is the number of copies then comes the list of points yrotate 0 45 You can apply transformations to lathed objects Compare the figure produced by the above to the polygon made with the same points polygon 0 5 1 1 3 0 1 1 0 5 xtranslate 6 Move it over so you can see it The extra vertical line from 0 5 back to 0 5 which is added to close the polygon is not used in the lathing operation The remaining sides form the figure that is rotated about the y axis by the lathe command Here are mor xamples red lathe 12 1 2 2 2 Lathing a single line to make a lamp shade xrotate 0 360 Tumble it about the x axis xtranslate 7 blue lathe 4 2 1 1 3 0 4 0 You can use number ranges translate 4 7 in the point list Extrusion is not quite so interesting as lathing In extrusion the copies of the original figure are made by translating the original in the z direction instead of by rotating it The copies are spaced one unit apart although you can change that of course by scaling in the z direction The extruded figure extends equally far behind the xy plane as it does in front of it The command for doing extrusion is extrude http math hws edu TMCM java xModels samples Tutorial5_PolygonsEtc txt 1 of 2 3 26 2000 12 50 38 PM http math hws edu TMC
123. and they can be used for putting the applets on your own web pages The jar files are part of the complete web archive that you can download in the previous section of this page See the README file from that archive for complete information about how to use them You can also download individual jar files using the following links DataReps jar xLogicCircuits jar xComputer jar xTuringMachine jar xTurtle jar xSortLab jar xModels jar On some computers you can run one of these files simply by double clicking on it If you have a recent version of Java from Sun Microsystems you can try commands of the following form on the command line java gjelie zLogicCircuits Jar If you are using Microsoft s version of Java in Internet Explorer in Windows then you can use the jview command in a command window to run the programs The command takes a form such as jview cp xLogicCircuits jar tmom xLogicCircuitsrrame Here tmcm xLogicCircuitsFrame is the name of the Java class within the jar file that actually defines the programs Similar names are used in the other jar files Lab and Tutorial Examples Here are two archives that make it easy to run the Labs examples and Information Tutorial examples outside of a Web browser One advantage of this is that you will be able to load and save files The Labs examples and applets from the The Labs section of the main page http math hws edu TMCM java download TMCM_Labs zip for Windo
124. animation for xModels animate 60 An animated scene MUST begin with the word animate followed by a specification of the number of frames in the animation Here there will be 61 frames numbered from 0 to 60 background yellow The background command is used to specify a background color for the scene Used here just for fun square scale 1 5 rotate 0 90 Specifies a different square in each scene The first square has size 1 and is not rotated at all The second square is a little bigger and is rotated a bit by 1 5 degrees to be exact The last square will be 5 units large and rotated through an angle of 90 degrees circle scale 1 5 5 1 translate 6 6 This starts out as a 5 by 1 ellipse and ends up as a 1 by 5 ellipse The translate command moves it to the upper right corner of the display area blue cube scale 2 translate 6 6 7 The cube moves along the bottom of the screen from the point 6 7 to 6 7 line scale 4 A four units long line rotate 0 180 rotate from 0 to 180 degrees translate 0 7 The rotating line is moved 7 units upwards Note this line is blue red line scale 4 A four units long line translate 0 7 is moved seven units upwards rotate 0 180 and from there rotates through 180 degrees about the origin Note that the order in which the transformations are applie
125. ar on the right hand edge of the applet Pause Resume Button This button is active while a program is running Click it to pause the program The name changes to Resume and you can then click on it to restart the program e Stop Button This button is active while a program is running or paused Click on it to stop the program permanently e Clear Button If the graphics area is displayed this button will clear it and restore the turtle to its starting point If a program is displayed it will erase it There is no way to undo this e Indent Button This button is available when a program is displayed It will indent the lines of the program to show the program s structure e Load Button Click on this button to load an xTurtle program from a text file on your hard drive Note that this is likely to fail because of security restrictions on applets e Save Button Click on this button to save the program to a file on your hard drive Note that this is likely to fail because of security restrictions on applets e Speed Pop up Menu This menu which is originally set to Fast controls the speed at which the turtle draws A delay is inserted after each turtle motion such as drawing a line drawing a circle or turning e No Turtles Checkbox When this box is checked the little black triangular turtles are invisible By the way this can speed up a program significantly especially in a multitasking program where there are a lot of turt
126. arting at location 30 and leave the answer The computer will add them in location 26 http math hws edu TMCM java xComputer samples TheBasics txt 2 of 2 3 26 2000 12 50 28 PM http math hws edu TMCM java xComputer samples Graphics txt Example 2 Graphics This is a very simple program that is meant to demonstrate a Graphics memory display If you select Graphics from the pop up menu above the scrolling memory display area of the xComputer the scrolling display will be replaced by t shows the entire contents of memory at a once Each pixel in the rectangle represents one bit in memory The pixel is white if that bit is zero and at bit is one The rectangle is 64 pixels wide so each row of dots represents four 16 bit memory locations As the computer executes a program you can watch the dots change as memory is modified This can be particularly nice if you set the Speed pop up menu to Fastest Speed The program simply stores the numbers 1 2 3 in consecutive memory locations starting at location 20 To run the program click the Translate button located below this program Once the computer reappears set the memory display pop up menu to Graphics The program will appear as a few dots at the top of the memory rectangle Set the run speed to Fastest Speed and then click the Run button You should see memory fill up w
127. as a comment and is ignored by the computer There are a few more things you can do in an assembly language program A program item can be preceded by a number followed by a This is a repetition count and is the same as typing the item the specified number of times For example 25 17 puts a 17 in each of the http math hws edu TMCM java xComputer info html 6 of 8 3 26 2000 12 50 30 PM xComputer Info next 25 memory locations 4 SHL is equivalent to four SHL instructions in a row Ordinarily a program is loaded into consecutive memory locations starting at location 0 However you can specify where loading is to take place by using the character followed by an address For example 100 specifies that the next item is to go into memory location 100 Items following that one will then go into location 101 102 etc You might use this feature to put subroutines at specific points in memory Finally you can store a string of ASCII characters into consecutive memory locations by using a string A string is just a series of characters enclosed between double quotes such as Hello World When the computer encounters a string in a program it stores the characters in consecutive memory locations one per location List of Assembly Language Instructions Here is a complete list of the assembly language instructions for xComputer In this listing X is data for the instruction it must translate into a 10 bit binary number
128. ath hws edu TMCM java labs DataRepsLab html 4 of 9 3 26 2000 12 50 04 PM Introductory Lab applet the basic pattern consists of lines radiating out from a command center There are two copies of this pattern One is fixed while the other drifts about Even this decorative applet allows some interaction If you click and drag your mouse on the Moir applet you can control the motion of the pattern To click and drag means to press the mouse button and then move the mouse while holding down the button If you shift click on the applet you can stop and restart its motion To shift click means to hold down the shift key while you click the mouse button If you are using a slow computer you might want to turn off the Moir applet so that it doesn t take computer processing time away from other things going on on this page Each of the labs for The Most Complex Machine uses an applet to help you learn something about computer science In order to make it more convenient to use the applets and read the labs at the same time the applets are set up to run in separate windows The lab worksheet contains a button that you can click to launch the applet In most of the labs this button is close to the beginning of the lab where it will be easy to find The button is itself a small applet that runs on the Web page In this lab you will use a fairly simple applet called DataReps You will use this applet to learn how the same binary
129. ation that you entered earlier You can fill in the password for your account or you can leave it blank If you leave it blank Netscape will ask you for it later If you are working with a newly created page then the Page Title and HTML Filename boxes will be blank You should fill in these two boxes Ordinarily the HTML Filename for your home page should be index html The Page Title can be anything you want this is the title that will appear in the title bar of a browser window when the page is viewed Once you have set up all this information click the OK button and Netscape will attempt to send your page to the Web server If it succeeds you will be able to view the page in a regular browser window and so will anyone else on the Internet who knows its URL Once your page has been published you can continue to make changes in the Composer window For those changes to take effect you will have to have to upload the page again by clicking on the Publish button If you want to return to edit your Web page at a later time all you have to do is start up Netscape again load your page into the browser window and then choose Edit Page from the File menu This will open a Composer window that you can use to edit the page and publish the new version In fact you can do this with any Web page that you would like to use as a starting point for a page of your own Adding Some Frills After you get the hang of using Composer you will
130. ble must be a real number such as 42 3 14159 1 or 12 3e 12 The last example used scientific notation which is legal in an xTurtle program The notation 12 3e 12 means 12 3 times 10 raised to the power 12 Very large and small numbers are written using scientific notation When a variable is first declared it has a special value called not a number It is illegal to use such a value in a computation and doing so will result in an error that will crash your program Variables and numbers can be used in mathematical expressions such as 1 InterestRate Principal Expressions can include the usual arithmetic operators plus minus times divide and exponentiation Expressions can also include built in functions and user defined function For example sin 2 angle 30 Parentheses are always required around the arguments of a function In the case of a function that takes no argument a set of empty parentheses is optional The predefined functions are e The usual trigonometric functions sin x cos x tan x sec x csc x cot x The arguments for these functions are measured in degrees Some inverse trigonometric functions arcsin x arctan x arccos x The exponential function exp x meaning e The natural logarithm ln x The square root function sqrt x The absolute value function abs x The function round x which rounds its argument to the nearest integer The function trunc x which trunca
131. board you can still move it to a new position but you have to drag it using the right mouse button Alternatively if you have a one button mouse for example you can drag a component by holding down the control key as you first press the mouse button on it You can delete components and wires that you ve added by mistake Just click on the component or wire to hilite it Then click on the Delete button at the bottom of the applet The hilited item will be deleted from the circuit board If you delete a component that has wires attached the attached wires will also be deleted along with the component If you delete an item or modify the circuit in some other way you get one chance to change your mind You can click on the Undo button to undo one operation Only the most recent operation can be undone in this way There is one shortcut that you might find useful if you like using Tacks You can insert a Tack into an existing wire by double clicking on the wire If you double click and hold the mouse down on the second click you can drag the tack to a different position However some browsers might not support double clicks After you build the practice circuit you can clear the screen since you won t need that circuit again in the rest of the lab However you ll get more practice building circuits in the Exercises at the end of the lab Complex Circuits and Subcircuits In order to have circuits that display structured complex
132. bs since the lab worksheets include instructions for using the applets The labs and applets are available for downloading So is source code for the applets The applets are also available as Java applications which can be run without a Web browser For more details see the downloading and information page You ll also find information there about how to use the applets on your own Web pages The Labs Introductory Lab The Web Java and DataReps This lab is mainly an introduction to the use of the World Wide Web and to the idea of Java applets A simple applet DataReps serves as an example of an applet It also serves to demonstrate how several different types of data are represented in a computer xLogicCircuits Lab 1 Logic Circuits Explores logic circuits created out of AND OR and NOT gates The relationship between http math hws edu TMCM java index html 1 of 4 6 25 2004 11 48 41 AM TMCM Labs and Software circuits and Boolean algebra is also covered xLogicCircuits Lab 2 Memory Circuits Shows how circuits that contain feedback loops can be used as memory circuits and how a RAM random access memory can be constructed and used xComputer Lab 1 Introduction to xComputer Introduces the xComputer a simple model computer and investigates how it operates in a fetch and execute cycle to carry out machine language instructions stored in its memory xComputer Lab 2 Assembly Language Programming Covers ass
133. by clicking on one of the five radio buttons Just type your data into the input box at the top of the applet and press return You can also click on the 8 by 4 grid of big pixels at the center of the applet The various data representations are described below This applet was originally written by David Eck for use with his introductory computer science textbook The Most Complex Machine However it can also be used on its own For a list of other applets and for lab worksheets that use the applets see the index page Sorry Your browser doesn t do Java Data Types The Data Representation Applet shows six different interpretations for the same string of thirty two bits The six interpretations are a binary number an integer a hexadecimal number a real number a string of four characters and an eight by four grid of pixels Here is a short explanation of each of the six data displays Binary This is the most direct display of the 32 bit binary number showing a zero or one to represent each individual bit Base ten Integer A binary number can be interpreted as a normal positive integer 0 1 2 3 4 written in the base ten With 32 bits you can represent 232 different numbers Usually you want to use both positive and negative numbers The scheme for representing negative numbers is a bit strange It is explained in Subsection 2 2 3 of The Most Complex Machine Using 32 bits the integers from 2147483648 to 2147483647 can be r
134. cCircuits Lab 1 Exercises Exercise 1 One of the examples in this lab was the circuit corresponding to the expression A and not B or B and not A This circuit is ON if exactly one of its inputs is on Another way to describe the output is to say that it is ON if one or the other of the inputs is on but not both of the inputs are on This description corresponds to the Boolean expression A or B and not A and B Build a circuit corresponding to the second expression and check that it gives the same output as the first circuit for every possible combination of inputs Exercise 2 When you checked every possible combination of inputs for the circuit in Exercise 1 how many combinations did you have to check If you wanted to check that the Two or More example circuit works correctly for every possible combination of inputs how many combinations would you have to check Why If you wanted to check that the 4 Bit Adder gives the correct answer for each possible set of inputs how many inputs are there to check Why Exercise 3 Consider the following three Boolean algebra expressions A and B and C or not B not not A and not B not A or B or A and B For each expression build a logic circuit that computes the value of that expression Write a paragraph that explains the method that you apply when you build circuits from expressions One note To build a circuit for an expression of the form X and Y an
135. can be followed by its own set of transformations as described below The objects can include basic objects named objects created with the define command and nested complex objects Because of this ability to nest complex objects inside other complex objects xModels is said to use hierarchical models Transformations Any object can be followed by a list of one or more transformations that affect the size position and orientation of that object This includes complex objects Any transformation applied to a complex object is applied to that object as a whole If an object inside a complex object has its own transformations they are applied first followed by the overall transformation of the object as a whole A transformation consists of a word specifying the type of transformation followed by one or more parameters For example the command rotate 30 specifies that the object is to be rotated through an angle of 30 degrees about the z axis Some transformations take a variable number of parameters For example scale 3 will magnify the object by a factor of 3 in all directions while scale 2 6 0 5 will scale it by factors of 2 in the x direction 6 in the y direction and 0 5 in the z direction When an object is followed by several transformations they are applied in the order given For example in square xtranslate 5 rotate 30 the square is first translated 5 units in the positive x direction and is then rotated by 30 degrees abo
136. ce x along the direction in which it is currently facing If x is negative the turtle actually moves forward moveTo x y moves the turtle from its current position to the point with coordinates x y move dx dy moves the turtle from its current position to a point that is dx units away horizontally and dy units away vertically turn dA rotates the turtle from its current heading through an angle of dA degrees If dA is positive the rotation is counterclockwise if dA is negative the angle is clockwise face A rotates the turtle to a heading of A degrees from the zero position In the zero position the turtle faces to the right Circle r draws a circle of radius r The current turtle position is on the circumference of the circle The turtle s heading is tangent to the circle If r is positive the circle lies on the turtle s left If r is negative the turtle lies on the turtle s right The effect of Circle r is exactly the same as the effect of Arc r 360 Note that the turtle s position and heading do not change Arc r A Draws an arc of a circle of radius r The arc subtends an angle of A The arc starts at the current position and heading of the turtle The turtle ends up at the other end of the arc If r and A are both positive then the turtle curves forward and towards its left If r is negative and A is positive the turtle curves forward and towards its right Negative angles move the turtle backwards
137. ch pair of arcs another small circle is added as decoration You can try changing the size of the arcs in the large circle For example change the 20 to 3 and you ll get a decoration every 3 degrees instead of every 20 degrees You could also change the radius in the arc command You can try using a different decoration For example try changing circle 0 5 to forward 5 back 5 You could be more creative Try using a triangle or a square as decoration Whatever commands you use to draw the decoration you should be sure that they return the turtle to the same position and heading as when it starts Try to find the prettiest variation on the necklace theme that you can find Exercise 4 The following program was used as an example earlier in the lab It draws 100 lines radiating out from a central point Each line is drawn with a different hue and the colors of the lines range throughout the entire spectrum DECLARE hue hue 0 LOOP hsb hue 1 1 forward 5 back 3 turn 360 100 hue hue 0 01 exit if hue 1 END LOOP How would you modify this program so that instead of changing the hue from one line to the next you change the saturation instead What does the resulting picture look like Try it and find out Exercise 5 The word random can be used in a program to represent a random value in the range from 0 0 to 1 0 Random is actually a function with no parameters but it acts like a variable that has a differen
138. cimal integers in the range 32768 to 32767 This is only one possible interpretation of the binary numbers that are stored in memory Using the display style pop up menu you can select from six different interpretations e The Instructions display shows the contents of each memory location as an assembly language instruction In this display style you should see the original counting http math hws edu TMCM java labs xComputerLab1 html 5 of 10 3 26 2000 12 50 09 PM xComputer Lab 1 program in memory locations 0 through 5 Most of the other locations contain Add 0 which just happens to be the assembly language instruction encoded by the 16 bit binary number 0000000000000000 Since not every 16 bit binary number corresponds to a legitimate assembly language instruction you might see some funny things in this display style e The Integers and Unsigned Ints displays show ordinary decimal integers The difference is that signed 16 bit integers are in the range 32768 to 32767 while unsigned 16 bit integers are in the range 0 to 65535 In either case there are 2 6 different possible values it s just a question of how they are interpreted See Subsection 2 2 3 in the text The Binary display shows a 16 bit binary number in each memory location this display style is closest to the actual physical contents of the memory The ASCII display interprets each sixteen bit number in memory as made up of two eight bit ASCII character c
139. count will be At that time the end The net resul an 8 sided polygon has been drawn This is an example of a counting loop c ount 1 8 IF count http math hws edu TMCM java xTurtle samples T Loops uence Some t from loop nd r s exit te r g 8 loop will lt is that utorial4_loop txt 1 of 2 3 26 2000 12 50 35 PM http math hws edu TMCM java xTurtle samples Tutorial4_loop txt As a final example the following example computes the average of 100 randomly chosen numbers You should expect the average to be close COSO Da DECLARE total average total 0 count 0 This was already declared LOOP total total random count count 1 EXIT IF count 100 END LOOP average total 100 PenUp MoveTo 8 8 PenDown blue DrawText The average was average http math hws edu TMCM java xTurtle samples Tutorial4_loop txt 2 of 2 3 26 2000 12 50 35 PM http math hws edu TMCM java xTurtle samples Tutorial5_if txt xTurtle Tutorial Example 5 IF An IF statement is used to choose among several possible courses of action The IF statement bases its decision on the value of one or more logical expressions A logical expression is something that can be either true or false such as x gt 0 A simple IF THEN ELSE makes a choice between two
140. cuits txt use the applet tag lt p align center gt lt applet archive xLogicCircuits zip code tmem xLogicCircuitsApplet class height 380 width 500 gt lt param name LOAD value SampleCircuits txt gt lt applet gt lt p gt The param name LOAD must be given in uppercase letters as shown Param names are case sensitive You can also use an input file with the launcher version of the applet lt p align center gt lt applet archive xLogicCircuits zip code tmem xLogicCircuitsLauncher class width 180 height 30 gt lt param name LOAD value SampleCircuits txt gt lt applet gt lt p gt The xComputer load several sample files REN the righ the param be careful to use names U xTuringMachine xTurtle The files musti URL1 URL2 and names without and xModels applets can be specified using so on You have to any omissions http math hws edu TMCM java tmcm java web site README txt 2 of 3 3 26 2000 12 50 02 PM http math hws edu TMCM java tmcm java web site README txt If there is no URL2 for example the applet won t even check for URL3 For example to use four sample input files with the launcher version of the xComputer applet you could use the following tag on your web page lt applet archive xComputer zip code tmcm xComputerLauncher class width 150 height 30 gt lt param name URL value SimpleCounter txt gt lt param name URL1 valu
141. d Z you should insert some extra parentheses which don t change the answer Think of the expression as X and Y and Z and build the circuit using two AND gates Exercise 4 Given a logic circuit that does not contain any feedback loops it is possible to find a Boolean algebra expression that describes each output of that circuit Open the circuit called For Ex 4 which was one of the sample circuits in the applet s pallette This circuit has four inputs and three outputs Assuming that the inputs are called A B C and D find the expression that corresponds to each of the three outputs Also write a paragraph that discusses the procedure that you apply to find the Boolean expression for the output of a circuit Exercise 5 Consider the following input output table for a circuit with two inputs and one output The table gives the desired output of the circuit for each possible combination of inputs Input 1 Input 2 Output http math hws edu TMCM java labs xLogicCircuitsLab1 html 7 of 10 3 26 2000 12 50 06 PM xLogicCircuits Lab 1 Construct a circuit that displays the specified behavior You have to build one circuit that satisfies all four rows of the table Section 2 1 of The Most Complex Machines gives a general method for constructing a circuit specified by an input output table You can apply that method or you can just try to reason logically about what the table says Write a paragraph discussing how you foun
142. d be equal to Aif Cis ON Select p Em and should be equal to B if D is ON Assume C and D are not both turned on at the same time The circuit has two inputs A and B at the top It also has two inputs C and D on the left which serve as control wires The only thing that makes an input of a circuit a control wire is that the designer of the circuit says it is but in general control wires are thought of as controlling the circuit in some way The control wires determine which of the inputs A or B gets to the output In order to do this exercise you should think logically That is try to http math hws edu TMCM java labs xLogicCircuitsLab1 html 8 of 10 3 26 2000 12 50 06 PM xLogicCircuits Lab 1 describe the output of the circuit using a Boolean expression involving A B C and D Then use that expression as a blueprint for the circuit Test your circuit and save it for use in Exercise 10 Exercise 10 For this exercise you should build a Mini ALU that can do either addition or subtraction of four bit binary numbers An Arithmetic Logic Unit or ALU is the part of a computer that does the basic arithmetic and logical computations It takes two binary numbers and computes some output The interesting thing is that an ALU can perform several different operations It has control wires to tell it which operation to perform You will build an ALU that can perform either addition or subtraction of four bit binary numbers It has
143. d by a text input area when you can type your program Enter the following program into that text area lod c 1 sto 12 lod 12 http math hws edu TMCM java labs xComputerLab1 html 4 of 10 3 26 2000 12 50 09 PM xComputer Lab 1 inc sto 12 jmp 2 This program counts It starts by putting the number 1 into memory location 12 and then it adds one to the number in that location over and over forever You ll see this in action in a moment There are several new instructions here Lod 12 tells xComputer to copy the number from memory location 12 into the accumulator Note how this differs from lod c 12 which puts the number 12 itself into the AC rather than the number stored in memory location 12 The inc instruction adds one to the value in the accumulator And jmp 2 is a jump instruction that sends the computer back to location 2 After typing this program click on the Translate button that is located below the text area on the left end of a row of buttons If the program contains some error an error message will be displayed If you ve typed the program correctly it will be translated into machine language and stored in the xComputer s memory The text area will be replaced by the computer display and the computer will be ready to run the program Click on the Run button to run the program and see how it operates You can watch as the PC counts off the instructions in the program You will see the assembly language instructions
144. d can help you understand what really goes on when a subroutine is called And it can also help you appreciate the elegance of more sophisticated computers and programming languages Exercises Exercise 1 The main program in the MultiplyTwoNumbers txt sample program is as follows leas 13 Set up to call the subroutine with sto N1 N1 13 N2 56 and ret_addr back lod c 56 sto N2 lod c back sto ret_addr jmp Multiply Call the subroutine back lod Answer When the subroutine ends it returns A control to this location and the A product of N1 and N2 is in Answer A This LOD instruction puts the answer in the accumulator hit Terminate the program by halting the computer Carefully explain each instruction in this program Explain exactly what each of the first 8 instructions has to do with calling the subroutine Exercise 2 Write a main program that uses the Multiply subroutine in Multiply TwoNumbers txt to compute the product 5 23 17 Do not modify the subroutine The main program should call the subroutine twice Exercise 3 Write a subroutine to add three numbers This is a pretty silly thing to do but the point is to demonstrate that you understand the basic concepts involved Your subroutine should have three parameters and a return value the three numbers to be added and their sum Write a main program that uses your subroutine to add 17 42 and 105 Your program will be very similar to the sample progr
145. d makes a big difference This line is red When you render this animation note how the image of A the cube changes as it moves http math hws edu TMCM java xModels samples Tutorial2_Animation txt 3 26 2000 12 50 37 PM http math hws edu TMCM java xModels samples Tutorial3_3D txt xModels Tutorial 3 Three dimensional Scenes The two previous tutorials included three dimensional objects but the transformations that were applied only affected two dimensions Transformations can in fact affect all three dimensions This file discusses three dimensional transformations and has more information about transformations animate 60 This will be a 61 frame animation circle scale 8 The translate command can take three translate 0 0 6 parameters giving changes in x y and z yrotate 0 360 A translation of 6 units in the z direction moves the circle forward six units towards the viewer From that position it is rotated 360 degrees around the y axis This sends it towards the right and away from the viewer then all the way around the axis and back to its original position red square xscale 5 xscale 3 is short for scale 3 1 1 ytranslate 8 This means translate 0 8 0 Similarly xrotate 0 360 there are commands yscale zscale Xtranslate ztranslate xrotate and zrotate zrotate is actually the same as the rotate comm
146. d paste So the work done on writing the subroutine doesn t have to be repeated over and over The subroutine can be reused In fact real computers have large libraries of subroutines that are available for use by programs The complex programs that are used on modern computers would be http math hws edu TMCM java labs xComputerLab3 html 1 of 7 3 26 2000 12 50 11 PM xComputerLab 3 extremely difficult to write if these libraries of pre written subroutines were not available In xComputer s assembly language calling a subroutine means jumping to the first instruction in the subroutine using a JMP instruction The execution of the subroutine will end with a jump back to the same point in the program from which the subroutine was called so that the program can pick up where it left off before calling the subroutine This is known as returning from the subroutine Other computers provide special commands for calling and returning from subroutines There is more to it than a few jump instructions though For one thing if the subroutine is to be reusable in a meaningful sense it must be possible to call the subroutine from many different places in a program If this is the case how does the computer know what point in the program to return to when the subroutine ends The answer is that the return point has to be recorded somewhere before the subroutine is called The address in memory to which the computer is supposed to return after
147. d xModels to use as an example in The Most Complex Machine a book that surveys the field of computer science The xModels applet is based on two similar programs that I wrote for Macintosh computers one for two dimensional and one for three dimensional graphics These programs are among several that I wrote for use with The Most Complex Machine All the Macintosh programs are available for downloading I am in the process of porting all the Macintosh programs to Java The xModels Applet The xModels applet is designed to be easy to use so the major thing you need to learn about is the scene description language which is discussed below The applet has two modes In its program mode it displays a text area where you can type and edit scene descriptions There is a row of control buttons along the bottom that can be used to render the scene to load a program from a file to save the current program in a file and to clear out all the text from the text area The applet is in this mode when it first starts up You can only switch to graphics mode by rendering a legal program If you click the Render button the computer will examine the program contained in the text area to see whether it is a legal scene description If the computer finds an error it will report it in a box at the top of the text area You can make this box go away by clicking on it if you like If there are no errors the applet will switch to graphics mode and the scene w
148. d your circuit Exercise 6 One of the examples in this lab was a circuit called Two or More which checks whether at least two of its inputs are on Consider the problem of finding a similar circuit with four inputs The output should be on if any two or more of the inputs are on A circuit that does this can be described by the Boolean expression A and B or C or D or B and C or D or C and D Use this expression to construct a Two or More circuit with four inputs Try to understand where this expression comes from Why does it make sense Hint Think of two cases one case where the input A is ON and the other case where the input A is OFF Write a paragraph explaining this The form of this expression can be extended to handle circuits with any number of inputs Write down a logical expression that describes a circuit with five inputs that turns on its output whenever two or more of the inputs are on Exercise 7 The structure of the 4 Bit Adder circuit reflects the structure of the compution it is designed to perform In what sense is this true What does it mean How does this relate to problem solving in general Exercise 8 Write a short essay of several paragraphs that explains how subcircuits are used in the construction of complex circuits and why the ability to make and use subcircuits in this way is so important Exercise 9 Build a Select circuit as shown in this illustration 4 B C select Output shoul
149. d zrotate instead of yrotate Next try the following example which illustrates a translation in the z direction followed by a rotation http math hws edu TMCM java labs xModelsLab2 html 3 of 7 3 26 2000 12 50 26 PM xModels Lab 2 animate 60 square scale 5 ztranslate 8 yrotate 0 360 The ztranslate command moves the square 8 units forward towards you The yrotate command then sends it circling away from you and back Try using xtranslate instead of ztranslate Try xrotate and zrotate in place of yrotate Make sure that you understand what you are seeing Of course a lot of the power of xModels comes from its ability to construct complex hierarchical models using the define command You can use define to define three dimensional objects just as you used it in two dimensions You ll work with some defined objects in the exercises at the end of the lab The example program NestedSquares3D uses several levels of object definitions to create what might be the ultimate nested squares example Each square rotates on its own but it also takes part in the rotation of all the squares in which it is nested I find the result visually interesting kind of like a mobile Lathing and Extrusion Modeling real objects like cars or faces in 3D requires that they be approximated with large numbers of polygons perhaps hundreds of polygons in one object You won t want to do anything so complicated with xModels But xModels does have two wa
150. diately after loading a file will restore the previous data Above the applet you ll also find a text input box labeled Title This is name of the circuit currently visible on the circuit board You can change the name by editing the contents of this text input box At the left of the strip of controls below the applet is a Speed pop up menu This menu affects the speed at which signals propagate through the circuit You might want to use the slower speeds to watch what is happening in more detail At the Fast speed it is possible in some browsers that the circuit will not be drawn correctly For example the Clock sample circuit should blink very quickly when the speed is set to Fast but your browser might not http math hws edu TMCM java xLogicCircuits index html 3 of 4 3 26 2000 12 50 27 PM xLogicCircuits Intro allow applets to draw to the screen quickly enough to show this Another interface note You should be able to insert a tack into the middle of an existing wire by double clicking on the wire If you double click and hold the mouse down on the second click you can drag the tack to a different position Again I note that some browsers might not support double clicks And one more It is not possible to draw a wire directly from an output of a gate or circuit to an input of the same gate or subcircuit However there is nothing to stop you from making loops out of several components as is done in two of the sample ci
151. ds 1 to the number in Loc and jumps back to the start of the loop The value stored in Loc is now the address of the second number in the list 72 So now when LOD I Loc is executed it loads 72 into the accumulator The next time through the loop it will load 902 then 164 and so on So each time through the loop a different location is processed even though the instructions in the loop don t change Loc is said to be a pointer since the value stored in Loc is not really the number we are interested in Instead the value in Loc indicates where to go to find the number we want It points to that value Pointers and indirect addressing are used in various ways even in high level languages In the next lab you ll see how useful indirect addressing can be in a jump instruction Dancing Bits There is another sample program that I ve provided mostly for your amusement but also because watching it run might just give you a better appreciation of what a computer is really doing as it computes Select the sample program PowersOfThree txt from the pop up menu in the xComputer Window Read the comments at the beginning of the file and then load the program into xComputer s memory by clicking on the Translate button Set the display style to Graphics and the run speed to Fastest and run the program You will see the bits in xComputer s memory dance as a non trivial computation is performed Exercises Exercise 1 The sample program Si
152. du WWW http math hws edu eck Department of Mathematics and Computer Science Hobart and William Smith Colleges http math hws edu TMCM java tmcm java apps README txt 3 of 3 3 26 2000 12 50 02 PM Apps Labs Tutorials a http math hws edu TMCM java tmcm java source README txt textbook The README file for the tmcm java source archive This archive con The applets were written for use with a Machine by David Eck concepts of comput applets and for a er science set of lab worksheets information ab that use the a For more March 2000 tains the source code for a set of Java applets Most Complex They are meant to help teach some basic out the pplets see http math hws edu TMCM java xxx NOTE This source code was not originally written with the intent of making it public There are very few comments in the code Some parts of the code are a bit strange because they were translated from Pascal programs So take the code for what it s worth H he source code All the classes tmcm and to its sub pac in the to subdirectories T deprecated methods whose later he applets were written in Java 1 0 use is When the source code is warning messages about deprecat The sub packages corr so they use many discouraged in Java 1 compiled you might ge d methods There will be MANY warning messages
153. e By typical here I really mean Algol like or Pascal like for those of you who know what that means These features include variables assignment statements loops if statements recursive subroutines and even some multitasking However xTurtle does not include objects or data structures of any type The xTurtle applet is based on a similar program that I wrote for Macintosh computers That program was one of several that I wrote for use with The Most Complex Machine All the Macintosh programs are available for downloading I am in the process of porting all the Macintosh programs to Java The xTurtle Applet This section is a meant as a brief user manual for the xTurtle applet The next section is a description of the programming language When the xTurtle applet first starts it displays a large white graphics area with a black triangular turtle in the center This turtle can move around in the graphics area Usually it draws a line as it moves The turtle can respond to a number of commands such as forward 5 which tells the turtle to move forward 5 units and turn 45 which tells the turtle to rotate counterclockwise through an angle of 45 degrees The turtle draws red lines unless you tell it to use a different color The position of the turtle is given by a pair of coordinates x y Values of x and y between 10 and 10 are guaranteed to be visible in the graphics area Since the graphics area is not exactly square
154. e MultiplyByAdding txt gt lt param name URL2 value ThreeNPlusOne txt gt lt param name URL3 value ListSum txt gt lt applet gt The preceding tags assume that the zip files and sample input files are in the same directory with the HTML source file of the Web page It s possible to put them in other directories If the zip file is not in the directory with the HTML file then you must specify a codebase in the applet tag The codebase in an lt applet gt tag is the directory that contains the compiled Java code for the applet It is specified relative to the directory that contains the Web page For example lt p align center gt lt applet codebase classes archive xLogicCircuits zip code tmem xLogicCircuitsLauncher class width 180 height 30 gt lt param name LOAD value SampleCircuit txt gt lt applet gt lt p gt Here the codebase directory is found by going up to the directory that contains the Web page specified as and then looking in that directory for a directory named classes I ve found that the at the end of the directory name is necessary at least for some browsers It s a good idea to have just one copy of a zip file even if you are going to use the applet on several Web pages Then if the user visits several of those pages the Web browser will only have to download one zip file That s why I put all the zip files in on
155. e classes directory on my own site You can also have sample input files in a different directory from the Web page Just include the directory name in the name of the input file For example samples SampleCircuits txt or models FirstModel txt The name should be given relative to the directory that contains the Web page David Eck Department of Mathematics and Computer Science Hobart and William Smith Colleges Geneva NY 14456 USA Email eck hws edu WWW http math hws edu eck http math hws edu TMCM java tmcm java web site README txt 3 of 3 3 26 2000 12 50 02 PM http math hws edu TMCM java tmcm java apps README txt README file for the tmcm java apps archive March 2000 This archive contains Java applets and sample input files for the applets The applets are meant to help teach some of the basic concepts of computer science They were written for use with my textbook The Most Complex Machine but they can also be used independently of the book For more information see http math hws edu TMCM java If you want to understand the applets you will have to look at the material at this address The material in this archive can be freely redistributed and used for non commercial purposes Several Java applications are included here that will let you run the applets without a Web browser One big advantage of doing this is that
156. e is turned on and the value in the PC register is copied into the ADDR register The PC register tells which memory location holds the next instruction that location number must be copied into the ADDR register so that the computer can read that instruction from memory e Second click COUNT becomes 2 The Load IR from Memory control wire is turned on and an instruction is copied from memory into the IR The ADDR register determines which instruction is read In this case the instruction is Lod c 17 e Third click COUNT becomes 3 The Increment PC control wire is turned on and the value in the PC register is incremented by 1 Ordinarily this prepares the PC for the next fetch and execute cycle This completes the fetch portion of the fetch and execute cycle The remaining steps in the cycle depend on the particular instruction that is begin executed in this case lod c 17 e Fourth click COUNT becomes 4 The Load AC from IR control wire is turned on The data part of the instruction in the IR register is copied into the accumulator In this case the value is 17 This is the only step necessary to execute the lod c 17 instruction e Fifth click COUNT becomes 5 but only briefly The Set COUNT to Zero control wire is turned on and immediately the value of COUNT is reset to 0 One fetch and execute cycle is over On the next click COUNT would become 1 again and the next cycle would begin As you click on the Step button in
157. e very top of the applet will have the same effect e The Show Program button will take you back to the scene description that produced the image or animation displayed on the graphics screen e The next four buttons are used to control animations If the scene description specifies a single image all four buttons are disabled The Go and Pause buttons can be used to start and stop an animation If an animation has been paused then the Next Frame and Previous Frame buttons can be used to move though the frames in the animation one frame at a time Next there is a pop up menu to control the speed at which animations are played back The default is 10 frames second which should be OK for most purposes This menu represents only a request for a given frame rate The computer might not be able to display frames as quickly as you request e Finally there is a pop up menu that determines what happens when the computer http math hws edu TMCM java labs xModelsLab1 html 2 of 10 3 26 2000 12 50 25 PM xModels Lab 1 reaches the end of an animation In the default setting Loop the computer will return to the beginning of the animation and replay and will keep doing this until you stop it For many animations the first frame is the same as the last and the Loop option produces what looks like continuous motion The second option in the menu is Back and Forth which makes the computer reverse direction at the end of the
158. e are a few other things that can occur in programs This program contains examples of the basic objects and some of the transformations that can be used in a program It also shows how to use color A semicolon like the one at the left is the beginning of a comment which is ignored by the computer A comment ends at the end of the line square A square is one type of basic object Putting its name in the scene description adds a square to the image A basic square i t s a rather small square at the center of he image square scale 3 This is ANOTHER square in the same image The transformation scale 3 placed fter an object causes that object to be agnified by a factor of 3 Every point in he object is moved away from the origin to hree times its original distance Since he basic square was centered at the origin a scaled square is also centered at the Origin 30 BP at coca red The command red tells the computer to draw the following objects up to the next color change in red Other color commands include green blue cyan magenta yellow black white and gray It is also possible to specify RGB colors and HSB colors See the full documentation for details circle translate 6 6 A circle is a small circle at the center of the screen but the translate transformation is used here to move it over 6
159. e how each algorithm works and you will also see that some sorting algorithms are much more efficient than others Sorting and the analysis of algorithms are discussed as one example in Section 9 3 of The Most Complex Machine Some of the material from that section is repeated in this lab However some background material and motivation is not repeated here and it would be worthwhile for you to read Section 9 3 before doing the lab This lab includes the following sections e Watching Bubble Sort Other Sorting Algorithms Using the Timed Sort Mode N2 and N log N Exercises You ll be using an applet called xSortLab Start by clicking this button to launch the applet in its own window Sorry your browser doesn t do Java For a full list of labs and applets see the index page http math hws edu TMCM java labs xSortLabLab html 1 of 11 3 26 2000 12 50 21 PM xSortLab Lab Watching Bubble Sort The xSortLab applet has two operating modes Visual Sort and Timed Sort There is a pop up menu at the very top of the applet that can be used to select one of these modes The pop up menu also contains an entry for a Log which records statistics about sorts that have been performed by the applet When the applet first starts up it is in Visual Sort mode and you will use this mode for the first part of the lab In this mode you can watch as the applet sorts sixteen bars into order of increasing height Later in the lab you
160. e in AC into location Y JMP X Jump to location X that is store X into the PC so that the next instruction will be loaded from X e JMP I X Let Y be the contents of memory location X and jump to location Y e JMZ X If the value in the AC is zero then jump to location X e JMZ I X If the value in the AC is zero then let Y be the contents of memory location X and jump to location Y e JMN X If the value in the AC is negative then jump to location X e JMN I X If the value in the AC is negative then let Y be the contents of memory location X and jump to location Y e JMF X If the value in the FLAG register is one then jump to location X e JMF I X If the value in the FLAG register is one then let Y be the contents of memory location X and jump to location Y HLT Halt That is stop the xComputer by turning on the Stop Clock control wire David Eck eck hws edu June 1997 minor editing May 1998 http math hws edu TMCM java xComputer info html 8 of 8 3 26 2000 12 50 30 PM The xTuringMachine Applet The xTuringMachine Applet TURING MACHINES are very simple computational devices A Turing machine has an infinitely long tape divided into cells Each cell can be blank or can contain a symbol chosen from some fixed finite list The Turing machine moves along the tape reading and writing symbols It has an internal state which can be either the halt state or an integer between zero and
161. e info html 12 of 13 3 26 2000 12 50 17 PM xTurtle Info ELSE more statements END GRAB In this case if the GRAB fails the computer does not wait Instead it executes the ELSE part of the grab statement The ELSE part can include fork exit and return statement David Eck eck hws edu June 1997 http math hws edu TMCM java xTurtle info html 13 of 13 3 26 2000 12 50 18 PM xTurtle Lab 2 Labs for The Most Complex Machine xTurtle Lab 2 Thinking about Programs THIS LAB CONTINUES THE STUDY of programming which was begun in the previous lab The emphasis here is on how a complex program can be developed to perform a specified task An organized approach to programming is necessary for all but the most simple programs Complex tasks can be broken down into simpler tasks and complex programs can be built up out of simple components The problem is how to determine what components are needed and how to piece them together Before beginning this lab it would be useful to be familiar with the material in Chapter 6 of The Most Complex Machine especially Section 6 3 In particular this lab uses the ideas of preconditions and postconditions This lab also uses the nested squares example from Section 6 3 You ll also find an introduction to subroutines in this lab Subroutines are covered in Chapter 7 of the text This lab includes the following sections e Preconditions e Postconditions e Subroutines e Exercise
162. e letters So you can write PenUp penUp penup or even PeNUp and they will all mean the same to the computer A program consists of a sequence of one or more of the following statements variable declarations subroutine declarations function declarations Subroutine and function declarations cannot be nested inside one another To provide for mutual recursion among subroutines and functions they can be predeclared This will be covered below The program is executed from beginning to end Declarations are much like statements in that you can think of them as being executed That is you can t use a variable subroutine or function until it has been declared Identifiers and Reserved Words Certain words are reserved for special purposes in the xTurtle language Reserved words cannot be used as names for variables subroutines and functions Note that since upper and lower case are equivalent reserving the word declare also reserved DECLARE Declare and so on Reserved words in xTurtle include Built in subroutine names listed below e Built in function names listed below Predefined read only variables listed below Logical operators and or and not Reserved words for declarations declare import end endfunction endsub function predeclare ref and sub e Reserved words for control statements else end endif endgrab endloop exit exitif exitunless grab if or orif loop return then and unless
163. e of the object and then by the specification of the object itself The object is generally a complex object enclosed between and but that is not a requirement Defining an object does not make the object appear in the scene To do that you have to include the object name as part of the scene description The following example defines a wheel to consist of a circle and three lines define wheel circle line line rotate 60 line rotate 60 A color can be specified by one of the following color names red green blue cyan magenta yellow black white gray lightGray or darkGray Color can also be specified by the rgb command or the hsb command The rgb command lets you specify a color by giving its red blue and green components It requires three parameters to specify the three values The values must be between 0 and 1 inclusive For example rgo 1 0 5 0 5 specifies a pinkish color http math hws edu TMCM java xModels info html 4 of 9 3 26 2000 12 50 33 PM xModels Info rgb 0 1 0 0 specifies a range of colors from black to red The hsb command is similar except it specifies a color by giving its hue brightness and saturation components Again these values must be between 0 and 1 You can look this up in a graphics textbook if you don t know what it means When a color command is given it sets the drawing color to be used for all subsequent objects up until the next color change Color changes
164. e that would greatly limit the generality of the subroutine Instead the number of steps would probably be provided as a parameter From the point of view of the subroutine the parameter is like input coming from somewhere outside just as input from the user comes from outside the program A subroutine definition begins with the word SUB and ends with the word END SUB Just after the word SUB comes the name of the subroutine and optionally a list of one or more parameter names The subroutine name and the parameters form the interface of the subroutine everything from there up until the END SUB is the implementation The sample program SpiralsSubroutine defines a subroutine named spiral Select this program from the pop up menu at the top of the xTurtle applet and read the program and comments When you click the Run Program button to run this program it will look like http math hws edu TMCM java labs xTurtleLab2 html 3 of 7 3 26 2000 12 50 19 PM xTurtle Lab 2 nothing has happened But in fact the effect of the program is to define the subroutine Ordinarily the computer has no idea what the word spiral means but once the computer compiles the subroutine definition it will then understand commands like spiral 61 and spiral 89 Such commands can be added to the program after the subroutine definition or they can be entered into the text input box below the drawing area in the xTurtle applet Try it Some of the pictur
165. e whole process is driven by a clock Each time the clock ticks one step of a fetch and execute cycle is performed That s a very brief description of the fundamental operation of a computer With some extensions it is true of all existing computers The xComputer applet simulates this fundamental operation for a computer with a 1024 location RAM and eight registers Like any computer the xComputer has a certain set of machine language instructions that it understands Machine language instructions are actually binary numbers and are not really meant to be read or written by humans Programs for the xComputer are therefore usually written in assembly language An assembly language program must be translated into machine language before it can be executed by a computer The assembly language for xComputer has 31 different instructions which are listed below The xComputer and its assembly language are discussed in detail in Chapter 3 of The Most Complex Machine This page does not cover all the details but it should have enough information to enable you to use the applet and even to write some assembly language programs The xComputer Applet The point of the xComputer Applet is to illustrate the step by step operation of a computer as it executes a program When the applet starts up it displays three sections A Control area a set of Registers and a Memory The Memory is a scrolling list occupying the right hand third of the applet It
166. earn how the xComputer works by giving it a short program and watching it execute that program A program is a sequence of assembly language instructions You have to enter the instructions into the xComputer s memory But first make sure that the addr input box in the Control area of the applet contains a zero The number in this box specifies the address in memory where the instruction that you type will be stored Then type the following instructions into the data input box Press return after each instruction or equivalently click the Data to Memory button Lod ca 17 add c 105 sto 10 hilt When you press return an instruction is translated into a machine language instruction and is stored in the xComputer s memory You ll actually see a number in the memory rather than the assembly language instruction that you typed For example the instruction lod c 17 is represented by the number 25617 Note that when you press return the number in the addr input box is automatically incremented by one to get ready for storing the next instruction that you type in the next memory location The first instruction of this program lod c 17 tells the xComputer to load the constant 17 into the accumulator The second instruction add c 105 tells the computer to add the constant 105 to whatever number is in the accumulator and to put the result back into the accumulator The sto 10 makes the computer copy the contents of the accumulator into
167. eceded by the reserved word ref which indicates that the parameter is to be passed by reference This is discussed below The word sub the subroutine name and the parameter list make up the subroutine header Following the header come the statements that make up the subroutine Finally end sub is used to mark the end of the subroutine Here are two sample subroutines SUB polygon N side DECLARE count count 0 LOOP forward side turn 360 N count lt count 1 EXIT IF count N END LOOP END SUB SUB UpdateAmount ref amount IMPORT InterestRate DECLARE interest interest InterestRate amount amount amount interest END SUB When a subroutine is called one parameter value must be provided for each parameter listed in the subroutine definition The parameter values in the subroutine call statement are called actual parameters Parameters can be passed by value or by reference as indicated by the absence or presence of the reserved word ref in the subroutine definition When a parameter is passed by reference the subroutine can change the value of an actual parameter that is provided to it when the subroutine is called The actual parameter for a ref parameter must be http math hws edu TMCM java xTurtle info html 10 of 13 3 26 2000 12 50 17 PM xTurtle Info a name it cannot be a constant or a complex expression This is illustrated by the UpdateAmount example given above It is possible to exit
168. ecuted The xTurtle language has built in subroutines like PenUp and moveTo x y It is possible to define new subroutines in a program A subroutine has a name and optionally a list of parameters Once a subroutine has been defined it can be called by giving its name and if it has a parameter list a list of values to be used for its parameters A subroutine consists of a list of statements and variable declarations When the subroutine is called all the statements within the subroutine are executed Variables declared within a subroutine are called local variables for that subroutine They are not visible from outside the subroutine and are deleted from memory when the subroutine ends Variables that are not defined within a subroutine are called global variables A subroutine does not have automatic access to global variables However it is possible to give a subroutine access to global variables by explicitly importing them into the subroutine This is done with an IMPORT statement which consists of the reserved word import followed by the names of one or more previously declared global variables separated by commas IMPORT statements can only occur inside subroutine and function definitions A subroutine definition starts with the word sub followed by the subroutine name followed optionally by a list of parameters The parameter list is just a list of parameter names separated by commas A parameter name can be optionally pr
169. ed by a given company organization or institution For example you might guess that the home page of the United States Senate is http www senate gov or that the Coca Cola corporation has a home page at http www cocacola com When you use a URL that omits the directory and file name you will usually get the home page or index page from the specified computer http math hws edu TMCM java labs DataRepsLab html 3 of 9 3 26 2000 12 50 04 PM Introductory Lab Searching the Web Because there is so much information on the Web finding what you want can be a problem There are several utilities that can help you to find things on the Web First of all there are hierarchical indices that list Web sites according to category One of the largest of these indices is Yahoo Another way to find things on the Web is to use a search engine A search engine consists of an index of millions of Web pages and a program for searching the index The index is made by a program that constantly downloads Web pages and adds their contents to the index No index can include all the data on the Web because the Web grows so quickly Also some of the data in an index will be out of date because people change or delete their Web pages To use an index all you have to do is type some words into a box and click on a button You can do more advanced searches but most search engines allow you to do simple searches in this way You ll get back a list o
170. ell the browser how to display the text and what else to put on the page besides text For example text can be displayed in bold face by enclosing it between the tags lt b gt and lt b gt If you want the words This is important to appear in bold face on the page like this This is important then you would put lt b gt This is important lt b gt into your HTML document Similarly a link to David Eck s home page which has a URL of http math hws edu eck could appear in an HTML document as http math hws edu TMCM java labs WebPublishingLab html 1 of 7 3 26 2000 12 50 13 PM Web Publishing with Netscape Composer lt a href http math hws edu eck gt Eck s Home Page lt a gt and this would appear in a Web browser as the link Eck s Home Page You can see the HTML source code for any Web page Most Web browsers have a command that will display the HTML source of the page that you are currently viewing In Netscape you can use the Page Source command under the View menu Try this command now to see the source for this page HTML started out a few years ago as a relatively simple and easy to use language As time has gone by and as newer versions of HTML have been introduced it has become much more cluttered and complicated This has made it possible to produce fancier Web pages but it has made it more difficult for ordinary people to produce state of the art pages just by typing in a few HTML commands Fortunately howev
171. embly language programming for the xComputer including labels and indirect addressing xComputer Lab 3 Subroutines Introduces the idea of a subroutine and shows how subroutines can be implemented by hand in the assembly language of xComputer even though that language does not offer direct support for subroutines xTuringMachine Lab Introduction to Turing Machines This lab is meant to illustrate the basic operation of Turing machines and to show that even the extremely simple operations performed by Turing machines are sufficient for performing complex computations Publishing on the Web This lab will cover some of the basics of Web publishing concentrating on the Composer utility in Netscape Communicator This lab is not closely related to The Most Complex Machine and it does not use any applets However it does sort of fit in with the theme of real computers and their impact on society which is covered in Chapter 5 of the text This lab is somewhat specific to Hobart and William Smith Colleges xTurtle Lab 1 Introduction to Programming Covers the basics of the xTurtle programming language including loops if statements variables and built in turtle graphics commands xTurtle Lab 2 Thinking about Programs Investigates how preconditions and postconditions can be used to help develop working programs that perform complex tasks Also introduces the idea of subroutines xTurtle Lab 3 Subroutines and Recursion Con
172. emory is accessible at any given time The ADDR register specifies that location So for example if the CPU needs to read the value in location 375 it must first store 375 into the ADDR register If you turn on the Autoscroll checkbox beneath the memory display then the memory will automatically be scrolled to the location indicated by the ADDR register every time the value in that register changes e The PC register is the program counter The CPU executes a program by fetching instructions one by one from memory and executing them This is called the fetch and execute cycle The PC specifies the location in memory that holds the next instruction to be executed e The IR is the instruction register When the CPU fetches a program instruction from main memory this is where it puts it The IR holds that instruction while it is being executed http math hws edu TMCM java labs xComputerLab1 html 2 of 10 3 26 2000 12 50 09 PM xComputer Lab 1 e The COUNT register counts off the steps in a fetch and execute cycle It takes the CPU several steps to fetch and execute an instruction When COUNT is 1 it does step 1 when COUNT is 2 it does step 2 and so forth The last step is always to reset COUNT to 0 to get ready to start the next fetch and execute cycle This is easier to understand after you see it in action Remember that as the COUNT register counts 0 1 2 just one machine language program is being executed You will l
173. en while the machine is running Click on the item you want to change then select a value from the palette The rule maker is somewhat more complicated The rule maker lets you set up one rule by editing any of the five values for that rule To set up the rule click on any of the values in the rule maker and edit it by selecting one of the values in the palette When the rule is complete click on the Make Rule button to add it to the rules table However if the In State and Reading items in the rule maker are the same as those for an existing rule the Make Rule button becomes a Replace button When you click it the rule in the rule maker will replace the rule in the table Everytime you make or replace a rule the rule maker is automatically updated to show the next consecutive rule since it is at least fairly likely that that is the rule you want to work on next You can use the mouse to drag the Turing machine into a new position on its tape or to drag the tape to a new position under the machine If you want to drag them both together use the right mouse button or hold down the Control key as you click Using the Keyboard You can use the keyboard to perform any editing task in the xTuringMachine applet Here s how Pressing the tab key will move the hilite among the three major areas the machine the rule maker and the rule table If there is no hilited item pressing the tab key might create a hilite in the rule maker i
174. epresented Hexadecimal It is difficult for humans to read long strings of zeros and ones Hexadecimal numbers are a kind of shorthand for writing such strings A hexadecimal number is written using the sixteen hexadecimal digits 0 1 2 3 4 5 6 7 8 9 A B C D E http math hws edu TMCM java DataReps index html 1 of 2 3 26 2000 12 50 26 PM Data Representations Applet and F Each hexadecimal digit stands for four bits So 0 represents 0000 1 represents 0001 2 represents 0010 E represents 1110 and F represents 1111 We could also say that in the base ten the hexadecimal digit A stands for the number 10 ten B stands for 11 eleven C stands for 12 D for 13 E for 14 and F for 15 A 32 bit binary number can be expressed as an 8 digit hexadecimal number Real Number Real numbers are numbers that can contain decimal points like 3 14159 or 234 5 or 12 0 They can also be written using scientific notation For example 2 15e12 is a way of writing 2 15 times 10 2 The representation used in computers for real numbers is very complicated And it allows some strange possibilities such as INF and INF which stand for infinity and minus infinity There are also NAN s NAN stands for not a number NAN s are used to represent the results of illegal operations such as taking a square root of a negative number Note that the integer 17 and the real number 17 have completely different representations in the computer
175. er it has become possible for people to produce Web pages without knowing any HTML at all Programs have been written that allow you to create Web pages in a WYSIWYG What You See Is What You Get environment These programs are very similar to word processing programs and in fact you will find that many word processors now include HTML authoring capabilities Netscape Communicator 4 0 includes an HTML authoring component called Composer With Composer you can create Web pages without ever seeing any HTML codes They will still be there in the background of course and you can use the View Page Source command to see them if you want Composer is not a complete tool for HTML authoring it does not give you access to many of HTML s advanced features However it is likely to be perfectly adequate for most people s needs and it is a good place for anyone to start Netscape Configuration You can use Composer to create a Web page and you can view that page on your own computer However in that case you ll be the only one in the world who can see it Suppose you want to publish your page so that it can be seen by any of the tens of millions of uses of the Web In that case you have to place your page on a Web server a computer that is connected to the Internet and that is running a program that lets it serve Web pages to other computers on the Net If your computer is permanently connected to the Internet you might be able to run your o
176. er of frames in an animation When the applet first starts up you should see a text area containing a scene description called Pinwheel It describes an animation showing a revolving colored pinwheel displayed on a black background Don t worry for now about the scene description itself Your first task is to learn how to get xModels to display the scene To see the scene represented by a scene description in xModels you have to render it by clicking the RENDER button below the text area When you click this button the applet first checks the scene description in the text area for errors Assuming that no errors are found the applet will switch to a Graphics panel where it will display the scene Try it now To the right of the displayed scene is a set of controls You should familiarize yourself with the controls Here is a brief description of each e A message at the top of the column of controls shows the number of the frame that is currently displayed An animation consists of a sequence of frames which are displayed one after another The Pinwheel animation has 121 frames which are numbered from 0 to 120 If you get tired of watching this message flash try clicking on it with your mouse This might make it stop depending on the version of Java that you are using e The New Program button will give you a blank text area where you can write your own scene description from scratch Choosing New from the pop up menu at th
177. er of the graphics display area The positive y axis extends upwards from this point and the positive x axis points to the right The z axis points directly out from the screen towards the viewer so that points in front of the screen have positive z values and points behind the screen have negative z values This http math hws edu TMCM java xModels info html 2 of 9 3 26 2000 12 50 33 PM xModels Info is a standard coordinate system for three dimensional computer graphics The graphics display area includes the square region with 10 lt x lt 10 and 10 lt y lt 10 Since the display area might not be square it can actually extend beyond this range in one direction There is no way to increase or decrease the basic square region that is displayed so scenes must be sized to fit into this region It is easy to scale objects up or down in size to fit The three dimensional world is projected onto the xy plane from a point on the positive z axis The z coordinate of this point is called the viewDistance and its value can be specified as part of a scene description This name is somewhat deceptive Since the display area always shows the same square region objects on the xy plane don t look smaller as the view Distance increases They just look more squashed in the z direction The viewDistance can be set to infinity to give what is called a parallel projection Fundamentally a scene description for xModels is a list of objects t
178. erators and or and not This association comes about when we think of ON as representing true and OFF as representing false In that case AND OR and NOT gates do the same computations as the operators and or and not Mathematical logic uses Boolean algebra in which the letters A B C and so on are used to represent logical values Letters are combined using the logical operators and or and not For example A and C or B and not C is an expression of Boolean algebra As soon as the letters in an expression are assigned values true or false the value of the entire expression can be computed Every expression of boolean algebra corresponds to a logic circuit The letters used in the expression are represented by the Inputs to the circuit Each wire in the circuit represents some part of the expression A gate takes the values from its input wires and combines them with the appropriate word and or or not to produce the label on its output wire The final output of the whole circuit represents the expression as a whole For example consider the sample circuit from the applet If the inputs are labeled A and B then the wires in the circuit can be labeled as follows http math hws edu TMCM java labs xLogicCircuitsLab1 html 3 of 10 3 26 2000 12 50 06 PM xLogicCircuits Lab 1 4 AMO NOT B OR B AND NOT Ad FA A AND NOT B B AND NOT A The circuit as a whole corresponds to the final output exp
179. erstand how scenes are constructed from objects transformations and colors Animation Let s face it static scenes are not all that exciting Animation makes things get a lot more interesting To make an animation in xModels you just have to do two things to your scene description put an animate command at the beginning and change some of the numbers in the scene description to number ranges Here is a simple example which can also be found in the sample scene description FirstAnimation http math hws edu TMCM java labs xModelsLab1 html 5 of 10 3 26 2000 12 50 25 PM xModels Lab 1 animate 30 circle scale 1 5 red polygon 4 3 4 3 5 5 4 blue square scale 7 15 1 rotate 0 60 The first line of this scene description is an animate command which specifies that 31 frames will be rendered There are 31 frames not 30 because the number in the animate command gives the length of the animation not the number of frames There are 30 intervals between frames so there are 31 frames The remaining lines are a standard scene description except that in some cases number ranges such as 1 5 or 0 60 appear instead of single numbers Where such a range appears the first value in the range is used in the first frame the second value is used in the last frame and intermediate values are used in intermediate frames If a range is used with translate the object moves during the animation if it is used with scale the objec
180. es of instructions stored in memory The computer fetches instructions one by one and executes them The program counter register or PC tells the computer which address to go to in memory for the next instruction When you want to run a program you should always first check that the value in the PC register is the address of the location that contains the first instruction of the program You can set the value in the PC to zero using the Set PC 0 button To set the PC to some other value type the value into the addr box and then click on the Addr To PC button This is important A common frustrating mistake when trying to run a program on xComputer is simply to forget to tell xComputer where in memory the program is located Note If you use the Translate button in programming mode to put a program into memory the PC will automatically be set to zero at the same time However after you run the program once you have to reset the PC manually if you want to run it again Once you have set the PC there are three different ways to run the program Click the Step button This performs one of the several small steps that make up each fetch and execute cycle You have to click on this between five and ten times depending on the instruction to execute each instruction http math hws edu TMCM java xComputer info html 3 of 8 3 26 2000 12 50 30 PM xComputer Info Click the Cycle button This is meant to perform one complete fe
181. es you can make are rather pretty Exercises Exercise 1 Consider each of the pictures b c d and e in the nested squares illustration shown above For each of these incorrect versions determine what small change in the program NestedSquares would produce that picture In each case it s a question of removing one or more statements from the correct program so that one or more of the required preconditions are not met In each case determine which statement to remove and what precondition or preconditions are unmet in the resulting program Exercise 2 Select the sample program Quadratic from the pop up menu at the top of the xTurtle applet When you run this program it will ask you to input three numbers A B and C It will then compute and display the solutions to the quadratic equation A x B x C 0 If you run the program and enter the values 1 1 and 1 for A B and C it will work fine However if you enter 1 1 and 1 as the values of A B and C the program will crash This crash can be traced to the fact that at a certain point in the program there is a precondition that might not be satisfied If it is not satisfied an error occurs and the program crashes What precondition is not properly checked by the program It has something to do with the square root function Recall that in some cases the quadratic equation has no solutions Modify the program so that it does not crash when the input values fail to meet t
182. esponsible for making sure that the required preconditions are met You should try to understand why each of these statements is required You will work with this example in Exercise at the end of the lab AT Gl Postconditions Preconditions are things that must be true at a given point in a program for that program to continue correctly A postcondition is something that is actually true at a given point in the program because of what has been done by the program so far A common way for programmers to think about programs is to ask At this point in the program do the postconditions from what comes before match up with the preconditions for what is done next In addition the effect of a program as a whole can be thought of as a set of one or more postcondition for the entire program The postconditions of a program are things that are true after the program has been executed That is they are things that are accomplished by the program For an xTurtle program the postconditions of the program include the picture that has been drawn on the screen The following picture shows a simple staircase with 5 steps and another staircase with 4 steps leaning at a 30 degree angle http math hws edu TMCM java labs xTurtleLab2 html 2 of 7 3 26 2000 12 50 19 PM xTurtle Lab 2 Suppose that you want a program to draw such staircases Let s say that the number of steps in the staircase will be input by the user You will have to use a loop
183. ess to a Koch curve by deciding randomly whether to detour to the left using turns of 60 120 and 60 or to the right using turns of 60 120 and 60 instead Make this change to the program KochCurves sample program and try it out In the subroutine you can declare a variable named x for example and set x RandomInt 2 Use the value of x to decide whether to detour to the left or to the right When you have made the change the SnowFlake subroutine will produce a Koch Island instead Try it Exercise 9 The idea of detouring used in making Koch curves can be used to make other interesting fractal pictures In a Koch curve the idea is to replace a straight line with a line containing a triangular detour like this Suppose that a square detour were used instead looking like this http math hws edu TMCM java labs xTurtleLab3 html 5 of 6 3 26 2000 12 50 20 PM xTurtle Lab 3 What would the resulting picture look like for higher degrees of complexity Find out by rewriting the subroutine Koch to use square detours instead of triangular detours Exercise 10 For this exercise you will write a recursive subroutine that displays an element of randomness The subroutine will be called mountain because it draws pictures that look a bit like a mountain range Here are two pictures produced by the subroutine Onl Each of these pictures was produced with the commands clear penUp moveTo 7 0 penDown mountain 7 0 1
184. et allows you to view the contents of memory in several different forms Select the view that you want from the pop up menu above the memory display The Instructions Integers Unsigned Ints Binary and ASCII display styles correspond to some of the data types listed above In the ASCII display style two characters are shown in each memory location Non printing characters are shown as ASCII code numbers enclosed between lt and gt For example lt 17 gt represents the character with ASCII code number 17 The Graphics display shows all of memory at once as a rectangle full of black and white dots Each dot represents one bit in memory A black dot represents a one and a white dot represents a zero The rectangle is 64 bits wide with each row of dots representing four memory locations of 16 bits each The Control Wires display style actually doesn t have anything to do with memory at all I ll discuss it below For example here is a short assembly language program that adds the numbers 105 and 17 stores the answer into memory location 10 and then halts lod c 105 add c 17 sto 10 hlt You could enter this program directly into memory by typing the lines one at a time into the data box Note that what you see in memory depends on the setting of the memory display style You might want to try entering this program and use it as an example as you read the next section Running a Program A program consists of a seri
185. ething like this after the program has run for a while Exercise 2 In the sample program Bugs ten bugs wander around on the screen Real bugs though are born and die Add birth and death to the Bugs program Add birth by programming a one in twenty five chance that a bug will split in two each time it moves You can program a one in twenty five chance by checking whether RandomInt 25 is 1 Similarly there should be a 1 in 25 chance that the bug will die To program death you will need to know about another built in xTurtle command KillProcess When a process executes the command KillProcess it dies The turtle for that process disappears from the screen Note that this command differs from Halt If any process executes a Halt command the entire program halts and so all the turtles die Exercise 3 The sample program TwoGraphs txt draws the graphs of two functions one after the other Instead of a single turtle that draws the graphs one after the other the program could use two turtles that draw the graphs at the same time Modify the program so that it does this You only need to do a bit of work on the half dozen or so lines at the very http math hws edu TMCM java labs xTurtleLab4 html 5 of 7 3 26 2000 12 50 23 PM xTurtleLab 4 bottom of the program Exercise 4 Write a program that uses two fork 9 statements to draw a multiplication table like this one on the screen 1 2 3 4 5 6 7 8 9 2 4 6 8 10 12 14 1
186. ey should not be used as a formal part of a course unless The Most Complex Machine is also adopted for use in that course David Eck eck hws edu Summer 1997 http math hws edu TMCM java labs xTurtleLab3 html 6 of 6 3 26 2000 12 50 20 PM xSortLab Lab Labs for The Most Complex Machine xSortLab Lab Sorting and the Analysis of Algorithms ONE OF THE MOST COMMON OPERATIONS performed by computers is that of sorting a list of items An example of this would be sorting a list of names into alphabetical order This lab deals with two natural questions How can sorting be done And how can it be done efficiently The second question is one that would be asked in a field of study called the analysis of algorithms Recall that an algorithm is an unambiguous step by step procedure for solving a problem which is guaranteed to terminate after a finite number of steps For a given problem there are generally many different algorithms for solving it Some algorithms are more efficient than others in that less time or memory is required to execute them The analysis of algorithms studies time and memory requirements of algorithms and the way those requirements depend on the number of items being processed In this lab you ll look at the time requirements of various sorting algorithms In the lab you will see five remarkably different algorithms for sorting a list Each algorithm solves the sorting problem in a different way You will se
187. f 4 3 26 2000 12 50 27 PM xLogicCircuits Intro destination This makes sense because when the circuit is running a destination takes its value from the single wire that leads to it On the other hand the value of a source can be sent to any number of wires that lead from it When you are drawing wires you ll notice some helpful visual clues Sources generally have a purple sort of color Destinations are green A Tack which can be both a source and a destination is green until a line has been drawn to that Tack then the Tack turns purple When you are drawing a wire and you move the mouse over a legal destination the component will be hilited A hilited gate is draw in blue a hilited Output is enclosed in a blue rectangle and a hilited Tack is enclosed in a blue circle Note that some components such as gates have multiple inputs When you move the mouse over a component with several available inputs the wire will jump to the nearest one Make sure that you get the wire attached to the one you want The gates in the pallette can be rotated into four different orientations Just click on the little red curved arrow on the left above the gate Once a gate has been dragged onto the circuit board it can t be rotated However it can be resized When the gate is hilited a box appears around it with small drag handles in each corner Drag one of these handles to change the size of a gate To hilite a gate or any component or wire j
188. f Web pages that contain the words you entered Here for example is a simple interface to the Alta Vista search engine To try it click in the input box type some words and the click the Submit button Search and Display the Results T e L There are many search engines including Alta Vista WebCrawler Lycos Excite and Infoseek You will have to use at least one of these search engines in order to do some of the exercises at the end of the lab To get the most out of a search engine you should read its help or instructions page Java and Applets The example of the search engines shows that a Web page can be more than just a passive collection of links A Web page can also be interactive The Alta Vista search engine uses a type of interaction known as a form or fill in form You enter some data in the form and click on a submit button Your Web browser sends your data to another computer which responds to your data by sending a new page for your Web browser to display Web pages can also provide other types of interactivity without involving a second computer One of the new technologies on the Web is Java a programming language that can be used to write applets which are small programs that run on a Web page Many Java applets are more decorative than useful like this Moir applet Sorry your browser doesn t do Java A Moir pattern is formed by the interference between two similar patterns In this http m
189. f not you have to use the mouse Within one these three major areas the up down left and right arrow keys can be used to move the hilite from one item to another When the hilite is in the tape or in the rule table the home and end keys can also be used Play around to see how they work You can always type one of the values displayed in the palette instead of clicking on it Note that a blank can be entered either by pressing the space bar or by typing a The default symbol other in the Reading column or same in the Write column is entered by typing a When working in the rule maker hitting the return key is the same as clicking on the Make Rule or Replace button http math hws edu TMCM java xTuringMachine index html 3 of 4 3 26 2000 12 50 31 PM The xTuringMachine Applet The Sample Machines The applet on this page is set up to load four sample Turing machines Here are brief descriptions e CopyXYZ txt This machine expects to be started on the left end of a sequence of symbols containing only x s y s and z s It will make a copy of its input and will halt on the left end of the copy e GatherDollars txt This machine should be started on the left end of a string of symbols Any of the symbols 0 1 x y and z are OK The machine will move all the s to the left end of the string of symbols leaving all the other symbols in the original order It halts on the left end of the string e Coun
190. files Your browser might not permit you to use them The table of rules is in the lower right section of the applet Each rule tells the machine what to do if it is in a certain state and if it reads a certain symbol The Move column tells the machine which direction to move L for left and R for right You can edit the Write Move and New State columns The columns labeled Reading and Write can contain the symbols 0 1 x y and z They can also contain the character which is used to represent a blank cell The Reading column might also contain other which represents a default value that means any other symbol for which no explicit rule is given If the Reading column contains other then the Write column can contain same which tells the machine to write the same character that it read Just above the rule table is a rule maker with a Make Rule button that can be used to add new rules to the table The blue rectangle between the machine and the rule maker is a palette that is used in making and editing rules changing the contents of the tape and changing the current state of the machine This is explained in the next two sections When the machine is running at Moderate speed or slower after each step the applet displays the next applicable rule in the rule maker box so you can see why the machine takes the action it does If there is no applicable rule in a give situation the machine will st
191. fined object can be used inside the definition of another object define wagon red square scale 4 2 blue wheel scale 2 rotate 0 720 translate 2 1 wheel scale 2 rotate 0 720 translate 2 wagon ytranslate 8 A wagon across the bottom of xtranslate 10 10 the screen http math hws edu TMCM java xModels samples Tutorial4_ ComplexObjects txt 2 of 2 3 26 2000 12 50 38 PM http math hws edu TMCM java xModels samples Tutorial5_PolygonsEtc txt xModels Tutorial 6 Polygons Lathing and Extrusion Models has a polygon for creating polygon objects he polygon command takes a list of x y points and onnects them with line segments An example is given below odeling real objects like cars or faces in 3D requires that they be approximated with large numbers of polygons perhaps thousands of polygons per object You won t want to do anything so complicated with xModels 3D But it does have two ways of producing fairly complicated but also fairly regular objects The methods are called lathing and extrusion The idea is to take a figure consisting of a connected sequence of line segments in the xy plane Some specified number of copies of this figure are made and then more line segments are added to join the copies lt SaQH x animate 30 In lathing the copies are made by rotating the original figure about the y axis The comm
192. g e mail USENET news groups and the World Wide Web This section of the lab is a brief introduction to the Web The World Wide Web also known as the WWW or simply as the Web consists of pages of information stored on computers all around the world These pages are available to anyone with a connection to the Internet They viewed with a Web browser such as Netscape or Internet Explorer A page can contain text pictures sounds three D graphics movies applets and even interactive features such as fill in forms Most important a page can contain links to other pages When you click on a link the Web browser will fetch the page that it refers to and display it to you So it s pretty easy to use the Web just point your http math hws edu TMCM java labs DataRepsLab html 1 of 9 3 26 2000 12 50 04 PM Introductory Lab mouse at a link and click Here for example are some links to pages you might want to Visit ABC News Cable Network News and the New York Times The Whitehouse the Senate and the House of Representatives The Nation Magazine for some left wing political opinion Discover Nature and Scientific American science magazines Sports Illustrated and ESPN The Web Museum featuring great art Views of the Solar System List of Colleges and Universities amazon com a place to buy books Map Blast a free map drawing utility Blue Mountain Arts where you can send free virtual greeting cards Dilbert comic
193. g of 90 when it is facing upwards towards the top of the screen and a heading of 90 when it is facing downwards Its position is given by two numbers an xcoord or horizontal coordinate and a ycoord or vertical coordinate http math hws edu TMCM java labs xTurtleLab1 html 1 of 10 3 26 2000 12 50 15 PM xTurtle Lab 1 The drawing area of the applet includes a twenty by twenty square in which the turtle can move and draw This square has horizontal coordinates from 10 on the left to 10 on the right and it has vertical coordinates from 10 at the bottom to 10 at the top Because the drawing area is unlikely to be exactly square the coordinates for the entire drawing area probably extend beyond the range 10 to 10 in either the horizontal or vertical direction The turtle starts out in the center of the screen at the point 0 0 facing to the right It can obey commands such as forward 5 which tells it to move forward five units and turn 120 which tells it to rotate in place through an angle of 120 degrees It turns counterclockwise if the number of degrees in positive and clockwise if the number of degrees is negative The number in parentheses is called a parameter for the command you can substitute any number you want The parameter in a forward command tells the turtle how far to move forward while the parameter in the turn command tells it how many degrees to turn The turtle can draw a line as it moves You can
194. g this lab Chapter 3 is rather technical and you might find that you need to work through both this lab and that chapter before you really understand either of them This lab includes the following sections e The xComputer Applet Writing Programs for xComputer e e Controlling Speed and Display Style e Count and Store Exercises Start by clicking this button to launch the xComputer applet in its own window Sorry your browser doesn t do Java For a full list of labs and applets see the index page http math hws edu TMCM java labs xComputerLab1 html 1 of 10 3 26 2000 12 50 09 PM xComputer Lab 1 The xComputer Applet The xComputer applet is divided into three sections The right hand third of the applet represents the main memory of the simulated computer This section of the applet shows the 1024 locations in xComputer s memory These locations are numbered from 0 to 1023 Each line in the memory shows a location number in blue and the value stored in that location When the program first starts up the memory contains only zeros The scroll bar can be used to view any part of memory The Control section of the applet is used to interact with and control the xComputer For example you can use text input boxes and buttons in the Control section to enter programs and data into the xComputer s memory Once a program has been loaded into memory you can tell the xComputer to execute it You ll learn about contro
195. guess is too low or You got it Although this program does something completely different from the random walk sample program nevertheless it is similar in general outline In particular you will use an if statement inside a loop Use a loop to allow for repeated guesses The loop will end when the user guesses correctly Your program can begin the following three lines before the loop DECLARE answer DECLARE guess answer randomInt 100 Your program should include comments Like the sample programs it should use indentation to show the structure of the program The Indent button can be used to automatically indent a program this feature is also useful for finding certain types of errors in a program such as a missing end if Exercise 10 This exercise assumes that you have completed Exercise 9 successfully Improve the program from that exercise so that after each game it will give the user the option of playing again You will need to add another loop to the program containing the loop that already exists You will also need to know a new command The YesOrNo command can be used to ask the user a yes or no question Specifically the command YesOrNo Do you want to play another game response will ask the user the given question It will store a zero in the variable response if the user answers no and will store a one in that variable if the user answers yes The outer loop should continue until the value of the response is
196. h binary numbers Such computations are one of the major functions of computers But computers also need at least two other abilities They need memory the ability to store and retrieve data And they need control the ability to control what data is stored where which computations are performed and in what order A program specifies a series of computations to be performed by a computer the computer stores program and data in its memory and the computer executes the program under its own control without any further direction from its user or programmer You already have some idea how circuits can perform computations In this lab you ll see how logic gates can be used to build memory circuits that can store binary numbers which are used to represent both programs and data As for control functions they can also be implemented with gates and wires There were some hints of this in the previous lab and you ll see more in this lab However the full mystery of how a computer can execute a program all on its own will not be solved until future labs The material in this lab is also covered in Sections 2 3 and 3 1 of The Most Complex Machine Not everything in the book is repeated here As usual you will find it useful to read the book before doing the lab You also definitely need to do the previous lab before this one This lab includes the following sections e Circuits that Remember e Registers e Random Access Memory e Exercises
197. h simulates a simple model computer which is also called xComputer The model computer is discussed in Chapter 3 of The Most Complex Machine The xComputer consists of a Central Processing Unit CPU and a main memory that holds 1024 sixteen bit binary numbers The CPU contains an Arithmetic Logic Unit ALU for performing basic arithmetic and logical computations It also contains eight registers which hold binary numbers that are being used directly in the CPU s computations a Control circuit which is responsible for supervising the computations that the CPU performs and a clock which drives the whole operation of the computer by turning its single output wire on and off The xComputer applet that you will use in this lab lets you load programs and data into the memory of the simulated xComputer You can then watch while those programs are executed and you can observe how numbers stored in the computer change as a program runs The applet displays only the registers and main memory You have to take the control circuit ALU and clock on faith This lab contains basic information about xComputer and its machine language It demonstrates how instructions are fetched from memory and executed by the CPU It will also explain the features of the xComputer applet and the process of programming the xComputer The next lab will cover the programming process in more detail You would find it useful to read through Chapter 3 of the text before doin
198. hat appear in the screen plus a few special commands Special commands are used to specify colors view distance and animation parameters There are a few basic named objects such as circle and cone There is also a command for defining new named objects Geometric transformations such as rotate and scale can be applied to objects to specify their size position and orientation You can make complex hierarchical objects that contain other objects which can have their own transformations Animation is done by letting parameters such as the scaling factor in a scale transformation vary through a range of values as the animation proceeds from frame to frame The rest of this file gives the details of the scene description language I should note that a scene description can contain comments A comment begins with a semicolon and continues until the end of the line For multiline comments a semicolon is required on each line A comment doesn t have to start at the beginning of a line Except in the case of comments xModels doesn t pay attention to ends of line They are treated just like spaces You can lay out your program any way you like on the page The xModels language is not case sensitive Upper and lower case letters are considered to be equivalent Names can consist of letters digits and the underscore character _ A name must begin with a letter or with an underscore Names can be of any length A word with a predefined meaning
199. he component onto the circuit board Make sure you drag it completely onto the board If you want a gate that is facing in a different direction you have to rotate the gate in the pallette before you drag it onto the circuit board Once some components are on the board you can draw wires between them using the mouse Every wire goes from a source to a destination To draw a wire move the mouse over the source click and hold the mouse button move the mouse to the destination and release the button You must draw the wire from source to destination not the reverse If you release the mouse button when the wire is not over a legal destination no wire will be drawn When there are two possible destinations in one component such as the two inputs of an AND or OR gate make sure that you get the wire connected to the right one Circuit Inputs are valid sources for wires So are Tacks So are the outputs of gates Valid destinations include circuit Outputs inputs of gates and Tacks You can draw as many http math hws edu TMCM java labs xLogicCircuitsLab1 html 4 of 10 3 26 2000 12 50 06 PM xLogicCircuits Lab 1 wires as you want from a source but you can only draw one wire to a destination This makes sense because when the circuit is running a destination takes its value from the single wire that leads to it On the other hand the value of a source can be sent to any number of wires that lead from it Once a component is on the
200. he precondition Instead of crashing the program should display an error message and halt Exercise 3 This is a continuation of Exercise 2 The Quadratic sample program actually exhibits another precondition which is violated if A equals zero Where does this precondition occur in the program and what exactly is the problem with having A 0 Exercise 4 This is a continuation of Exercises 2 and 3 Another way to deal with a precondition is to write a loop that can only end when the precondition is satisfied Modify the Quadratic program so that the input from the user is read in a loop that can only end if the user has entered legal values for A B and C After the loop the program can safely compute and print the solutions to the equation Exercise 5 Write a program that can draw staircases like those shown in the picture above The program you write must meet the following requirements 1 The user will be asked to specify the number of steps 2 Each step is one unit high and one unit wide 3 The orientation of the staircase will depend on the starting orientation of the turtle as shown in the second example in the picture This means that you should draw the staircase using only forward back and turn commands Do not use face or moveTo http math hws edu TMCM java labs xTurtleLab2 html 4 of 7 3 26 2000 12 50 19 PM xTurtle Lab 2 4 After the staircase is drawn the position and heading of the turtle will be the same as
201. http math hws edu TMCM java xTurtle samples Tutorial5_if txt N randomInt 4 f N as 17 2 BS or 4 3 ace 0 This is done in case N is 1 OR IF N 2 THEN face 90 This is done in case N is 2 OR IF N 3 THEN face 180 This is done in case N is 3 ELSE face 270 This is done in any other case which in this example can only happen if N is 4 END IF Marks the end of the IF statement forward 0 5 Moves forward a bit in the direction that has just been chosen at random EXIT IF xcoord lt 9 OR xcoord gt 9 OR ycoord lt 9 OR ycoord gt 9 The loop ends when the turtle moves outside the x and y coordinates in the range from 9 to 9 END LOOP marks the end of the loop http math hws edu TMCM java xTurtle samples Tutorial5_if txt 2 of 2 3 26 2000 12 50 36 PM http math hws edu TMCM java xTurtle samples Tutorial6_subroutines txt xTurtle Tutorial Example 6 Subroutines It is possible to define subroutines and functions that can be used just like built in subroutines such as forward x and built in functions such as sqrt x A subroutine is just a list of statements to be executed A function is similar except it returns a value to be used in further computation SUB Triangle Begin definition of a subroutine named Triangle forward
202. hws edu TMCM java labs xComputerLab2 html 3 of 8 3 26 2000 12 50 10 PM xComputer Lab 2 reset the Program Counter to zero You should also read the program and note how it uses the five labels NextN Odd Even Done and N The label Odd is defined but is never referred to in the program It is really just there for human readers Another sample program MultiplyByAdding txt adds two numbers by adding one of the numbers to itself over and over The program is set up to multiply 13 by 7 Read the program and try it out Use it to multiply some other pairs of numbers Make sure that you understand these programs and the general ideas of loops and decisions You will need to understand them to complete the exercises at the end of the lab Indirect Addressing The next sample program is ListSum txt This program illustrates a common type of processing where the computer processes a sequence of consecutive locations in memory In ListSum txt the computer adds up the numbers stored in consecutive locations It stops when it gets to a location that contains a zero In the exercises you will write two programs based on this one Before doing those exercises you should read the sample program run it and try to understand how it works The ListSum txt program uses indirect addressing to access numbers in the list Indirect addressing is used in several assembly language instructions including LOD I STO TI ADD I and
203. ic way of dealing with parameters An area of memory called the stack is used to hold the parameters for all subroutines In fact the stack also holds return addresses and data values used internally by subroutines The stack is just a list of values When a subroutine is called the parameters and return address for the subroutine are added to the end of the list When the subroutine ends the return address and parameters are removed from the stack The jump to subroutine instruction stores the return address on the stack and return from subroutine removes it from the stack when it s time for the subroutine to http math hws edu TMCM java labs xComputerLab3 html 4 of 7 3 26 2000 12 50 11 PM xComputerLab 3 end Typically a computer has a register called the Stack Pointer to keep track of how big the stack currently is And machine language typically includes instructions called push and pop to add items from the stack and to remove items from the end of the stack When one subroutine calls another all the data for the second subroutine is simply added to the stack on top of the data that is already there When the second subroutine ends its data is removed from the stack but the data for the first subroutine is still there so that the first subroutine can simply pick up where it left off The whole system is really rather elegant Maybe it s not so crazy to write a few subroutines for xComputer after all since doing everything by han
204. if is not an independent statement It simply marks the end of the IF statement Between the if and the end if there are lots of options Here are some examples that exhibit the options with comments that explain what they mean IF d gt 0 THEN Simple choice do the following statements or skip them ri t b sqrt d 2 a r2 b sqrt d 2 a END IF IF n 2 trunc n 2 THEN Branch if condition is true do the n n 2 statements between THEN and ELSE ELSE if the condition is false do the n 3 n l statements between ELSE and END IF END IF IF grade gt 90 THEN Multiway Branch Each condition TellUser Grade is A is tested in turn As soon as one is OR IF grade gt 80 THEN found that is true the statements TellUser Grade is B following that condition s THEN are OR IF grade gt 70 THEN executed and then the computer jumps TellUser Grade is C out of the IF statement to whatever OR IF grade gt 60 THEN statement follows the END IF If TellUser Grade is D none of the conditions are true ELSE then the statements between ELSE and TellUser Grade is F END IF are executed The ELSE part is http math hws edu TMCM java xTurtle info html 9 of 13 3 26 2000 12 50 17 PM xTurtle Info END IF m m a m m User defined Subroutines optional If it is absent and if all the conditions are false then none of the statements within the IF statement are ex
205. ight be defined as a trunk with two smaller trees attached to it This is OK as long as we say that the smaller trees are simpler than the main tree In the following subroutine the level tells how simple the tree is When the level gets down to zero only a trunk is drawn with no attached trees SUB Tr si Level IF level lt 1 THE forward size back size ELSE forward size 2 turn 45 Te si 2 level 1 N http math hws edu TMCM java xTurtle samples Tutorial7_recursion txt 1 of 2 3 26 2000 12 50 36 PM http math hws edu TMCM java xTurtle samples Tutorial7_recursion txt turn 90 Tree size 2 level 1 turn 45 back size 2 END IF END SUB PenUp MoveTo 5 8 PenDown green face 90 Tree 15 6 Draw a level 6 tree http math hws edu TMCM java xTurtle samples Tutorial7_recursion txt 2 of 2 3 26 2000 12 50 36 PM http math hws edu TMCM java xTurtle samples Tutorial8_multitasking txt xTurtle Tutorial Example 8 multitasking urtles in xTurtle have the cute ability o split themselves into a specified umber of turtles Each turtle hen goes on to execute the rest of he program If the split occurs nside a subroutine all the extra urtles are gone before the subroutine returns Turtles are split up in this way with the Fork command teeter opdctyH
206. ill be displayed The second mode is a graphics mode in which the applet displays the rendered scene In this mode there is a column of controls along the right edge of the applet This column contains Frame number label shows the currently displayed frame number during an animation If you find this distracting click on it http math hws edu TMCM java xModels info html 1 of 9 3 26 2000 12 50 33 PM xModels Info e New Program button takes you back to program mode with a new blank text area e Show Program button takes you back to program mode to the program that produced the current scene e Go button used to restart an animation that has been paused e Pause button stops an animation and makes the Go Next Frame and Previous Frame buttons available e Next Frame button goes to the next frame of a paused animation When the last frame is reached it goes back to frame zero e Previous Frame button goes to the previous frame an animation When frame zero is reached it goes to the final frame Speed pop up menu selects the desired speed for animation ranging from one frame per second to 30 frames per second However note that the actual rate can be less than the selected rate depending on the complexity of the scene and on your computer s speed Looping pop up menu Specifies what happens in an animation when the last frame is reached If this menu is set to Loop the animation
207. ingMachineLab html 7 of 9 3 26 2000 12 50 12 PM xTuringMachine Lab on a tape that does not contain two s to the right of the machine s starting position then the machine will never halt Exercise 2 One of the examples in the lab is a Turing machine called FindDoubleX This machine moves to the right until it comes to two x s in a row Then it halts on the first of the two x s Create a new machine that will move to the right until it finds three x s in a row It should halt when it finds a group of three consecutive x s Ideally it should move back to the first of the three x s and halt there Exercise 3 This exercise assumes that you have done Exercise 2 Given any sequence of x s y s and z s describe how you could construct a machine that will move to the right until it finds the given sequence For example if the sequence is xyzzyx it should move to the right until it has found the symbols x y z z y and x in consecutive squares and then it should halt What is the minimum number of states that such a machine would need assuming that you don t care which square it halts on Why Exercise 4 Construct a Turing machine to do the following Assume that the machine is started on a tape that contains nothing but a string of s The machine is started on the left end of this string The purpose of the machine is to multiply the length of the string by 3 For example if it is started on a string of seven s it should halt
208. ion of the object in that frame The object can change from one frame to the next because a different transformation is used in each frame Animation An animation is just a sequence of frames Each frame contains a separate image If the images don t change too much from one frame to the next the viewer will perceive continuous motion as the frames are played back in rapid succession In xModels a scene description that starts with the command animate N where N is a positive number is an animation with N 1 frames The frames are numbered from 0 to N You should think of N as the number of intervals between frames Then to get any kind of motion or change in the animation you need to make some quantity change from frame to frame This is done by using number range in place of a number A number range consists of a starting value followed by a colon followed by a final value In each frame of the animation the number range represents a different value For example in an 11 frame animation the number range 0 5 represents O in frame 0 0 5 in frame 1 1 in frame 2 and 5 in frame 11 Thus the scene description animate 10 circle scale 0 5 shows a circle that grows from a size of 0 in the first frame to a size of 5 in the last frame And animate 30 square scale 5 rotate 0 90 shows a 5 by 5 square pivoting through a 90 degree turn about the origin Note that the value 5 in this example is the same in each frame You don t need t
209. ircuit by storing a different four bit number in each location Explain how you can check that your circuit has stored the numbers correctly Exercise 6 The 2 Bit RAM sample circuit uses a 1 Bit Decode circuit This circuit has one input and two outputs It decodes its input by turning one of its outputs on when its input is ON and by turning the other output on if the input is OFF Similar decoder circuits with more inputs are also useful For this exercise build a two bit decoder circuit Your circuit should have two Inputs and four Outputs The two inputs can have any of the following pairs of values 00 01 10 or 11 Each of these pairs corresponds to one of the Outputs The decoder circuit should turn on a different output for each pair of inputs That is if the inputs have the value 00 both OFF then the circuit should turn on its first Output if the Inputs have the value 01 it should turn on its second Output and so on So at any given time exactly one of the outputs will be ON This is a fairly simple circuit Begin by finding a Boolean algebra expression for each of the outputs Exercise 7 This is a continuation of Exercise 6 The two bit decoder circuit that you built for Exercise 6 can be used as a component in a four location RAM The four locations in the RAM will be Guarded 1 Bit Mem circuits The RAM will have two ADDRESS wires which connect to the two inputs of the decoder The four outputs from the decoder should co
210. is repeated starting back at frame zero If it is set to Back And Forth the animation is played backwards then forwards again and so on If it is set to Once Through the animation is paused when it reaches the final frame At the very top of the applet there is another pop up menu This menu is available in both programming mode and graphics mode and you can use it to switch between modes and among all the programs that the applet knows about The first item in this pop up menu is Graphics When the applet is in programming mode selecting Graphics from the pop up menu is exactly the same as clicking on the RENDER button That is the applet will check the current program for errors and if no errors are found will switch to graphics mode and display the rendered scene The second item in the pop up menu is New Choosing this item will let you write a new program starting with an empty text area This is the same as clicking the New button while in graphics mode The new program will have the name Untitled 1 or Untitled 2 Or The remaining items in the menu are names of programs Selecting one of these names will take you directly to that program If you do this while the program is in graphics mode it will switch back to programming mode The Scene Description Language Scenes in xModels are described in terms of three coordinates x y and z The computer s screen is the xy plane with the origin 0 0 at the cent
211. isplay style doesn t show memory at all If you select it the computer s memory display will be replaced by a list of control wires These control wires are the key to understanding how the xComputer works The basic idea is that turning control wires on and off makes things happen in the computer They are turned on and off by a Control Circuit and they control the operation of other components of the CPU Each control wire has a function Turning that wire on causes something to happen such as moving a number from main memory into the AC register or adding the numbers in the X and Y registers and putting the answer into the AC Executing a program is just a matter of turning the right wires on and off in the right sequence The Control Wires display lets you see what wires are turned on during each step in the execution of an instruction Try it with the instruction lod c 17 by doing the following First enter the instruction lod c 17 into some memory location and set the PC to the http math hws edu TMCM java labs xComputerLab1 html 6 of 10 3 26 2000 12 50 09 PM xComputer Lab 1 address of that location Next set the display style to Control Wires Then use the Step button to go through the fetch and execute cycle one step at a time Here s what you will see e First click on the Step button COUNT becomes 1 indicating that the first step in the fetch and execute cycle is being performed The Load addr from PC control wir
212. ith a vather attractive pattern Note This is a self modifying program an old fashioned but cute idea The commands in locations 2 and 4 are changed as the program runs so that they load and store into different locations each time they ar xecuted lod c 1 Put the starting number in location 20 sto 20 lod 20 Add 1 to the number in location 20 and put the inc 3 result into location 21 sto 21 lod 2 Modify the instruction in location 2 so it inc loads from the next location sto 2 lod 4 Modify the instruction in location 4 so it inc s stores into the next location sto 4 jmp 2 Go back to the LOD instruction in location 2 http math hws edu TMCM java xComputer samples Graphics txt 3 26 2000 12 50 28 PM http math hws edu TMCM java xComputer samples Labels txt Example 3 Labels Many assembly language instructions refer to addresses of memory locations This could force you to count instructions in order to find the address number of the location you want to refer to Fortunately there is a way around this Use labels to refer to memory locations A label is just a name for a memory location You define a label by writing the name of the label followed by a colon followed by the contents of the memory location The value f the label is the address of that location ou can use the label anywhere in the program he
213. ithm that is to be applied to the arrays There is a also a Start Sorting button Once you have selected the sorting method and set up the size of the arrays and the number of arrays click on the Start Sorting button to begin If you are dealing with a large number of items there will be a noticeable time interval before the computer starts sorting The pause occurs while the computer is filling the arrays with random numbers When you click the Start Sorting button the name of the button will change to Abort Use the Abort button if you want to terminate the sorting operation before the computer finishes The xSortLab applet displays several different statistics about the sorts its does For this lab you will only need the Approximate Compute Time This is different from the Elapsed Time because as it is computing the applet allows some time about 20 of the time available for other activities such as redrawing the screen It is only the time actually devoted to sorting that you are interested in The compute time is approximate because it is possible for your browser or other programs on your computer to steal time from the applet The applet might incorrectly include this time in the compute time it reports However if you are not doing anything else with your computer at the same time that the applet is sorting then the reported time should be reasonably accurate The computer measures time in units of 1 1000 of a second a
214. itten to be used with The Most Complex Machine A Survey of Computers and Computing an introductory computer science textbook by David Eck For the most part the labs are also useful on their own and they can be freely used and distributed for private non commercial purposes However they should not be used as a formal part of a course unless The Most Complex Machine is also http math hws edu TMCM java labs xTurtleLab2 html 6 of 7 3 26 2000 12 50 19 PM xTurtle Lab 2 adopted for use in that course David Eck eck hws edu Summer 1997 http math hws edu TMCM java labs xTurtleLab2 html 7 of 7 3 26 2000 12 50 19 PM xTurtle Lab 3 Labs for The Most Complex Machine xTurtle Lab 3 Subroutines and Recursion SUBROUTINES WERE INTRODUCED in the previous lab This lab will continue the study of subroutines The lab concentrates on the idea of a subroutine as a black box and on recursive subroutines that call themselves either directly or indirectly You should be familiar with the material from Chapter 7 of The Most Complex Machine especially with the material on recursive subroutines from Section 3 The Koch curve and the binary tree introduced in that section will be used in the lab This lab includes the following sections e Black Boxes e Recursive Trees and Recursive Walks e Exercises Start by clicking this button to launch xTurtle in its own window Sorry your browser doesn t do Java For a full list
215. ity it is important to be able to build on previous work when designing new circuits Once a circuit has been designed and saved it should be possible to use that circuit as a component in a more complex circuit A lot of the power of xLogicCircuits comes from the ability to use circuits as components in other circuits Circuits used in this way are called subcircuits A circuit that has been saved as an icon in the pallette can simply be dragged into another circuit More exactly a copy of the circuit is created and is added to the circuit board The copy is a separate circuit editing the original will not change the copy This ability to build on previous work is essential for creating complex circuits You can open a circuit from the pallette to see what s inside or to edit it Just click on the icon to hilite it and then click on the Enlarge button The icon will be removed from the pallette and the circuit will appear on the circuit board At the same time any circuit that was previously on the circuit board will be iconified and placed on the pallette You should also be able to enlarge a circuit just by double clicking on it By the way you can change the name of the circuit on the circuit board by editing the text input box at the top of the applet This box contains the name that appears on the iconified circuit http math hws edu TMCM java labs xLogicCircuitsLab1 html 5 of 10 3 26 2000 12 50 06 PM xLogicCircuits Lab 1 The
216. l the computer executes a HLT instruction or until you stop it You should Try this now Make sure that the PC contains a zero Then click on the Run button If you have done everything correctly the program will run You will see things happening although you will probably not really understand them at this point But you will notice that the instructions in the program appear one by one in the IR register as they are executed Eventually the HLT instruction will be executed and the computer will stop running The correct answer to the computation 122 will be in memory location 10 This gives you the general idea of how programs are executed by xComputer Your goal in the rest of the lab is to understand the details After running the program once you should run it again First reset the PC to zero This time instead of using the Run button use the Cycle button Clicking on Cycle makes the computer run but only until the value in the COUNT register is 2 At that point the computer has just loaded a new instruction into the IR and is about to execute that instruction When you click on Cycle again the computer will execute that instruction and fetch the next instruction Thus the Cycle button lets you step through a program one instruction at a time Try it Keep clicking on Cycle until you get to the HLT instruction Finally you can run the program one more time this time with the Step button Clicking on the Step bu
217. le The word same under the Write column in that rule tells the machine to write the same character that it read Without this default rule the machine would need six separate rules to tell it what to do when it is in state 0 and it reads one of the symbols y z 0 1 or blank For an example of a more complex word processing Turing machine you can try out the http math hws edu TMCM java labs xTuringMachineLab html 4 of 9 3 26 2000 12 50 12 PM xTuringMachine Lab sample machine called CopyX YZ This machine will make a copy of a string of x s y s and z s Try it out Making New Machines In this part of the lab you will learn how to construct new machines in the xTuringMachine applet To begin a new machine select New from the pop up menu at the top of the applet This will give you an empty rule table that you can fill in to define the machine you want The xTuringMachine applet does not allow you to simply type in a rule Instead it has procedures for adding a new rule to the table and for modifying rules that are already in the table The type of editing that you can do is similar to what you already know about setting the Turing machine s state and changing the contents of its tape New rules are added to the rule table using the Rule Maker that is located just above the table of rules The Rule Maker has a set of five boxes where you create the rule and a Make Rule button that you can click to add the ru
218. le 4 Transformations can be applied to the objects inside a complex object Complex objects can be nested inside other objects circle translate 5 circle translate 5 rotate 45 45 The rotation command applies to the entire complex object consisting of two circles red A complex object can contain color commands in addition to objects line scale 8 rotate 90 xtranslate 4 4 scale 0 5 1 2 The entire complex object grows from half of its basic size to 1 2 times that size Note At this point the drawing color is black A The color change INSIDE the object has no effect outside On the other hand a color change made BEFORE the object does leak into A a complex object define wheel Begin the defintino of an object named wheel circle line A wheel contains a circle and three line rotate 60 lines which act as spokes line rotate 60 The end of the definition Wheel has been defined but no wheel has been put into the scene Now we add two wheels with different colors sizes and rotation speeds to the scene wheel scale 2 rotate 0 360 xtranslate 8 This one is black green wheel scale 4 rotate 0 180 xtranslate 8 http math hws edu TMCM java xModels samples Tutorial4_ ComplexObjects txt 1 of 2 3 26 2000 12 50 38 PM http math hws edu TMCM java xModels samples Tutorial4_ ComplexObjects txt A de
219. le 4 translate 0 5 The cylinder shows up 5 units above the origin line scale 6 translate 0 7 Finally a humble line The basic line is one unit long extending along the x axis from 0 5 0 to 0 5 0 Here it is scaled to a length of 6 and moved down 7 units You can render this scene by clicking on the RENDER button You should be able to find all the objects listed above in the picture The colors will help you identify them The 3 dimensional objects will look sort of distorted because they are being projected onto the screen from the point 0 0 20 The near side of the cube for example looks bigger than the far Side as it should really http math hws edu TMCM java xModels samples Tutorial1_Basics txt 2 of 2 3 26 2000 12 50 37 PM http math hws edu TMCM java xModels samples Tutorial2_Animation txt xModels Tutorial 2 Animation Moving images are more interesting than still images An animated image is displayed on the computer screen by showing a sequence of frames in rapid succession with small changes from one frame to the next In xModels a number range such as 1 5 is used to specify a value that changes from frame to frame in the animation For 1 5 the value is 1 in the first frame and is 5 in the last frame Between the first and last frame the value changes by the same amount in each frame This file defines an
220. le to the table You can edit any of the five items in the Rule Maker Just click on the item that you want to change The item will be hilited In the above picture the second item other is hilited The blue rectangular palette will display the values that you can legally put in the hilited spot You can either type the value you want or click on it in the palette Note that other is represented in the palette by a If you want to enter the value other you have to type or click on it Once you ve set up the rule you want in the Rule Maker you can either click the Make Rule button or press the Return key to add it to the table of rules The rule has no effect on the Turing machine until you add it to the table A newly added rule will be displayed in the table in red The rule shown in red is selected You can delete the selected rule from the table by clicking on the Delete Rule button You can select any rule in the table by clicking on the rule Once a rule has been added to the table you can edit the last three columns in the rule Click on the item you want to change and edit it in the usual way Note that the last three columns of the table specify the action that the Turing machine will take when it is in the specified state and reading the specified symbol You are only allowed to change the action part of the rule once it is in the table Often the easiest way to create a table of rules is to quickly create a bunch of
221. les e Lock Step Checkbox This box only has an effect on multitasking programs When it is http math hws edu TMCM java xTurtle info html 2 of 13 3 26 2000 12 50 17 PM xTurtle Info unchecked each turtle gets to execute a small random number of commands before control passes to the next turtle When the box is checked multiple turtles get to execute commands in strict alternation one after the other This often looks nicer but the random version is a more realistic simulation of multitasking One thing that the applet doesn t have is the ability to print This should be in a future version although with the same security restrictions as loading and saving files The xTurtle Language What follows is somewhat informal but complete specification of the xTurtle programming language as implemented in the xTurtle applet For many purposes you might find the tutorial examples more useful You might want to look at them first in any case Program Structure A program can contain comments A comment begins with and ends with Comments can be nested Comments are for human readers only They are ignored when the program is run The layout of a program on the page is ignored You can have more than one command on a line and you can split commands over several lines You can t have spaces in the middle of words The command PenUp for example cannot be written as Pen Up No distinction is made between upper and lower cas
222. list of x y points joins those points with line segments and then rotates the resulting curve about the y axis to obtain a three dimensional object The original curve is actually copied several times at different angles of rotation These copies are then joined with further line segments The number of copies must be specified as the first parameter to the lathe command The remaining parameters specify the x y points For example the following command makes four rotated copies of the line segment from 0 5 to 3 0 and then connects them with lines to produce a pyramid lathe 4 0 5 3 0 It is legal to have a lathe command with just one point The result will be a regular n sided polygon lying in the xz plane The extrude command is similar to lathe in that it makes several copies of a curve that lies in the xy plane and it then joins those copies with lines However extrude makes the copies by translating the original curve along the z axis Each copy is separated from the next by one unit along the z axis The z values are centered about 0 for example for extrude 2 the http math hws edu TMCM java xModels info html 5 of 9 3 26 2000 12 50 33 PM xModels Info two z values are 0 5 and 0 5 Besides all these basic objects you can make complex objects A complex object is a list of items enclosed between a left bracket and a right bracket It can include objects and color specifications Each object in a complex object
223. lling the xComputer as you work through the lab The Registers section of the applet shows the xComputer s eight registers Remember that a register is simply a memory unit in the CPU that holds data being used directly in the CPU s computations Each register plays a particular role in the execution of programs by the CPU These roles are described in detail in the text and will be illustrated during the course of this lab but here for your reference is a brief summary e The X and Y registers hold two sixteen bit binary numbers that are used as input by the ALU For example when the CPU needs to add two numbers it must put them into the X and Y registers so that the ALU can be used to add them e The AC register is the accumulator It is the CPU s working memory for its calculations When the ALU is used to compute a result that result is stored in the AC For example if the numbers in the X and Y registers are added then the answer will appear in the AC Also data can be moved from main memory into the AC and from the AC into main memory e The FLAG register stores the carry out bit produced when the ALU adds two binary numbers Also when the ALU performs a shift left or shift right operation the extra bit that is shifted off the end of the number is stored in the FLAG register e The ADDR register specifies a location in main memory The CPU often needs to read values from memory or write values to memory Only one location in m
224. lod 2 inc sto 2 add 1 to the number stored in memory location 2 But if you look at what s stored in that location you ll find the instruction lod 12 which is part of the program This seems odd What happens when you add 1 to an instruction Remember that machine language instructions are really just numbers There is no problem with adding to a number However the meaning of the instruction represented by the number is changed If you add 1 to the number that encodes lod 12 the meaning of the answer is lod13 If you want to understand exactly why this is true look at the binary representations of the machine language instructions The details are given in Section 3 2 of the text if you want to check there Run this program and see what it does To fully appreciate this program you should run it at Fastest Speed with the memory display set to Graphics You can watch as the memory is gradually filled with numbers Exercises Exercise 1 You can use the xComputer to translate from one type of data to another by entering it in one form in the data input box and viewing it in memory in another form Use this method to do the following conversions and explain briefly how you do each part 1 Find the ASCII code for the character The ASCII code is the integer that represents this ASCII character 2 Find the character whose ASCII code is 99 3 Find the binary representation of 233 4 Find the unsigned integer tha
225. lready You should also type an input string of x s y s and z s onto the Turing machine s tape and move the machine to the leftmost symbol in the input Then you can start making the rules one by one and adding them to the table When you are all done you should have a machine that will perform as advertized One more feature of the applet deserves to be mentioned here Suppose that you click the Step or Run button and the Turing machine finds itself in a situation that is not covered by any rule in the rule table In this case the machine will stop and will display the message No Rule Defined It will also set up the Rule Maker with the its current state and the symbol that it is reading so that it is all set for defining the missing rule It s possible to define a machine using this feature Start with an empty table of rules Click Step The machine will protest You can define the rule and click Step again You can proceed in this way until the whole rule table has been defined However you have to be careful to make sure that you have in fact covered all the situations that might arise http math hws edu TMCM java labs xTuringMachineLab html 6 of 9 3 26 2000 12 50 12 PM xTuringMachine Lab Binary Arithmetic The operations of incrementing adding one to or decrementing subtracting one from a binary number are simple enough to be done easily by Turing machines The algorithm for adding one can be described as follo
226. lue to be stored on the lower of the two Inputs on the left of the circuit Turn the upper Input ON wait a while until the circuit settles down and turn the upper Input OFF The value that you ve stored will appear on the output wire This value will remain stored in the circuit as long as the upper Input is OFF If you don t wait long enough before turning the upper Input OFF the value will not be properly stored In fact strange things can happen that are different from what would happen in a real electrical circuit David Eck eck hws edu August 1997 http math hws edu TMCM java xLogicCircuits index html 4 of 4 3 26 2000 12 50 27 PM xComputer Intro The xComputer Applet The applet at the bottom of this page assuming that you have a Java enabled browser simulates the CPU and memory of a model computer called xComputer The applet lets you write assembly language programs for this computer and see how the computer executes them The applet was written by David Eck for use with his introductory computer science textbook The Most Complex Machine However it can also be used on its own The applet below is set up to load some sample programs These programs contain some basic instructions for using the applet Select a program from the pop up menu at the top of the screen Read the comments in the program Then click on the Translate button to translate the program into machine language and load it into the compute
227. memory cannot such as count The count register is used in one of the exercises at the end of the lab but mainly it is here to show you that registers can be made to do more than just store numbers Random Access Memory A random access memory or RAM is a memory circuit that can hold several different binary numbers Each binary number is stored in a separate location The locations are numbered 0 1 2 3 and so on The number of a location is called its address Every computer has a RAM which it uses as a main memory where it stores the data and programs that it is working with A RAM can have any given number of locations In a typical computer the RAM has several million locations The binary numbers that are stored in a RAM can have any given number of bits In a typical modern computer each location holds an eight bit binary number In this section you ll see how a very simple RAM can be constructed The RAM you will look at has only two locations and each location holds just a single bit The exercises at the end of the lab will investigate how larger and more useful RAM s can be built The sample RAM is named 2 Bit RAM It is one of the sample circuits loaded by the xLogicCircuits applet Find it in the applet s pallette and open it You ll see a circuit with one data input two control inputs and one output LOAD DATA Guarded DAT A IN Po OU m DAT A OUT Guarded 1 Fit ae tem 1 Bit a i ADDRESS wire is u
228. memory location 10 And the final instruction hlt tells the computer to halt The net effect is that the program adds 105 to 17 and stores the answer in location 10 After the program halts you can look in memory at location 10 to find the answer Now how do you make the computer run the program All the computer ever does is fetch instructions from memory and execute them The value stored in the PC register tells the computer which memory location to go to to get the next instruction Before running the program you have to make sure that it will begin with the first instruction of the program which is in memory location zero This means that the PC register should contain a zero If this is not the case you can put a zero into the PC by clicking the Set PC 0 button in the Control section of the applet Zero is the most common starting value for the PC but if you want to start at a different location you can type the address of that location into the addr input box and click the Addr to PC button Once you have checked the value of the PC register you can just click on the Run button to run the program You should think of this as turning on the xComputer s clock As soon as you do this the clock stars ticking the value in the COUNT register starts changing and http math hws edu TMCM java labs xComputerLab1 html 3 of 10 3 26 2000 12 50 09 PM xComputer Lab 1 the fetch and execute cycle proceeds This will continue unti
229. mpleCounter txt is a copy of the program that counts forever which was discussed earlier in this lab Modify this program so that it counts to 16 and http math hws edu TMCM java labs xComputerLab2 html 5 of 8 3 26 2000 12 50 10 PM xComputer Lab 2 then halts This was also an exercise in the previous lab except that in that lab you didn t use labels Add a HLT statement after the JMP statement Use the name Done as a name for that statement Jump to Done when the Count reaches 16 Exercise 2 Here is a copy of the CountAndStore program that was used in the previous lab A copy was also loaded as one of the sample programs by the xComputer applet on this page Rewrite this program to use labels instead of numerical addresses for locations 2 and 4 Do you think the program is easier to understand with labels lod c 1 Start with a 1 in location 12 sto 12 lod 12 This instruction is stored in location 2 inc sto 13 This instruction is stored in location 4 lod 2 Add 1 to the number in location 2 inc sto 2 lod 4 Add 1 to the number in location 4 inc sto 4 jmp 2 Go back to the instruction in location 2 Exercise 3 Modify the ThreeNPlusOne txt program so that it counts the number of steps it takes for N to become equal to 1 To do this add another labeled location at the end of the program Call it Count Change the program so that it starts by storing a zero in location Count Each time through the
230. must be an exit statement which gives a condition for ending the loop In the sample program the statement exit if heading 0 includes the condition heading 0 Since the heading is the direction that the turtle is facing this condition is true when the turtle is facing in the direction zero that is directly towards the right When a loop is executed the computer will execute the statements in the loop repeatedly Each time the exit statement is executed the computer tests the condition specified by that statement If the condition is satisfied the computer jumps out of the loop Ordinarily after exiting from a loop the computer jumps to the statement that follows the end loop In this example there is no further statement after the loop so the program ends when the loop ends To run a program in the xTurtle program select it from the pop up menu if necessary so it is visible on the screen Then click on the Run Program button If there are no errors in the program the computer will switch back to the drawing area and execute the program You can control the rate of execution with the speed pop up menu You can pause the execution with the Pause button and you can terminate it permanently with the Stop button After the program has been executed you can run it again by clicking the Run Program button Note that every time you run a program the turtle starts out in its initial configuration at the center of the drawing a
231. n Sort and Insertion Sort are fairly straightforward but they are relatively inefficient except for small lists Merge Sort and QuickSort are more complicated but also much faster for large lists QuickSort is on average the fastest Bubble Sort is the slowest Bubble Sort is often the first and sometimes the only sorting method that students learn Here are brief descriptions of the four remaining algorithms with some information about what you see when xSortLab executes them Selection Sort is probably the easiest sorting method to understand In each major phase of the algorithm the next largest item is found and moved into position at the end of the list In the picture below the four black bars have already been moved into position and the algorithm is in the middle of the next phase It is important to remember that the program can t just look at all the bars and pick the biggest one in one step as you can It is restricted to comparing two items at a time To find the largest item in a list the computer moves through the list one item at a time keeping track of the largest item it has seen so far After looking at all the available items it knows which is the largest item overall It moves the largest item into the next available spot at the end of the list by swapping it with the item that is currently occupying that spot In the picture during the current phase of the sort the computer has looked at items number 1 through 7 An
232. n a complex program subroutines are a tool for breaking a complex problem down into smaller more manageable subproblems Recursive Trees and Recursive Walks A recursive subroutine is one that calls itself A recursive subroutine is a black box that uses itself as a black box Section 7 3 in the text introduces recursive subroutines using the example of a binary tree The program for this example is in the Sample program BinaryTrees Select this program from the pop up menu at the top of the xTurtle applet and run it Nothing will happen since the file only defines some subroutines The main subroutine defined in the file is called TestTree If you enter this into the text input box beneath the drawing area of the applet you will be asked to specify a complexity level The computer will draw a tree with the complexity that you specify Try this for example for a complexity level of 5 A binary tree of complexity zero is defined to be a single straight line segment A binary http math hws edu TMCM java labs xTurtleLab3 html 2 of 6 3 26 2000 12 50 20 PM xTurtle Lab 3 tree of complexity greater than zero is defined to consists of a trunk which is just a line segment with two branches attached to it Each of the branches is a binary tree which is smaller than the complete tree and which has smaller complexity than the complete tree This is a recursive definition because we are saying that a tree contains pieces which are themsel
233. n have crashed This is a bug You are warned Stick to a reasonable number of items At the bottom of the panel are a pop up menu that you can use to choose the sort method and a Go button that you can click to start the sort This changes to Abort while a sort is in progress When you begin a sort the first thing the computer does is to fill up the arrays with random numbers If there are a lot of numbers this will take a noticeable amount of time Then the computer begins to sort As the sorting operation proceeds statistics are displayed about twice per second The statistics include the number of comparison and copy operations that have been performed the number of arrays that have been sorted so far the elapsed time since the computer began sorting and the approximate compute time that the computer has devoted to sorting The compute time is not the same as the elapsed time since the applet is doing other things besides sorting such as redrawing the screen The applet tries to use 80 of the time for sorting and to leave 20 for other tasks The applet can measure the 20 of its time that it gives away voluntarily but if other things are going on in your computer it might lose some other time that it can t measure This is why the measured compute time is approximate So you should not try to run a timed sort in the background Just sit and watch or go get a coffee http math hws edu TMCM java xSortLab index html 2 of 3
234. n is available about the applet and the xTurtle language on xTurtle Info page A set of tutorial examples is also available For a list of other applets and for lab worksheets that use the applets see the index page Java not available David Eck eck hws edu June 1997 http math hws edu TMCM java xTurtle index html 3 26 2000 12 50 31 PM xTurtle Tutorial xTurtle Tutorial Examples The xTurtle Applet let s you write and execute programs written in a simple programming language also called xTurtle The applet at the bottom of this page will try to load eight tutorial examples To read an example select it from the pop up menu at the upper left corner of the applet Then to run it click on the Run Program button For full information on the applet and the language see the xTurtle Info page The eight tutorial files are also available as text files using the following links 1 2 3 4 5 6 7 8 Warning This applet seems to stretch or exceed the limits of some browsers Java not available David Eck eck hws edu June 1997 http math hws edu TMCM java xTurtle tutorial html 3 26 2000 12 50 31 PM http math hws edu TMCM java xTurtle samples Tutorial1_basics txt xTurtle Tutorial Example 1 Basics This file demos some of the built in commands of the xTurtle language First lesson This is a comment Since it is enclosed between and Comments are ignored by the
235. nal tool for learning the basics about logic circuits In particular only the logical behavior is simulated not the electrical components from which real gates are made The xLogicCircuits applet is one of several applets written by David Eck for use with his introductory computer science textbook The Most Complex Machine They can also be used independently of the book For a list of other applets and for lab worksheets that use the applets see the index page The applet is set to load some sample circuits You should see an XOR circuit with two inputs on the left some gates and wires that compute the exclusive or of the inputs and an output on the right The definition of XOR is that the output is ON if one of the inputs is ON and the other is OFF To run a circuit you first have to turn the power on using the Power checkbox at the bottom of the applet Then you can click on the circuit s inputs to turn them on and off The signals from the inputs propagate along the wires through the circuits More instructions and more details are given on this page below the applet Java not available Building Circuits You can build circuits by dragging components from the scrolling pallette on the left of the applet This pallette always contains at least the six standard components NOT gate OR gate AND gate Input Output and Tack The gates are components that do computations An AND gate for example has two inputs and one out
236. nd upon or change the heading of the turtle circle x draws a circle of radius x You should think of the turtle moving in a circle starting from its current position and returning to that position at the end Note that the turtle position is on the circle If x is positive the turtle curves to its left as it draws the circle and the center of the circle is x units to the left of the original turtle position If x is negative the turtle curves to the right and the center of the circle is to the right of the original position arc x y draws part of a circle of radius x A full circle would be 360 degrees arc x y draws an arc of y degrees As with circle x the turtle curves to the left if x is positive and to the right if x is negative If y is negative then the turtle will back up along an arc Note that the turtle changes position and heading as it draws HideTurtle and ShowTurtle make the turtle the small black triangle invisible and visible The turtle can still draw while it is invisible There is a check box labeled No Turtles in the control strip to the right of the drawing area When this box is checked the turtle will always be invisible regardless of whether the program uses any HideTurtle or ShowTurtle commands Draw some pictures using these basic commands Here are a few things you can try for example circle 7 circle 5 circle 3 circle 1 arc 5 90 arc 5 90 arc 5 90 arc 5 90 forward 5 turn 120
237. nd this also limits the accuracy of measurements In particular you should not try to use measurements that are less than say 0 1 seconds Ideally you should adjust the number of arrays so that the compute time is at least a couple of seconds Your task in this part of the lab is to gather timing statistics about each of the five available sorting methods You want to measure how long it takes each method to sort arrays of various sizes You will need this data for the exercises at the end of the lab so you should record the data as you work For each experiment that you do record the array size the number of arrays and the compute time that is reported by the applet You should apply each method to arrays of at least the following sizes 5 10 100 and 1000 In addition you should apply Merge Sort and QuickSort to arrays of size 10000 You might also want to try Merge Sort and QuickSort on arrays with 100000 items And you might try Bubble Sort Selection Sort and Insertion Sort with 10000 items For the largest array sizes it will be good enough to sort a single array For the smaller array sizes you will have to set the number of arrays to be rather large to get a decent measurement Don t be afraid to sort 10000 or even 100000 arrays of size 5 Use your judgement If the arrays require more memory than your computer has available you should just get an error message However this has crashed many systems that I tried it on http
238. ndirect addressing in a LOD I instruction This is a nice example that demonstrates once again the usefulness of pointers and indirect addressing Reality Check It s actually kind of crazy to try to write subroutines for xComputer The limited variety of machine language instructions for xComputer makes it very hard to express the idea of a subroutine in that language Not surprisingly real computers have special purpose machine language instructions for working with subroutines The first thing that a machine language needs is a pair of instructions for calling a subroutine and for returning from a subroutine These instructions might be called jump to subroutine and return from subroutine The jump to subroutine instruction would automatically save a return address and then jump to the starting point of the subroutine The computer could figure out the return address on its own instead of leaving it up to the programmer by looking at the value in the Program Counter register The Program Counter holds the address of the next instruction after the one that is currently being executed and that s exactly the point that the subroutine should jump back to The return from subroutine instruction would get the return address that was previously saved by jump to subroutine and jump back to that address These two instructions would make it unnecessary for a programmer to even think about return addresses Real computers also have a more systemat
239. ne However it can also be used on its own The applet below is set up to load some sample programs Click on the RENDER button to see the image or animation described by a program Use the pop up menu at the top of the applet to select among the sample programs Full information is available about the applet and its scene description language on the xModels Info page A number of tutorial examples are also available Java not available David Eck eck hws edu June 1997 http math hws edu TMCM java xModels index html 3 26 2000 12 50 32 PM xModels Info xModels Info Computer generated graphics images are usually constructed in two stages modeling followed by rendering In the modeling stage a geometric representation of the objects in the scene is constructed The rendering stage produces the actual images based on information in the model The xModels Applet lets you describe scenes in a simple scene description language Scenes are rendered as wireframe models a very minimal kind of rendering which shows just the edges of all the objects in the scene even edges that are behind other objects The main point of the applet is not to produce fancy images the point is to learn some of the basic ideas of geometric modeling This file contains fairly complete information about the xModels Applet and about the scene description language that it uses Also available on a separate page are some tutorial examples I invente
240. ne level that can then be used on higher levels An object definition takes the form of the word define followed by a scene description enclosed in square brackets and For example define wheel circle line line rotate 60 line rotate 120 When a definition like this one occurs in a scene description it does not immediately add anything to the overall scene It just defines the word wheel for the computer as a new type of object made up of the specified parts Once this definition has been made a wheel can be used like any other object You can apply the same transformations to wheels that apply to other objects For example wheel scale 2 xtranslate 2 5 The word wheel becomes part of the language of xModels on an equal basis with square and circle It can even be used in the definitions of other objects The sample program named Wagon contains an example in which wheels are defined and used Open the file read it and render it to see what it looks like Note that the wheels on the wagon rotate Another example is given in the sample program Houses which you should also look at http math hws edu TMCM java labs xModelsLab1 html 7 of 10 3 26 2000 12 50 25 PM xModels Lab 1 Exercises Exercise 1 Write a scene description for a still image that shows five squares of different colors nested inside one another like this Use any colors you like as long as you don t use the default color white
241. ng that variable This is the mutual exclusion problem In xTurtle the grab statement is provided to make mutual exclusion possible A grab statement takes the form GRAB lt global variable name gt THEN lt statements gt END GRAB Only one process at a time is allowed to grab a given variable When a process comes to a grab statement the computer checks to see whether another process has already grabbed the variable If so then the second process must wait until the first process releases its lock on the variable by finishing the execution of its grab statement Only then is the second process allowed to grab the variable and execute the statements in its own grab statement Of course this can cause big problems if a process grabs a variable and doesn t release it Other processes that want to grab the variable will never get a chance to run at all The statements inside a grab statement are called a critical region As long as access to shared variables is confined to critical regions processes can use the variables to communicate in relative safety Even with the grab statement communication among processes can still be very complicated A relatively straightforward example can be found in the sample program SynchronizedRandomWalk txt Select this program from the pop up menu read the comments and run the program You will see two turtles executing identical random walks One of the turtles selects a random angle to be used in the
242. nless the files are in the same directory with the applets The applets themselves are contained in the file tmcm jar This is a Java archive file In addition to the applets this file contains the three applications described above The names of these applications are tmcm Apps tmcem Labs and tmcm Tutorials The funny names arise because the applications are in the Java package named tmcm When you run one of these applications a window will pop up The window contains several buttons Click on a button to launch one of the applets For the applications tmcm Labs and tmcm Tutorials the applets will load the appropriate sample files For tmcm Apps the applets do not load any files You can move tmcm jar to another location and still use it to run tmcm Apps However if you want to run tmcem Labs or tmcem Tutorials the tmcm jar file must be in the same directory as the sample files To run the applications you need the tmcm jar file plus some additional Java software Here are specific instructions for various platforms http math hws edu TMCM java tmcm java apps README txt 1 of 3 3 26 2000 12 50 02 PM http math hws edu TMCM java tmcm java apps README txt For Windows If you have Microsoft Internet Explorer with Java support then you should be able to use the Jview command in a DOS Window To run the ap
243. nnect to the GUARD wires of the four Guarded 1 Bit Mem circuits This allows the http math hws edu TMCM java labs xLogicCircuitsLab2 html 8 of 9 3 26 2000 12 50 07 PM xLogicCircuits Lab 2 values on the ADDRESS wires to be used to select one of the four locations For this exercise build such a four location RAM As in the original 2 Bit RAM example each location should hold just one bit Exercise 8 Based on your work in Exercises 5 and 7 explain how it would in principle be possible to build a RAM containing any given of locations with any given number of bits in each location Exercise 9 Write a short essay explaining what you learned in this lab about constructing complex circuits from subcircuits This is one of a series of labs written to be used with The Most Complex Machine A Survey of Computers and Computing an introductory computer science textbook by David Eck For the most part the labs are also useful on their own and they can be freely used and distributed for private non commercial purposes However they should not be used as a formal part of a course unless The Most Complex Machine is also adopted for use in that course David Eck eck hws edu Summer 1997 http math hws edu TMCM java labs xLogicCircuitsLab2 html 9 of 9 3 26 2000 12 50 07 PM xComputer Lab 1 Labs for The Most Complex Machine xComputer Lab 1 Introduction to xComputer THIS LAB INTRODUCES the xComputer applet whic
244. number can be used to represent different types of data To launch the applet click on this button Sorry your browser doesn t do Java The window that opens when you click this button will probably be marked with some kind of warning to alert you to the fact that the window was created by an applet For example on my computer there is a warning bar like this one along the bottom of windows opened by applets A Unsigned Java Applet window ol Why the warning A Java applet is a program that you have downloaded from the Internet Whenever you download a program there is a danger that the program is malicious that it will try to damage your computer or steal information from you A great deal of attention has been paid to making Java applets secure that is to making sure that they can t damage your computer or access private information stored on your computer However nothing can stop you from entering private information such as a password into an applet The warning on applet windows is there to stop malicious applets from tricking you into entering such information For example without the warning the applet might imitate a window from a program that has a legitimate need for the information Data Representations You ll be using the DataReps applet which you launched above in some of the exercises at the end of the lab For now you should read about it and experiment with it to see what it does http math hws
245. o mak ire paddles object each of the second and the object There is an extra th For example the command creates an animation with a segment that followed by a segment The segments are spliced together becaus al frame of the first segment is the first frame of the second segment that contains the same as This file defines saturation brightness Eight flaps rotate into position during the first segment of the animation After that the y rotation of each flap remains constant for the next two segments Then all the flaps rotate back to their original positions rotates around the y axis third segments is ALSO rotating about the constant 15 degree rotation In the asiest to view object http math hws edu TMCM java xModels samples Tutorial6_Segments txt 3 26 2000 12 50 39 PM http math hws edu TMCM java tmcm java web site README txt HADME file for the tmcm Jjava web sit archive T applets that are also available on line at http math hws edu eck TMCM java March 2000 he tmcm java directory in this archive contains Web pages and The Web pages include some lab worksheets that were written to be used with my introductory computer science textbook Complex Machine other pages If you would for commercial Contact main Web page is index html purposes They can also be used on their
246. o use a number range for each value in an animation only for the values that you actually want to change during the animation By adding additional parameters to the animate command you can make segmented animations For example the command animate 30 50 specifies an animation with two segments The first segment has 31 frames and the second segment has 51 The final frame of the first segment is also the first frame of the second segment so there are 81 frames in all Remember that the numbers 30 and 50 actually specify the intervals between frames An animation can contain any number of segments The first frame of the animation the last frame and any frame that is on the boundary between two segments are called key frames A number range used in a segmented animation must specify a value for each of the key frames Thus it must have exactly as many colons as there are segments in the animation For example the number range 10 5 7 could be used in a two segment animation During the first segment the value ranges from 10 to 5 and during the second segment it ranges from 5 to 7 The number range 0 0 10 has the constant value 0 throughout the first segment and then its value ranges from 0 to 10 during the second segment Sometimes you want a quantity that changes at a constant rate during the whole animation rather than at different rates in different segments The notation for doing this is to use two or more colons in a row htt
247. odes and shows the two characters Some eight bit binary numbers do not represent visible ASCII characters These numbers are shown in the form lt N gt where N is the number in decimal form Thus for example the 16 bit binary number 0000000000000000 is shown in ASCII display style as lt 0 gt lt 0 gt e The Graphics display is very different from the others It shows the entire memory at once Each bit in memory all 16 times 1024 of them is represented by one pixel on the screen That pixel is white if the bit is zero and is black if the bit is one If you choose the Graphics display now the memory will be almost entirely white except for a few black dots at the top that represent the program you entered into memory You can try out the various memory display styles You ll be using them in Exercise 1 at the end of the lab I should note that when you enter information into Memory using the data input box in the Control area of the applet you can type the information in several of the above display styles as well as in assembly language You can for example enter ordinary numbers in the range 32768 to 65535 You can enter a binary number but you must precede it by the letter B For example B1011010111 Finally you can enter one or two ASCII characters but you must precede them by a quote mark For example 1 or A You will need to do this for Exercise 1 There is another option in the pop up menu Control Wires This d
248. oduces the if statement This is the sample program RandomWalk which should already be loaded into the xTurtle applet Select the RandomWalk program from the pop up menu and run the program several times This program makes the turtle do a random walk in which it repeatedly moves in a randomly chosen direction Read the program and the comments on it and try to understand how it works In particular look at the if statement in the Random Walk program An if statement is used to decide among alternative courses of action An if statement begins with the word if and ends with the words end if The end if here is not a separate command it is merely a required syntactic marker to mark the end of the if statement It is very different from an exit if statement and you should try not to confuse them The exact rules for using if statements are rather complicated and are covered in The Most Complex Machine and in the detailed on line information about xTurtle However you should be able to get the basic idea by looking at the example in the sample program Interacting with the User Any real programming language needs to provide some way for a program to communicate with the person who is using the program The xTurtle programming language provides only minimal support for input and output but what it provides is enough for a program to have a simple dialog with the user http math hws edu TMCM java labs xTurtleLab1 html 6 of 10
249. of Computers and Computing an introductory computer science textbook by David Eck For the most part the labs are also useful on their own and they can be freely used and distributed for private non commercial purposes However they should not be used as a formal part of a course unless The Most Complex Machine is also adopted for use in that course David Eck eck hws edu Summer 1998 http math hws edu TMCM java labs xComputerLab3 html 7 of 7 3 26 2000 12 50 11 PM xTuringMachine Lab Labs for The Most Complex Machine xTuringMachine Lab Introduction to Turing Machines TurING MACHINES are extremely simple calculating devices A Turning machine remembers only one number called its state It moves back and forth along an infinite tape scanning and writing symbols and changing its state Its action at a given step in the calculation is based on only two factors its current state number and the symbol that it is currently scanning on the tape It continues in this way until it enters a special state called the halt state In spite of their simplicity Turing machines can perform any calculation that can be performed by any computer In fact certain individual Turing machines called universal Turing machines can actually execute arbitrary programs just as a computer can You won t see any universal Turing machines in this lab but you will experiment with Turing machines that can perform non trivial calculations Turing
250. om To use this command w the directory that co to specify the full p For example nave in Linux or U in a DOS comma For Linux UNIX th For DOS Windows e t These script it should b but NI en I 1d a e ith ntains ath X nd window have included script files that will compile file ed compile sh a DOS batch file named compile bat re is here s jar archive containing all the compiled You can get more information by reading the e possible have not y written http math hws edu TMCM java tmcm java source README ixt 1 of 2 3 26 2000 12 50 03 PM http math hws edu TMCM java tmcm java source README txt with CodeWarrior for Macintosh David Eck Department of Mathematics and Computer Science Hobart and William Smith Colleges Geneva NY 14456 USA Email eck hws edu WWW http math hws edu eck http math hws edu TMCM java tmcm java source README ixt 2 of 2 3 26 2000 12 50 03 PM
251. omposer You might have to http math hws edu TMCM java labs WebPublishingLab html 2 of 7 3 26 2000 12 50 13 PM Web Publishing with Netscape Composer click on a small plus sign or triangle next to the word Composer in order to see Publish In the Publish dialog box make sure that the two boxes under Links and Images are checked Then fill in the following information under Default Publishing Information substituting your own username for username Publish to FIP or HTTP ftp username escher hws edu export home username www Browse to HTTP http escher hws edu username Then click the OK button This will allow Netscape Composer to find your account on escher hws edu so that it can upload your pages into that account You will need the password for the account later when you have a page ready to go Note Netscape Communicator includes an on line help facility that has lots of information about Composer and HTML as well as about all of Communicator s other features To access this information choose Help Contents from the Help menu To get information about Composer in particular select the link to Creating and Editing Web Pages in the help window that appears Making Your First Page There are several ways to start up Netscape Composer e From Netscape s File menu select the New submenu and then select Blank Page e Click on the small Composer icon in the bottom right corner of a Netscape b
252. ons They are not as easy as neat or as safe as subroutines in a high level language but they can still be a useful tool Furthermore by working with subroutines on xComputer you ll get to see some of the details of how subroutines can be implemented on a very low level You should understand though that the machine languages of real computers do provide more support for subroutines than what is covered here Before doing this lab you should be very familiar with the xComputer applet and with assembly language programming for xComputer as covered in xComputerLab 1 and xComputer Lab 2 The material in this lab is not covered in The Most Complex Machine This lab includes the following sections e There and Back Again e Parameters and Local Names e Passing Pointers Reality Check e Exercises Start by clicking this button to launch the xComputer applet in its own window Sorry your browser doesn t do Java For a full list of labs and applets see the index page There and Back Again The idea of subroutines is simple enough A subroutine is just a sequence of instructions that performs some specific task Whenever a program needs to perform that task it can call the subroutine to do so The subroutine only has to be written once and once it is written you can forget about the details of how it works If the same task needs to be performed in another program then it can simply be copied from one program to another using cut an
253. op and will display the message No Rule Defined You could then use the rule maker to make the missing rule If the machine moves outside the applet as it is computing the machine along with its tape will jerk back about 1 4 of the width of the applet By the way if you somehow lose the machine off the edge of the applet clicking the Run or Step button will make it reappear Using the Mouse It is possible to work with the xTuringMachine applet using only the mouse and completely avoiding the keyboard Here s how Before you can edit any item it must be hilited The currently hilited item if any is surrounded by a bright blue green outline You can always hilite an editable item by clicking on it Whenever an item is hilted the palette will display a list of legal values for that item The palette is the blue rectangle just below the machine You can choose one of these values by clicking on it You can also type the value you want http math hws edu TMCM java xTuringMachine index html 2 of 4 3 26 2000 12 50 31 PM The xTuringMachine Applet As long as the Turing machine is not running you can edit the current state of the machine and the contents of the tape Click on the machine or on one of the tape s cells then select a value from the palette When you enter a symbol for the tape the hilite moves one cell to the right You can edit the Write Move and New State columns of the rule table at any time ev
254. op up menu at the top of the applet that can be used to switch among the three panels Note Changing panels while a sort is in progress will abort the sort The applet starts in Visual Sort mode in which 16 bars are sorted step by step using one of the sorting algorithms Bubble Sort Selection Sort Insertion Sort Merge Sort or QuickSort Below the area where the bars are displayed are two message areas which display a running commentary when a sort is in progress The lower message area displays a detailed comment on each step in the sort The upper area displays more general messages about major phases in the sort The lower message area is not used when the sort is being run at Fast speed To the right of the bars is a column of controls The first of these is a pop up menu that can be used to select the sorting method Again doing this in the middle of a sort will abort the current sort Next comes a checkbox that can be used to determine whether or not the sort is done at Fast speed When this box is not checked you get to see a cute animation of moving bars also a longer delay is inserted between steps when you run the sort with the Go button The Go and Step buttons are used for executing a sort The Start Again button gives you a new randomized list of 16 bars http math hws edu TMCM java xSortLab index html 1 of 3 3 26 2000 12 50 32 PM The xSortLab Applet Two basic operations are used in sorting compa
255. or S a l of items centered text sizes for effect I suggest that you start by typing some text for your page Start with a headline for the page on a line by itself Press return a couple of times and type in a paragraph or two of introductory text As with a word processor you should press return only at the end of a paragraph lines within a paragraph will be http math hws edu TMCM java labs WebPublishingLab html 3 of 7 3 26 2000 12 50 13 PM Add a table to the page Image H Line Table Spelling Web Publishing with Netscape Composer wrapped automatically to fit in the window where the page is displayed Once you ve gotten some text on the page you can go back and add formatting First of all you should try changing the color of the text and of the page background To do this you need to access a Page Properties dialog box Click on the page with the right mouse button A pop up menu will appear Choose Page Properties from the pop up menu Note that on a Macintosh you can click and hold the mouse button to get the same pop up menu This dialog box has several panels You should be looking at a panel called Colors and Background This dialog box has several panels Click on one of these three tabs to select the panel you want Use custom colors Save colors in page E Normal Text Normal text E Link Text Link text E Active Link Text Active selected link HES Followed Link Text
256. ored Output DATA OUT represents i Eit F the value currently stored in the memory circuit To store a value in the circuit turn the DATA IN wire ON or OFF to represent the value ON for one or OFF for zero Turn LOAD DATA on and off You have to do this slowly enough to allow the circuit time to react When you turn LOAD DATA on the value from DATA IN will flow into the circuit When you turn LOAD DATA off the value in the circuit will be locked and cannot change until the next time LOAD DATA is turned on You can always check what value is stored in the circuit by looking at its output wire DATA OUT Open the 1 Bit Mem circuit turn on the power and work with it to make sure that you know how to use it Registers With the basic one bit memory as a starting point you can build more complex memory circuits Just as you can line up several Adder circuits to get a multibit addition circuit you can combine several one bit memory circuits to get a multibit memory circuit As one of the exercises at the end of the lab you will construct a 4 bit memory circuit A 4 bit memory circuit can store a 4 bit binary number Similarly you can build memory circuits to store 8 bit binary numbers 16 bit numbers or any number of bits Memory circuits of this type are important components in the central processing unit of a computer A memory circuit that is used in the central processing unit to store a binary number is called a regi
257. orms a sort it will tell you how may comparison and copy operations it has done so far This information is displayed in the lower right section of the applet Your first task in the lab is to understand Bubble Sort using the xSortLab applet that you launched above The basic idea of Bubble Sort is to compare two neighboring items and if they are in the wrong order swap them The computer moves through the list comparing and swapping At the end of one pass the largest item will have bubbled up to the last position in the list On the second pass the next to largest item moves into next to last position and so forth Here is a picture of what the applet will look like when it is partway through the sort I ve added some comments to help you understand what you see http math hws edu TMCM java labs xSortLabLab html 2 of 11 3 26 2000 12 50 22 PM xSortLab Lab Whenever the applet compares two bars it draws magenta colored boxes around them Often ane or both of them will be When a bar is colored black it moved soon after the boxes are drawn is in its final position HE Fast as sitalttlaatllll eta ete E S iUi ia ia ii alien ile Start Again Comparisons Bubble Sort Control Area 50 Copies Statistics about the 126 sort that is in progress Phase 4 nest largest item bubbles up to position 13 Is item 6 bigger than item 97 Yes so swap them Bottom message gives the details of a single step in the sort
258. ormula that gives the number of line segments in a Koch curve of any given complexity Exercise 7 This exercise asks you to find the number of line segments in a binary tree of a http math hws edu TMCM java labs xTurtleLab3 html 4 of 6 3 26 2000 12 50 20 PM xTurtle Lab 3 given complexity It is similar to the previous exercise but it s harder to find a formula in this case Run the BinaryTrees example program and then use the TestTree subroutine to draw trees of complexity 0 1 2 3 4 and 5 For each of these trees count the number of straight line segments that it contains For example in a tree of complexity 1 the number of line segments is 3 each branch is a single line and the trunk is the third line You should try to find a formula that gives the number of line segments for any given complexity You might not be able to find a formula that gives the number directly but you should at least be able to find a formula that tells how the number of line segments changes as you go from one complexity level to the next One way to approach this problem is first to determine how many new lines are added to the tree when you go from a tree of complexity N to one of complexity N 1 Then use that to figure out the total number of line segments Another approach is to think recursively Remember that a tree of complexity N 1 is made up of a trunk plus two trees of complexity N Exercise 8 The text notes that you can add randomn
259. orward turn PenUp PenDown clear and home Here are a few more basic commands In this list x and y are parameters You can replace a parameter with a number when you use the command e back x tells the turtle to back up x units that is to move x units in the direction opposite to its current heading For example back 3 tells the turtle to back up three units Negative numbers are allowed as parameters for both forward and back http math hws edu TMCM java labs xTurtleLab1 html 2 of 10 3 26 2000 12 50 15 PM xTurtle Lab 1 Back x is provided only as a convenient shorthand for forward x face x makes the turtle turn to a heading of x degrees from heading zero For example face 90 points the turtle straight up face 90 points it straight down and face 180 points it to the left Note the distinction between turn and face turn specifies a change in direction from the current heading while face specifies a new heading without any reference to whatever the old direction might have been moveTo x y tells the turtle to move from wherever it happens to be to the point with coordinates x and y move x y is related to moveTo x y in the same way that turn x is related to face x That is while moveTo x y says move from the current location whatever it is to the point with coordinates x y move x y says Move x units horizontally and y units vertically from the current location Note that these commands do not depe
260. ource fil The classes Da and so on e same directory as the HTML so taReps zip are in files ip mercial Web pages might want to create To do that However modified contents of that you that page must have You can There is xComputer zip To use one of the applets you can copy the corresponding zip file into urce file e will have an pplet he appl et X dt OM HtO KX An e lt appl This applet tag must refer to the class LogicCircuits applet is For example t lt p align center gt lt applet archive xLogicCircuits lt applet gt he applet ip code tmem xLogicCircuitsApplet class height 380 width 500 gt lt applet gt for your Web page tag to load the zip file and to class for the tmem xLogicCircuitsApplet class t gt tag for using this applet has the form http math hws edu TMCM java tmcm java web site README txt 1 of 3 3 26 2000 12 50 02 PM http math hws edu TMCM java tmcm java web site README txt lt p gt Th tm so th In e classe cm DataR on In e web pa the la Wh s for the epsApplet addition other applets are named similarly ei to tmcm xComputerApplet class and ts which appear right on ass these applet ge ther n th pag in are tmcm and so on xLogicCire lt p ali lt appl lt appl lt p gt
261. outine and the rest of a program In the next section we ll look at other methods of communication You should read the MultiplyBySeven txt sample program and be sure you understand it Load it into memory with the Translate button and execute it You might want to execute it by hand with the Cycle button so that you can follow in detail how it works Modify the program so that it computes 103 7 instead of 34 7 Would you have thought of multiplying a number by seven using the method in this subroutine Of course a major point about subroutines is that when you are using a subroutine that someone else has written for you you don t really care so much how it performs its task as long as it does it correctly You use the subroutine as a black box Parameters and Local Names It is not always possible to pass parameter values in registers In xComputer for example there is only register the accumulator that can be used for parameter passing But some subroutines require two or more parameters The solution is to use reserved memory locations for the parameter values just as is done for the subroutine s return address Similarly a return value from a subroutine can be placed in a reserved memory location rather than in a register This method is a little more difficult than using registers but it is also more flexible Look at the sample program MultiplyTwoNumbers txt This sample program includes a subroutine that can multiply any
262. ow did you go about finding it Exercise 4 Guess the URL of the home page of each of the following Explain your reasoning Check the Web to see whether you are right The IBM corporation e The FBI an agency of the US government e Harvard University e The SPCA an animal rights organization http math hws edu TMCM java labs DataRepsLab html 7 of 9 3 26 2000 12 50 04 PM Introductory Lab Exercise 5 Pick out one or two of the following phrases Each phrase is a fragment of a reasonably well known quotation Search the Web for uses of the phrase Use the Alta Vista advanced search enter the phrase in quotes into the text input box This will not work with the regualar Alta Vista search Try to find the complete phrase and the original source of the phrase Also try to find a few interesting variations that people have used on their Web pages e a truth universally acknowledged e yes Virginia there is e on the shoulders of giants Exercise 6 In addition to working on some of the above exercises you should spend some time surfing the World Wide Web Write a short essay describing your experiences with the Web and speculating on its possible impact and importance Exercise 7 Use the DataReps applet to find the following In each case indicate briefly what you did with the applet to answer the question e Find the ASCII code of the upper case letter X e Find the character that has an ASCII code equal to 63
263. own also some information tutorial pages for each applet The applets can The purpose but a course unless I will consider You are welcome this archive on You are also welcome to creat use the applets your own sample inp be lab worksheets ask my to post the entire your own Web server will probably want version of address h USING THE T APPLE T the appl tmcm java apps whic ttp ma TS The Most There are The and it includes links to all the like to use any of the material in this archive please contact me for permission information is given below freely used for any non commercial purpose can be used for any private that they not be used as an official textbook is adopted for that course making exceptions to t non commercial part of his un If you do this ets ON YOUR OWN WEB T non com ut files for the applets to download the stand alone application That version is in an archive named h is available through a link at the th hws edu TMCM newjava DownloadingAndInfo htm1 you PAGES To use one of the applets on a Web page access to the compiled Java program for that applet find these programs in the directory named classes inside the tmc on LogicCircuits m java directory e zip file for each applet ip 5 a Web page y y e HTML s
264. p math hws edu TMCM java xModels info html 8 of 9 3 26 2000 12 50 33 PM xModels Info with no numbers between For example 0 10 represents a quantity that varies evenly from 0 to 10 across both segments of a two segment animation David Eck eck hws edu June 1997 http math hws edu TMCM java xModels info html 9 of 9 3 26 2000 12 50 33 PM xModels Tutorial xModels Tutorial Examples The xModels Applet displays wireframe models of still images and animations which are specified in a simple scene description language The applet at the bottom of this page will try to load six tutorial examples To read an example select it from the pop up menu at top of the applet Then to see the image it produces click on the RENDER button or select Graphics from the pop up menu For full information on the applet and the language see the xModels Info page The six tutorial files are also directly available as text files using the following links 1 2 3 4 5 6 Java not available David Eck eck hws edu June 1997 http math hws edu TMCM java xModels tutorial html 3 26 2000 12 50 34 PM http math hws edu TMCM java xModels samples Tutorial1_Basics txt xModels Tutorial 1 Basic Ideas A program written in the xModels scene description language is basically a list of the objects in the scene with transformations that say how the objects are sized oriented and placed Ther
265. p you need to test whether the number is sixteen If it is jump to a HLT instruction at the end of the program Testing whether a number is sixteen http math hws edu TMCM java labs xComputerLab1 html 9 of 10 3 26 2000 12 50 09 PM xComputer Lab 1 requires two steps First subtract 16 from the number and then test whether the answer is zero Use a JMZ instruction to test whether the answer is zero This is like a JMP instruction except that the jump only occurs if the number in the AC is zero Write a paragraph explaining how your program works Lod e 1 This is the original counting program sto 12 lod 12 inc sto 12 jmp 2 NIE Add a halt instruction at the end Exercise 8 Describe what is done by the CountAndStore program which you encountered earlier in the lab Discuss how it works in some detail To do a good job on this exercise you will have to step through several executions of the loop in the program and study how it works Exercise 9 Discuss what you learn from the CountAndStore program about data and instructions and the relationship between them The memory of a computer can hold both data and instructions How does the computer distinguish between them Does it Exercise 10 Run the CountAndStore program at Fastest Speed with the display set to Graphics If you let the program run long enough it will halt How is this possible since the program contains no HLT instruction To figure this
266. perText Transfer Protocol HTTP is the most common method used for communication on the Web Another common protocol is File Transfer Protocol FTP an older method for transferring files from one computer to another You might also run across some other protocols in URL s A domain name such as math hws edu identifies a particular computer on the Internet Most of the computers that are used as servers of data on the Web have domain names that begin with www such as www whitehouse gov You can often read some information about a computer from its domain name The computer named math hws edu is in the Mathematics Department math at Hobart and William Smith Colleges hws which is an educational institution edu The last part of the domain name such as gov or edu is called the top level domain Top level domains include e COM for commercial purposes e EDU for educational institutions e GOV for government computers e MIL for the military e ORG for other organizations e NET for certain Internet services These domains are usually used by computers in the United States Computers in other countries generally use two letter country codes for their top level domains For example a domain name ending in it indicates a computer in Italy and ca is used by Canadian computers Many companies organizations and institutions have home pages on the Web If you know something about domain names you can often guess the URL us
267. plications in tmcm jar open a DOS window and change to the tmcm java apps directory This is the directory that you got when you unzipped this archive Tip Open a directory window for this directory Then select the Run command from the Start menu and enter command in the dialog box that pops up This will open a DOS window already set to use tmcm java apps as its working directory You have to tell jview to put tmcm jar on its classpath This is done by adding the option cp tmcm jar to the command So the commands for running the three applications are jview cp tmcm jar tmcm Apps jJview cp tmcm jar tmcm Labs jJview cp tmcem jar tmcm Tutorials Alternatively if you have the JDK Java Development Kit installed on your computer you can use the JDK s Java command to run the applications This is similar to the jview command but unfortunately you also have to specify the location of the standard system classes These are contained in a file named classes zip in one of the JDK directories You need the full path name of this file such as C jdk1 1 8 lib classes zip This is the correct name if you using version 1 1 8 of the jdk and did the default installation For other versions of the jdk only the numbers should be different Once you ve found this file the commands for running the applications are java classpath tmem jar C jdk1 1 8 lib cla
268. program Names can be any number of characters Rate 0 07 Decimal numbers are OK DECLARE money interest More variables money 1000 interest Rate money PenUp MoveTo 8 8 PenDown DrawText Interest on S money is interest The value of a variable can be included in a string Just include the character followed by the name of the variable When the string is actually printed the value of the variable is shown x random Assign a random value in the range 0 0 to 1 0 to x The value will be different every http math hws edu TMCM java xTurtle samples Tutorial2_variables txt 1 of 2 3 26 2000 12 50 35 PM http math hws edu TMCM java xTurtle samples Tutorial2_variables txt time the program is run Note that x was already declared so I don t have to declare it again In fact it would be an error to do so y randomInt 100 y is assigned a random integer in the range 1 to 100 DrawText Here s a random number x DrawText Here s a random integer y http math hws edu TMCM java xTurtle samples Tutorial2_variables txt 2 of 2 3 26 2000 12 50 35 PM http math hws edu TMCM java xTurtle samples Tutorial3_io txt xTurtle Tutorial Example 3 I O I O or Input Output refers to the exchange of information between a program and the person using the program All the turtle graphics commands
269. put It turns its output on if both of its inputs are on An OR gate also has two inputs It turns its output on if either one of its inputs is on or if both are on The NOT gate has one input and one output It turns its output on if and only if its input is off Inputs and Outputs can be placed anywhere along the outer boundary of the circuit An Input represents an input for the circuit as a whole When the power is on you can turn Inputs on and off manually by clicking on them An Output represents a value computed by the circuit The values of Outputs cannot be set manually A Tack is simply an attachment point for wires You might want to use Tacks to help make your circuits neater Once some components have been dragged onto the circuit board you can draw wires to connect them Every wire leads from a source to a destination To draw a wire you have to click the mouse first on the source Then hold the mouse button down while you move the mouse to the destination When you release the mouse button the wire will be added to the circuit If you release the mouse button when the mouse is not over a valid destination no wire will be drawn Circuit Inputs are valid sources for wires So are Tacks So are the outputs of gates Valid destinations include circuit Outputs inputs of gates and Tacks You can draw as many wires as you want from a source but you can only draw one wire to a http math hws edu TMCM java xLogicCircuits index html 1 o
270. quation to predict the running time T for any array size N even for arrays that are two big for you to experiment with Use the equation to predict the value of T when N is equal to one billion One billion is 1000000000 or 10 This is the amount of time that your computer would take to sort one billion items using Selection Sort The equation gives T in terms of seconds but you should convert your answer to years Similarly you can use the equation T K N log N and the value of K that you found in Exercise 8 to predict the running time T for QuickSort for arrays of any size N What is the prediction for the running time of QuickSort on an array of one billion items Give your answer in terms of hours Comment on the answers to the two parts of this exercise This is one of a series of labs written to be used with The Most Complex Machine A Survey of Computers and Computing an introductory computer science textbook by David Eck For the most part the labs are also useful on their own and they can be freely used and distributed for private non commercial purposes However they should not be used as a formal part of a course unless The Most Complex Machine is also adopted for use in that course David Eck eck hws edu Summer 1997 http math hws edu TMCM java labs xSortLabLab html 11 of 11 8 26 2000 12 50 22 PM xTurtleLab 4 Labs for The Most Complex Machine xTurtle Lab 4 Multiprocessing A CENTRAL PROCESSING UN
271. quence The purpose of the machine is to separate the x s from the y s For example given the input XXYXYYXYXx it will change the tape to read xxxxxxyyyy The output string does not have to be in the same place on the tape as the input string but it should be the only thing on the tape when the machine halts There are many ways to make such a machine Exercise 9 Write a description of the algorithm that is used by the sample machine AddBinaryNumbers to add two binary numbers on its tape Your object is to express an understanding of the process used A description that is on too high a level such as It adds the numbers digit by digit from the right doesn t really explain the process A very low level description doesn t provide any understanding of the goals or purpose of the actions taken Exercise 10 The Turing machines you worked with in this lab can use only the symbols 0 1 x y z and blank But this is an arbitrary limitation imposed by the xTuringMachine applet In fact a Turing machine could be built to use any finite number of different symbols But no matter how many symbols a Turing Machine might use the same computation could be done by a machine that uses only the symbols 0 1 and blank Why is this true Think about the way data is represented in a real computer If this is the case then why bother with Turing Machines that use more than the minimum number of symbols Exercise 11 I have claimed that Turing m
272. r In this picture there are seven bumps Note that the number of vertical lines is one more than the number of horizontal lines PLJ LI LILI LU LI Exercise 10 Convert your program from Exercise 9 into a subroutine in which the number of bumps is specified by a parameter How would your subroutine be used to produce a picture with seven bumps like the one shown above Exercise 11 The contract of a subroutine is defined to be everything you need to know about a subroutine in order to use it correctly This includes the name of the subroutine and its list of parameters It also includes specifications of what must be true before the subroutine is called and what will be true after it finishes execution These specifications are the preconditions and the postconditions of the subroutine In an xTurtle subroutine the preconditions and postconditions usually include statements about the position and orientation of the turtle and about what is drawn on the screen Here are two square drawing subroutines Describe the contract of each subroutine Include complete specifications of the preconditions and postconditions for each subroutine SUB square r g b size SUB square x y S1ze rob r g bD PenUp forward size moveTo x y turn 90 PenDown forward size move size 0 turn 90 move 0 size forward size move size 0 turn 90 move 0 size forward size END SUB turn 90 END SUB This is one of a series of labs wr
273. r s memory You will then be able to run the program or to step through it one step at a time The sample programs are also available as plain text files 1 2 3 4 This is a rather technical applet and you will probably need to read the documentation to understand it Documentation is available on the xComputer Info page For a list of other applets and for lab worksheets that use the applets see the index page Java not available David Eck eck hws edu June 1997 http math hws edu TMCM java xComputer index html 3 26 2000 12 50 27 PM http math hws edu TMCM java xComputer samples TheBasics txt Example 1 B asics This file contains a fairly simple program written in the assembl Y assemb y language programs language of xComputer It illustrates a few basic language instructions and the format of assembly Note that a semicolon and anything that follows it on a line is a comment The program computes the sum of a list of numbers The list can only contain non zero numbers A zero marks the end of the list 7 of this fil as part of the program The list of numbers is at the end They are actually treated by the computer is simply stored in memory other hand i that instruction in machine number that is actual A number on a line by itself An instruction on the s translated into a number that
274. random walk and records it in the shared variable angle The other turtle reads the value from the shared variable and uses it A second shared variable control is used in a grab statement to control access to angle Exercise 6 asks you to modify this program so that more than two processes are involved http math hws edu TMCM java labs xTurtleLab4 html 4 of 7 3 26 2000 12 50 23 PM xTurtleLab 4 Another example of shared variables is given in the sample program ThreeNPlusOneMax txt Read the comments in the program and run the program It will take a few seconds to run and you won t see anything happening until the end when the program reports the value that it has computed In Exercise 7 you will work with a similar example The ThreeNPlusOneMax program also illustrates what happens when a fork command is used inside a subroutine At the end of the subroutine all the processes are rejoined into one process before the subroutine terminates After the subroutine finishes there is only one process to carry on The forking is part of the subroutine s black box it has no effect outside the subroutine In the sample program there is only one process to execute the TellUser statement at the end of the program Exercises Exercise 1 Modify the sample program Bugs txt so that each bug will leave a trail behind it as it wanders randomly around on the screen Each of the trails should be a different color The screen should look som
275. ransformation scale 5 magnifies an object by a factor of 5 To shrink an object you would use a scaling operation with a factor less than 1 as for example in square scale 0 5 The scale command can also be used with two numbers The first number gives a horizontal scaling factor and the second a vertical scaling factor For example square scale 2 5 specifies a rectangle that is 2 units wide and 5 units tall By the way the comma in 2 5 is optional The xModels applet ignores commas You can put them in if you like for human readability The transformation rotate 45 pivots an object through an angle of 45 degrees in a counterclockwise direction about the point 0 0 A negative angle would rotate the object in a clockwise direction It is possible to specify a different pivot point For example square rotate 45 about 0 5 0 5 would pivot the square about its upper right corner 0 5 0 5 instead of about 0 0 The transformation translate 3 7 moves an object 3 units to the right and 7 units up Negative numbers can be used to move the object to the left and down If the translate command is used with just one number as in translate 5 it indicates horizontal movement to the left or right For convenience there are also commands xtranslate and ytranslate for moving an object horizontally or vertically only For example square ytranslate 5 produces a square translated five units upwards You can apply a sequence of transformations to the
276. rc 2 90 forward 3 Arc 2 90 forward 3 A box with rounded corners has been drawn PenUp MoveTo 5 5 Move again PenDown black Draw in black DrawText Hello Write the message Hello at current cursor position DrawText World This lines up under the Hello http math hws edu TMCM java xTurtle samples Tutorial1_basics txt 2 of 2 3 26 2000 12 50 34 PM http math hws edu TMCM java xTurtle samples Tutorial2_variables txt xTurtle Tutorial Example 2 Variables A variable is a name that can be used to hold a value Variables must be declared before they are used A variable can be assigned a value with an assignment statement Variables and functions can be used to compute values from complex expressions such as 3 sin x 3 DECLARE x y Allows you to use the variables named x and y x 2 Assignment statement puts the value 2 into into the variable x y 2 sqrt x Computes sqrt 2 multiplies it by 2 and assigns the resulting value to y Sqrt computes the square root There are other predefined functions forward x Variables can be used in commands t rnt 135 Negative turn rotates the turtle in a clockwise direction forward y turn 135 forward x These commands have drawn a Z shape DECLARE Rate Declares another variable They don t have to be declared at the start of the
277. rcuits About the Sample Circuits The sample circuits loaded by the applet on this page are all fairly standard examples of logic circuits The XOR circuit which is visible on the circuit board when the applet starts up is discussed above The 4 Bit Adder is a circuit that can be used to add two 4 bit binary numbers When the numbers are put on the eight input wires at the top of the circuit the sum which can have five bits appears on the five output wires on the bottom and left of the circuit The output on the left is the carry bit The Clock circuit has one input and one output If you turn on the power it will start turning its output wire on and off If you turn on the input however the clock will stop ticking It is worthwhile to watch this example with the speed set to Moderate or Slow You can slow down the rate of ticking by inserting more Tacks into the loop This is because of the way signals are propagated through circuits The simulated circuits in this applet use discrete time At each discrete moment of time each component in a circuit gets the values from its input wires and computes values for each of its output wires Real circuits don t work this way Nevertheless the logical behavior of most simulated circuits is with a few exceptions the same as the behavior of real circuits The One Bit Mem circuit is a memory circuit that remembers the value of one bit To store a bit ON or OFF put the va
278. rcuits that have the same name but that are different internally My advice of course is don t do it By the way a circuit can have multiple outputs When you draw a wire from a subcircuit to another component make sure that the wire starts from the output that you want Other Features The Clear button can be used to clear all the components from the circuit board If several circuits are stacked up on the board it only affects the one on top The Clear button does not remove circuits from the pallette If the circuit you Clear is an enlarged subcircuit that is part of another circuit the Clear button does not remove the circuit Inputs and Outputs This is on the theory that they are probably connected to other components in the containing circuit and you probably don t want to delete all the connecting wires However you can still delete the Inputs and Outputs individually if you insist Note You can use the Undo button to undo a Clear provided that you do so before you do any other operation The Save and Load buttons are for working with files Hoewever it is likely that your browser s security policy will prevent you from using them The Save command saves the entire state of the applet including all the circuits in the pallette and on the circuit board When you Load a file everything in the applet is thrown away and replaced by the data in the file Note that the Load command is undoable Pressing the Undo button imme
279. re used in assembly language programming and why they are so important Give examples of things that can be done with labels that would be much harder to do without them This is one of a series of labs written to be used with The Most Complex Machine A Survey of Computers and Computing an introductory computer science textbook by David Eck For the most part the labs are also useful on their own and they can be freely used and distributed for private non commercial purposes However they should not be used as a formal part of a course unless The Most Complex Machine is also adopted for use in that http math hws edu TMCM java labs xComputerLab2 html 7 of 8 3 26 2000 12 50 10 PM xComputer Lab 2 course David Eck eck hws edu Summer 1998 http math hws edu TMCM java labs xComputerLab2 html 8 of 8 3 26 2000 12 50 10 PM xComputerLab 3 Labs for The Most Complex Machine xComputerLab 3 Subroutines A SUBROUTINE IS A SET OF INSTRUCTIONS for performing some task chunked together and thought of as a unit Like loops and decisions subroutines are useful in the construction of complex programs The machine language for xComputer does not provide direct support for subroutines But then again it doesn t really provide direct support for loops and decisions which must be implemented by the programmer with jump and conditional jump instructions Similarly it is possible to implement subroutines using jump instructi
280. re you could use a number For example he command JMP start will jump to the ocation with label Start KH t KO The program in this file uses several labels such as loop doAdd N1 and ANS Some of these label refer to instructions and some of them refer to data Both of these uses are very common Note by the way that the way this program is formatted isn t important as long as there is at most one instruction or data value per line Also you should know that the computer doesn t distinguish between upper and lower case letters in instructions or in label names This program multiplies two numbers stored in locations N1 and N2 The result is left in location number ANS How this works isn t important but essentially it is a loop that looks at the bits in N1 When a bit is found that is 1 N2 is added to ANS In any case each time through the loop N2 is multiplied by 2 For this to give the correct answer the answer must be in t u he range of numbers that can be represented Sing 16 bits The program lod c 0 Start by putting a zero into ANS sto ANS loop lod N1 If N1 is zero the process is complete jmz done shr Otherwise shift N1 one bit right sto N1 jmf doAdd If the bit shifted off the end of N1 was a one jump to doAdd to add N2
281. rea facing right with the pen down and with the drawing color set to red Run the Necklace program and try to understand how it works As another example click on the New Program button and then type in and run the following program Instead of typing it you might want to be clever and use cut and paste DECLARE hue hue 0 LOOP hsb hue 1 1 http math hws edu TMCM java labs xTurtleLab1 html 5 of 10 3 26 2000 12 50 15 PM xTurtle Lab 1 forward 5 back 5 turn 360 100 hue hue 0 01 exit if hue 1 END LOOP This program uses a variable named hue You can use any names you want for variables as long as you avoid words that already have a special meaning such as loop and if A variable is just a memory location which has been give a name and which can be used to store a value In xTurtle you give a name to a memory location with a declare statement Once you have declared a variable you can store a value in it with an assignment statement which has the form lt variable name gt lt value gt The operator is called the assignment operator It tells the computer to calculate the value on the right and to store it into the variable on the left The value on the right can be given as a number as another variable or as a mathematical formula For example hue hue 0 01 x 17 newAmount oldAmount cost length width costPerSquareFoot Next we turn to an example that intr
282. register is a 1 then the program should add 1 to Count The loop continues until the value of Num becomes zero At that point Count contains the number of 1 s that were in the original number Exercise 5 Just as it is possible to multiply by adding over and over it is possible to divide by subtracting over and over Suppose you want to know how many times N1 goes into N2 Start with N2 and subtract N1 repeatedly until the answer is less than N1 The number of subtractions you performed is the number of times that N1 goes into N2 For example you can compute that 4 goes into 14 three times by computing 14 4 4 4 2 The number 2 that you end up with here is the remainder when 14 is divided by 4 Write a program to compute how many times a number N1 goes into another number N2 Your program will be somewhat similar to the sample program MultiplyByAdding txt You still need a loop and you still need to count how many times that loop is executed However the set up before the loop the action performed in the loop and the test for ending the loop are different Note that to test whether A lt B you can subtract B from A and test whether the result is negative In the language of xComputer you can use a JMN instruction to test whether a number is negative Exercise 6 The sample program ListSum txt adds up a list of numbers Modify this program so that instead of computing the sum of the numbers in the list it will find the largest n
283. rent x coordinate of the turtle ycoord gives the current y coordinate of the turtle Assignment Statements The value of a variable can be changed by using an assignment statement An assignment statement takes the form lt variable gt lt expression gt where lt variable gt is any declared variable or the name of a parameter in a user defined subroutine or function and lt expression gt can be a number a variable or any expression created using operators and functions as described above Here are some example assignment statements Rate 0 7 y i Oe 2 a aL count count 1 r exp theta Built in Subroutines The xTurtle language includes many predefined subroutines Most of the predefined subroutines are turtle graphics commands which move or turn the turtle or affect its state Two predefined subroutines related to multitasking Fork n and KillProcess are discussed later The others built in subroutines are http math hws edu TMCM java xTurtle info html 5 of 13 3 26 2000 12 50 17 PM xTurtle Info forward x moves the turtle forward by a distance x along the direction in which it is currently facing If x is negative the turtle actually moves backward Whether it draws a line and what color that line is depends on the current state of the turtle This same proviso applies to all the commands that move the turtle and I will not repeat it back x moves the turtle backwards by a distan
284. ression A and not B or B and not A This expression in turn serves as a blueprint for the circuit You can use it as a guide for building the circuit The expression given earlier A and C or B and not C corresponds to another sample circuit shown in the illustration above provided you label the inputs appropriately To sum up given any expression of Boolean algebra a circuit can be built to compute that expression Conversely any output of a logic circuit that does not contain a feedback loop can be described by a Boolean algebra expression This is a powerful association that is useful in understanding and designing logic circuits Note Feedback occurs when the output of a gate is connected through one or more other components back to an input of the same gate Circuits with feedback are not covered in this lab However they have important uses that are covered in the next lab Building Circuits You can build your own circuits in the xLogicCircuits applet Click on the Iconify button at the bottom of the applet This will put away the Basic Gates circuit by turning it into an icon on the pallette You ll have a clear circuit board to work on As an exercise try to make a copy of the sample circuit shown above which corresponds to the Boolean expression A and C or B and not C To add a component to your circuit click on the component in the pallette hold down the mouse button and use the mouse to drag t
285. rforms this task Exercise 2 Suppose that Bubble Sort is applied to the following list of numbers Show what the list will look like after each phase in the sort 73 21 15 83 66 7 19 18 Exercise 3 Suppose that Selection Sort is applied to the list of numbers given in Exercise 2 Show what the list will look like after each phase in the sort Exercise 4 Suppose that Merge Sort is applied to the following list of numbers Show what the list will look like after each phase in the sort 73 21 15 83 667 19 18 21 44 58 11 91 82 44 39 Exercise 5 Suppose you have a list of names You could sort the list into alphabetical order either by first name or by last name Suppose that the list is already sorted by last name For example Phil Doe Jane Doe Fred Doe Bill Jones Jane Jones Mary Smith http math hws edu TMCM java labs xSortLabLab html 9 of 11 3 26 2000 12 50 22 PM xSortLab Lab Fred Smith Jane Smith Now suppose that you take this list and sort it into alphabetical order by first name In the new list Jane Doe Jane Jones and Jane Smith will be grouped together The question is will they be in that order That is will people with the same first name still be in alphabetical order by last name For some algorithms the answer is yes Other algorithms however can mess up the relative order of a group of people with the same first name A sorting algorithm that will always preserve the order of people with the same fi
286. rial before working on the lab This lab includes the following sections e Multiple Turtles e Scheduling e Shared Variables e Exercises Start by clicking this button to launch xTurtle in its own window Sorry your browser doesn t do Java For a full list of labs and applets see the index page http math hws edu TMCM java labs xTurtleLab4 html 1 of 7 3 26 2000 12 50 23 PM xTurtleLab 4 Multiple Turtles After launching xTurtle select the first sample program Bugs txt from the pop up menu at the top of the xTurtle window Run the program by clicking on the Run Program button You will see ten turtles wandering around on the screen This is a very simple program but it illustrates the basic multiprocessing command in xTurtle the fork statement The statement fork 10 causes a single process to split into ten processes Any commands in the program that follow the fork statement will be executed by each process independently and simultaneously In the Bugs program each of the ten processes goes into a loop that sends its turtle on a random walk and so you see all ten turtles wandering aimlessly on the screen Each turtle follows the same program but each turtle chooses different random numbers and so each turtle follows its own random path The first two exercises at the end of the lab ask you to add a few modifications to this program When a process is forked all of the processes that are created start out in e
287. ring two items to see which is bigger and copying an item from one place to another The number of comparisons and the number of copies used in the current sort are displayed below the controls Timed Sort Mode If you switch to the Timed Sort panel you ll see a large message area with some instructions This panel is used to obtain statistics about the running times of various running algorithms The interesting question is how the running time depends on the number of items being sorted There is a text input box at the top of the panel where you can specify the size of the array that is to be sorted You can also specify the number of arrays to be sorted The point is that a small array takes so little time to sort that the time cannot be measured accurately So you should sort a number of arrays all of the same size You can measure the total time it takes to sort them all The time required to sort one array can be obtained by dividing the total time by the number of arrays You probably want to adjust the number of arrays so that the total time is at least a couple of seconds Note Your computer must have enough memory to store all the numbers you want to sort If you are running the applet at all you probably have enough memory to work with at least one million items If you ask for more numbers than you have room for you should just a message telling you that you don t have enough memory However most systems that I have tried this o
288. rks behind the scene to sort arrays of randomly generated numbers An array is just a numbered list of items the size of the array refers to the number of items in the list As the computer sorts the arrays it displays various statistics in the large green area in the center of the applet The statistics are updated about twice every second At the top of the applet there is a text input box where you can type the size of the arrays to be sorted There is also a box where you can type the number of arrays to sort The computer will create the number of arrays that you specify Each array will have the size http math hws edu TMCM java labs xSortLabLab html 6 of 11 3 26 2000 12 50 22 PM xSortLab Lab that you specify The computer fills all the arrays with random numbers Then it sorts each array one after the other The reason for using more than one array is that for small arrays the time it takes to sort a single array is a tiny fraction of a second Since xSortLab can t measure very small time intervals accurately the only way to get an accurate idea of the sorting time for small arrays is to sort a lot of arrays measure the time it takes to sort them all and divide the total time by the number of arrays For larger array sizes using more than one array is not so important but it might still give you a more accurate measurement At the bottom of the applet you will see a pop up menu that can be used to select the sorting algor
289. ronizedRandomWalk txt so that instead of showing two turtles moving in identical random walks it shows five turtles moving in identical random walks Each of the turtles should start from a different position and should draw in a different color The hard part of this exercise is passing off the control from one http math hws edu TMCM java labs xTurtleLab4 html 6 of 7 3 26 2000 12 50 23 PM xTurtleLab 4 turtle to the next You have to make sure that the control goes through the values 1 2 3 4 5 and then back to 1 so that each turtle will get a chance to move Just as in the original program Turtle 1 should select the random angle Each of the other four turtles should use the same angle Exercise 7 The Sample program SumOfSquares txt is a failed attempt to write a program that computes the value of the sum 12 22 32 252 Run the program several times It will give a different answer each time If you ve turned on the Lock Step checkbox then you ll get the same answer each time but it will still be an incorrect answer Use a grab statement to fix the program so that it gives the correct answer See the ThreeNPlusOneMax txt sample program for an example of using a grab statement for a similar purpose Write a short essay explaining carefully what goes wrong when the grab statement is omitted and how adding the grab statement fixes the problem Exercise 8 Design your own parallel processing xTurtle program Try
290. rowser window Select Page Composer from the Netscape menu Use any one of these methods to open a window where you can create your page There will be a large area where you can type your page and several toolbars along the top of the window One toolbar is used to set the style of the text you type You can have italic text big text colored text centered text and so on The other toolbar is used to add HTML features such as graphics links and tables to the page The toolbar commands are also available in Insert and Format menus in case you prefer using menus Click to add a hypertext link or just drag a link from another page The Composer Toolbars f Click to add an i mage Check spelling The Publish butt sed t j send ar E Click Preview to see your or just drag an image of the text on server account page ina browser window from another page the page New Open Save Publish Preview Cut Copy Paste Print Find Link Target i Heading 1 7 Variable Width 24 7 Increase or decrease indentation of selected text Select common text styles bold italic underlined or plain Paragraph style pop up Select Heading 1 2 or 3 for headlines Heading 1 is biggest For mostother Text size pop up Use these buttons i i Color pop u eee ral om lene vee rises ebb i for als if aA to create bulletted Choose left justified at Normal 1 1 color or numbered lists right justified
291. rst name is said to be stable Is Selection Sort a stable algorithm Why or why not How about Bubble Sort Why or why not You might want to apple Bubble Sort and Selection Sort to the above list to see what happens Exercise 6 Consider the data that you collected on the compute time of the five sorting algorithms For arrays of size 100 how do the algorithms rank according to speed How about for arrays of size 5 The two orderings should be very different How can this be If one algorithm is faster than another for arrays of size 5 why shouldn t it be faster for arrays of size 100 Exercise 7 Selection Sort is an N algorithm You should be able to use data you collected in this lab to compute the value of K in the equation T K N2 for Selection Sort running on your computer Recall that N here is the array size and that T is the time it takes to sort one array of size N Also remember that the equation is only approximately true Make a table showing the following information for each array size N for which you collected data The array size N the number of arrays you sorted the total computation time to sort the arrays the computation time for one array T and the computed value T N N which is an approximation for K Based on the data in your table what is your best guess for the actual value of K Explain your reasoning For your convenience here is an applet that you can use to do the computation Enter the array size
292. s The Web is huge and it has information on almost anything you can think of There are millions of computers on the Internet Each of those computers can run a Web site and publish Web pages No one controls this no one has to authorize it at least not yet In fact you can publish your own information on the Web One of the later labs will deal with this URL s and All That Every page of information on the Web is identified by a URL Uniform Resource Locator Other resources such as pictures and sounds are also identified by URL s When you are viewing a page with a Web browser the URL of that page is usually displayed in a box near the top of the browser s display window If you know the URL for a page you can go directly to that page by entering the URL in that box and pressing return A typical URL is http math hws edu TMCM java index html This is the URL for a page that describes all the labs and applets that I have written for use with The Most Complex Machine This URL has several meaningful parts http math hws edu TMCM java labs DataRepsLab html 2 of 9 3 26 2000 12 50 04 PM Introductory Lab Protocol tells the Web browser what method to use to fetch the page a Domain name specifies which computer contains the page http math pws edu TMCM java index htm Directory gives the location of the page on the computer File name is the file that contains the contents of the page The Hy
293. s Start by clicking this button to launch xTurtle in its own window Sorry your browser doesn t do Java For a full list of labs and applets see the index page Preconditions The xTurtle applet that you have launched should have loaded a sample program called NestedSquares Select this program using the pop up menu at the top of the applet Read the program and the comments and run the program by clicking on the Run Program button For this example and for much of the lab I suggest that you use the speed pop up menu to reduce the speed at which programs are executed so that you will better understand what is going on As explained in the text the key to getting this program correct was making sure that the preconditions for drawing each square were set up properly A precondition is something that must be true at a certain point in a program if the program to continue correctly from that point http math hws edu TMCM java labs xTurtleLab2 html 1 of 7 3 26 2000 12 50 19 PM xTurtle Lab 2 The following picture taken directly from Figure 6 9 in the text shows the correctly drawn squares and the results of five incorrect attempts to draw them For each of the incorrect versions the error can be traced to the fact that one or more preconditions was not met in the program that produced that picture a b e d fai In the NestedSquares program there are several statements near the end of the loop that are r
294. s The lab is based on the material in Section 12 1 of The Most Complex Machine Some of the questions at the end of Chapter 12 and their answers in the back of the book are also relevant The lab includes the following sections e Introducing xModels Basic Objects and Basic Transformations Animation Defined Objects and Structured Complexity e Exercises Start by clicking this button to launch the xModels applet in its own window Sorry your browser doesn t do Java For a full list of labs and applets see the index page http math hws edu TMCM java labs xModelsLab1 html 1 of 10 3 26 2000 12 50 25 PM xModels Lab 1 Introducing xModels The xModels applet that you launched above is set up to load several sample programs Programs for xModels are actually scene descriptions written in a scene description language A scene description consists of a list of objects in a scene together with geometric transformations to be applied to the objects and attributes that affect the object s appearance In xModels the only attribute that an object can have is a color A scene description can include definitions of objects to be used later perhaps repeatedly in the scene Such object definitions are very much like subroutines in a programming language Finally there are a few special purpose commands in the xModels scene description language that can be used to control such things as the background color and the numb
295. s inside the unit cube and a cylinder is a similarly sized cylinder These objects are pretty small but they can of course be scaled For example if you want to see what a cone looks http math hws edu TMCM java labs xModelsLab2 html 2 of 7 3 26 2000 12 50 26 PM xModels Lab 2 like try a scene description that contains the command cone scale 10 There is also a polygon_3D command which constructs a polygon from a list of three dimensional points instead of two dimensional points Later in the lab you ll see two other commands lathe and extrude which can produce interesting objects Just as in two dimensions the geometric transformations in three dimensions include scaling translation and rotation The scale command can be used with one two or three parameters With one parameter as in scale 5 it magnifies an object equally in all three directions If three parameters are given they specify different scaling factors in each direction For example cube scale 5 0 5 2 makes a rectangular solid that is 5 units long in the x direction 0 5 units high in the y direction and 2 units thick in the z direction If a scale has only two parameters then the same scaling factor is used in the z direction as in the y direction This version is provided mostly for use in two dimensions where any scaling in the z direction has no effect in any case The translate command can also be used with one two or three parameters In its
296. s like a truncated pyramid You could also try adding another point or two to the end of http math hws edu TMCM java labs xModelsLab2 html 4 of 7 3 26 2000 12 50 26 PM xModels Lab 2 the lathe command The extrude command is similar to lathe It also takes a sequence of points in the xy plane connects them with line segments copies the resulting figure a specified number of times and then joins the vertices of the copies with more line segments However in this case the copies are translated in the z direction rather than rotated around the y axis The copies are stacked up in front of and behind the screen Each copy is separated from the next by a distance of one unit The simple example extrude 10 1 0 1 0 will create a ladder like object with 10 rungs It will lie along the z axis so if you want to see it you should apply an xrotate 90 to it The sample program LatheAndExtrude contains several examples of lathing and extrusion You should read the scene description and render it Exercises Exercise 1 Make an animation showing three cubes of different colors nested inside one another One cube should rotate about the x axis one about the y axis and one about the z axis Exercise 2 The Flaps example program shows an abstract sort of paddle wheel that rotates about the y axis Paddle wheels are supposed to rotate vertically Modify the Flaps example so that the wheel is vertical and rotates about the x axis This
297. s page contains links for downloading a set of labs and applets that were written by David Eck for use with his introductory computer science textbook The Most Complex Machine The labs and applets are also available on line at http math hws edu TMCM java Information about using this material is in the README files for the downloads which are also available below for reading on line In addition to the archives a pdf version of the labs and applet information is available at the bottom of this page Note that many of the downloads are available in two formats ZIP archives with file names ending in zip and TAR GZ archives with file names ending in tar gz The contents are identical except that text files in ZIP archives are in Windows DOS format while text files in TAR GZ archives are in Linux UNIX MacOSX format For most purposes it doesn t matter which archive you use as long as you can unpack it ZIP archives can be used directly in Windows XP In any version of Windows you can unpack a ZIP archive using WinZip available from www winzip com or Aladdin Expander available from www aladdinsys com You Web browser might already be configured to unpack the archive when you download it In MacOS X your Web browser should unpack any archive that you download If not you can use Stuffit Expander available from www aladdinsys com If you are still using MacOS 9 0 or earlier see the bottom of this page On Linux UNI
298. screen will move in lock step While this might not be an accurate simulation of multitasking it can be pretty to watch You might want to try executing some of the sample programs with this option turned on http math hws edu TMCM java labs xTurtleLab4 html 3 of 7 3 26 2000 12 50 23 PM xTurtleLab 4 Shared Variables In all the examples you have seen so far the multiple processes are completely independent The various turtles go about their business without interacting with the other turtles in any way This is not quite true since the turtles have to share the same screen You might have noticed that one turtle will sometimes wipe out the image of another turtle temporarily Things can get more interesting when the processes have to communicate with each other In xTurtle processes communicate through shared variables When a variable is declared before a fork command there is only one copy of that variable which is shared by all the processes If any of those processes changes the value of the variable then all the other processes can see the new value This is the only form of communication between processes that can occur in xTurtle As explained in The Most Complex Machine great care must be taken when shared variables are used for communication so that one process does not change the value of a variable while another process is using that value A process must obtain exclusive access to a shared variable while it is usi
299. sed For example ADD C 17 indicates that the constant 17 is to be added to the number in the accumulator while ADD 17 indicates that a number is to be read from memory location 17 and that number is to be added to the number in the accumulator As you can see the data for the instruction simply follows the instruction It must be on the same line You can t split instructions over two lines and you can t have more than one instruction on a line Not all instructions need data If you provide data for an instruction that doesn t need it it is legal but the data will be ignored when the instruction is executed The data for an instruction is a 10 bit binary number It can be given in any of the following http math hws edu TMCM java xComputer info html 5 of 8 3 26 2000 12 50 30 PM xComputer Info forms a number between 0 and 1023 a binary number between BO and B1111111111 a hexadecimal number between 0 and 3FF a single ASCII character preceded by a left single quote mark a label name The last possiblilty a label name brings us to a whole new aspect of assembly language An assembly language program can contain more than just a sequence of items representing 16 bit numbers It can contain other things to make programming easier by letting the computer do more of the work A label is a name that stands for a number A label represents a 10 bit binary value and can appear anywhere in the program where such a value co
300. sed to select which location is to be used for storing or reading data http math hws edu TMCM java labs xLogicCircuitsLab2 html 5 of 9 3 26 2000 12 50 07 PM xLogicCircuits Lab 2 The ADDRESS wire picks out one of the two locations in the RAM When the ADDRESS wire is OFF one location is used the location with address zero When the ADDRESS wire is ON the other location is used the location with address one The DATA OUT wire shows the contents of the selected location Turning the LOAD DATA wire on and off stores a value in the selected location The DATA IN wire specifies the value that is to be stored For example suppose you want to store a in location 0 Then you should e Turn the DATA IN wire ON representing the value 1 e Turn the ADDRESS wire OFF representing the address of location 0 e Turn the LOAD DATA wire ON e Wait long enough for the signals to propagate through the circuit e Turn the LOAD DATA wire OFF To read the value stored in location 0 all you have to do is turn the ADDRESS wire OFF to represent the address of the location you want to read The value stored in location 0 will appear on the DATA OUT wire If you want to work with location 1 instead of with location 0 all you have to do is turn the ADDRESS wire ON A real RAM should have more than one ADDRESS wire Every combination of values that can be put on the ADDRESS wires specifies a different address For example if there are three
301. side the subroutine Unfortunately in the simple assembly language of xComputer it is not possible to actually hide these names from the main program and you have to be careful http math hws edu TMCM java labs xComputerLab3 html 3 of 7 3 26 2000 12 50 11 PM xComputerLab 3 not to use the same name for a different purpose in the main program In my sample subroutines I have tried to use local names that are not likely to occur elsewhere in the program such as loop_mand done_um In real programming languages local names are actually invisible to the rest of the program so there is no possibility of a conflict Passing Pointers The final sample program ListSumSubroutine txt illustrates one more aspect of parameter passing The subroutine in this example is meant to add up an entire list of numbers There is no limit placed on the number of items in the list How is it possible to pass a potentially limitless number of parameters to the subroutine The solution is that the numbers in the list are not passed to the subroutine at all Instead the main program tells the subroutine where in memory to look for the list There is only one parameter the address of the starting location of the list This address is said to be a pointer to the list In the ListSumSubroutine txt example the main program stores a pointer to the list in the memory location labeled ListStart The subroutine then accesses the numbers in the list using i
302. some specified maximum value When a Turing machine enters the halt state it stops computing Although Turing machines are very simple any computation that can be done by any computer can also be done by some Turing machine The action that a Turing machine takes depends only on its state and on the symbol displayed in the cell where the machine is currently located Given this information the Turing machine takes three actions It writes a symbol to the cell possibly the same one that is already there it moves one cell to the left or one cell to the right and it sets its internal state possibly to the same state that it is currently in The Turing machine has a table of rules that tells it what to do for various combinations of its current state and the symbol it reads from the current cell The xTuringMachine applet is designed to show Turing machines in action The Turing machines that it works with have a maximum of 25 states and they can only use the symbols 0 1 x y z and Nevertheless they can do some non trivial computations The applet is set up to load several sample machines More information about the applet can be found below This applet was originally written by David Eck for use with his introductory computer science textbook The Most Complex Machine However it can also be used on its own For a list of other applets and for lab worksheets that use the applets see the index page Sorry Your browser doesn t do Ja
303. sses zip tmcm Apps java classpath tmem jar C jdk1 1 8 lib classes zip tmcm Labs java classpath tmem jar C jdk1 1 8 lib classes zip tmcm Tutorials You can download the JDK for Windows from Sun Microsystem s Web site at http java sun com products jdk 1 1 For Macintosh You need to have the MRJ Macintosh Runtime for Java installed on your Macintosh in order to run the applications in tmcem jar This might have been installed with your original system If not it can be downloaded from http www apple com java I think you will need version 2 1 4 or higher but I haven t tried it with earlier versions The Macintosh version of the tmcm java apps archive includes three double clickable applications Double click the program named Run TMCM Applets to run tmcm Apps You can move this program to another location as long as you include a copy of the tmcm jar file in the same directory The other two programs need both tmcm jar and all the sample files Double click the program named Run With Lab Examples to run tmcm Labs and double click the program named Run With Tutorial Examples to run tmcm Tutorials For Liunx and UNIX If you have the JDK Java Development Kit installed on your computer you can use the JDK s Java command to run the applications The JDK is included in most Linux distributions although it might not have been ins
304. starts up The applet that you launched with the button above should have loaded several sample programs that you will use in this lab You can also write new programs from scratch You can select among the programs that the applet knows about using the pop up menu at the very top of the applet You can begin a new program by clicking on the New Program button or by choosing New from the pop up menu There are also buttons for loading programs from files and for saving programs to files however the configuration of your Web browser might prevent these buttons from functioning One of the sample programs for this lab is called Necklace Select this program from the http math hws edu TMCM java labs xTurtleLab1 html 4 of 10 3 26 2000 12 50 15 PM xTurtle Lab 1 pop up menu at the top of the xTurtle applet This program contains an example of a loop The program itself reads PenUp moveTo 0 5 PenDown LOOP are 5 20 circle 0 5 EXIT IF heading 0 END LOOP In addition to these commands the program contains a lot of comments A comment is anything enclosed between braces and Comments are meant for human readers of the program and are completely ignored by the computer You should read the comments on the sample program to help you understand what it does and how it works In an xTurtle program a loop consists of the word loop then a sequence of instructions then the words end loop One of the instructions
305. ster Multibit memory circuits can also be used in the main memory of a computer Recall that main memory contains a sequence of numbered locations Each location stores a binary number so each location can be a simple multibit memory circuit For some purposes a more sophisticated type of multibit memory is needed As an example look at the Count Reg circuit which you will find in the pallette of the xLogicCircuits applet This circuit is a register that counts in binary Turn its control wire on and off several times allowing as always enough time for the circuit to respond As you keep turning the control wire ON and OFF the three outputs of the circuit will cycle through the values 000 001 010 011 100 101 110 111 and back to 000 Read the outputs from bottom to top If you convert these binary numbers to decimal numbers the circuit is counting from zero to seven A count register of this sort could be used in a CPU to count off the steps in a computation for example The count register is made from three Flip Flop circuits It is not important for you to http math hws edu TMCM java labs xLogicCircuitsLab2 html 4 of 9 3 26 2000 12 50 07 PM xLogicCircuits Lab 2 understand how a flip flop works but if you look inside you ll see that it is made from two interconnected one bit memories of the type you have seen above In fact a flip flop is itself a kind one bit memory but it can do things that the simpler one bit
306. such as square or animate cannot be reused as the name of a defined object Numbers can include decimal points and exponential notation For example 17 3 14 5 1 2e5 With just a few exceptions anyplace where a number can appear in a program a number range can also appear Number ranges are used with animation as described later in this file Examples of number ranges are 1 10 1 3 10 and 12 0 The only places where number ranges cannot be substituted for numbers are in the animate command and for the first parameter of the lathe or extrude command As a final preliminary point I will note that commas can be included in a program to help make it more readable by humans However the computer ignores commas More specifically it treats them exactly the same as spaces http math hws edu TMCM java xModels info html 3 of 9 3 26 2000 12 50 33 PM xModels Info Special Commands The special commands in xModels are animate viewDistance background define and various commands for specifying the color to be used for drawing If the animate command occurs at all in a program it must be the first word in the program not counting any comments the might precede it This command which is used to specify the number of frames in an animation is defined below The viewDistance command specifies the point along the z axis that is used as the center of projection An x y z point is projected onto the xy plane by drawing a line from
307. t STARTING POINT OF SUBROUTINE The first line reserves a memory location to hold the return address The main program which uses the subroutine stores the return address in this memory location It then jumps to the location Times7 which is where the instructions for the subroutine begin The last instruction in the subroutine is JMP I RetAddr which returns control back to the main program The return address is not the only item of information that the program has to send to the subroutine The task of the subroutine is to multiply a number by seven The main program has to tell the subroutine which number to multiply by seven This information is said to be a parameter of the subroutine Similarly the subroutine has to get its answer the result of multiplying the parameter value by seven back to the main program This answer is called the http math hws edu TMCM java labs xComputerLab3 html 2 of 7 3 26 2000 12 50 11 PM xComputerLab 3 return value of the subroutine In MultiplyBySeven txt the program puts the parameter value in the accumulator before calling the subroutine The subroutine knows to look for it there Before it jumps back to the main program the subroutine puts its return value in the accumulator The main program knows to look for it there Passing parameter values and return values back and forth in a register such as the accumulator is a very simple and efficient method of communication between a subr
308. t aS zero minus one in ct and jump to jmp next next to get ready for the next sequenc num 0 starting value of sequence Cts 0 number of terms in the sequence N 0 current value of N in sequence Loc 0 address where answer is to be stored 5 0 Put 5 extra zeros in memory just to leave space http math hws edu TMCM java xComputer samples Three_N_Plus_One txt 2 of 2 3 26 2000 12 50 29 PM xComputer Info xComputer Info A computer stores programs and data in its main memory or RAM It has a central processing unit or CPU that fetches instructions from memory one by one and executes each instruction This is called the fetch and execute cycle A single fetch and execute cycle is itself made up of small steps Each of these little steps performs a very simple operation such as copying data from one location inside the CPU to another adding two numbers or moving information between main memory and the CPU Each step is accomplished by turning control wires on and off These control wires are attached to the main memory and to various components in the CPU A control circuit turns the control wires on and off based on just a few pieces of information including the instruction that is being executed and the value of a counter that counts off the little steps of each fetch and execute cycle All the values that CPU is currently working with are stored in registers which are small memory units contained within the CPU Th
309. t board is turned on and off using the Power checkbox below the circuit board The power is ON when the box is checked Click on the Power checkbox now to turn on the power Why does the wire leading from the NOT gate come on when you do this When the power is on you have control over the Inputs on the circuit board you can turn an input ON and OFF by clicking on it The circuit does the rest signals from the Inputs propagate along wires through gates and other components and to the Outputs of the circuit Try it with the sample circuit If you have a problem make sure the power is on and that you are clicking on an Input not an Output You should check that the AND OR and NOT gates at the top of the circuit board have the expected behavior when you turn their inputs ON and OFF You can also investigate the circuit in the bottom half of the logic board Below the circuit board to the left of the Power switch you ll find a pop up menu that can be used to control the speed at which signals propagate through the circuit The speed is ordinarily set to Fast You can use the pop up menu to change the speed to Moderate or Slow if you want to watch the circuit in slow motion For the most part though you probably want to leave the speed set to Fast Logic gates and logic circuits are associated with mathematical logic which is the study of the computations that can be done with the logical values true and false and with the logical op
310. t grows or shrinks and if with rotate the object rotates through a range of angles The FirstAnimation example shows a circle that grows from size 1 to size 5 over the course of the animation It contains a red polygon in which the x coordinate of one of the vertices ranges from 5 to 5 And it has a blue rectangle that both changes size and rotates during the animation Try out the example and make sure you understand it Try modifying it and adding to it Computer animation uses the idea of key frames The key frames in an animation are specified explicitly Other frames which bridge the gaps between key frames are created by the computer by interpolating between the key frames The sample animation given above has just two key frames one at the beginning and one at the end In a number range such as 1 5 the first number gives the value for the first key frame and the second gives the value for the second key frame The xModels applet computes intermediate values for the intermediate frames In xModels you can create animations with more than two key frames I call such animations segmented animations You can specify how many frames there are in each segment between the key frames For example animate 15 30 10 specifies that there are four key frames Therefore there are three segments in the animation The first segment contains 15 frames the second contains 30 and the third contains 10 The key frames are frames number 0 15
311. t has the same binary representation as the signed integer 233 http math hws edu TMCM java labs xComputerLab1 html 8 of 10 3 26 2000 12 50 09 PM xComputer Lab 1 5 Find the unsigned integer that represents the assembly language instruction sto 1023 6 Now Add 1 to the number that represents sto 1023 and find the assembly language instruction represented by the resulting number Why do you get a completely different instruction Note Do the addition yourself you don t have to program the computer to do it Exercise 2 In reality the memory of a computer contains only binary numbers Machine language in particular consists of binary numbers Translate the counting program which is repeated below into the binary numbers of machine language and write a paragraph or two explaining why computers use binary numbers instead of something more readable lod c 17 sto 12 lod 12 inc sto 12 jmp 2 Exercise 3 Write an assembly language program that computes 34 17 103 12 The instruction for subtracting a constant from the accumulator is sub c Exercise 4 Earlier in the lab you were asked to step through the execution of the instruction lod c 17 which tells the computer to load the number 17 into the accumulator The instruction lod 17 tells the computer to copy the contents of memory location 17 into the accumulator Use xComputer to watch as this instruction is executed step by step just as you did above for the lod c 17
312. t value each time it is used What happens if you substitute the command rgb random random random for the command hsb hue 1 1 in the program from Exercise 4 Why Explain carefully what the modified program does Exercise 6 Modify the RandomWalk sample program so that each line is a different randomly chosen color Exercise 7 In the RandomWalk sample program the computer chooses one of the four directions 0 90 90 and 180 at random Modify the program so that it chooses one of the http math hws edu TMCM java labs xTurtleLab1 html 8 of 10 3 26 2000 12 50 15 PM xTurtle Lab 1 three directions 0 120 and 120 instead It should have an equal chance of choosing any of these directions Make sure that you test your program Exercise 8 Write a program that can draw a square in any of three different colors It should let the user of the program decide which color to use Ask the user to Enter 0 for red 1 for blue and 2 for green If the user enters an invalid response you should display an error message instead of a square Exercise 9 With what you have learned in this lab you can write a simple guessing game program which will use none of the graphical capabilities of xTurtle Write a program in which the computer chooses a random integer between 1 and 100 and the user tries to guess the number Each time the user makes a guess the computer should honestly tell the user Sorry your guess is too high Sorry your
313. tInBinary txt Expects to be started on the right end of a sequence of zeros and ones which is interpreted as a binary number The machine adds one to its input and repeats this process forever If started on a blank tape it will start counting from one Run it at Fastest speed e BinaryAddition txt The input for this machine should be two binary numbers separated by a blank The machine should be started on the right end of the second number It computes the sum of the two binary numbers The second number is erased in the process The first number is replaced by the sum The machine halts on the right end of the sum David Eck eck hws edu August 1997 http math hws edu TMCM java xTuringMachine index html 4 of 4 3 26 2000 12 50 31 PM xTurtle Intro The xTurtle Programming Applet The applet at the bottom of this page assuming that you have a Java enabled browser lets you write and run programs written in the xTurtle programming language This applet was written by David Eck for use with his introductory computer science textbook The Most Complex Machine However it can also be used on its own The xTurtle language is designed to be simple enough to learn easily but complex enough to teach some important programming concepts The applet below is set up to load some sample programs Use the pop up menu in the upper left corner of the applet and click on the Run Program button to see what it does Full informatio
314. talled by default JDK for Solaris can be downloaded from the Sun http math hws edu TMCM java tmcm java apps README txt 2 of 3 3 26 2000 12 50 02 PM http math hws edu TMCM java tmcm java apps README txt Website http java sun com products jdk 1 1 For other versions of UNIX To use the java command wit he location of the standard s file named classes zip in you re on your own h tmem jar you will need to know ystem classes These are contained in the lib subdirectory of the JDK uSE Linux system this is us t a installation You need the full path name of this file On my S h The java command is in the bi Once you ve found the classes r lib java lib classes zip If you ave trouble finding it on your system try using the command type java to find out the full path name of the java command n subdirectory of the JDK installation zip file you can use the following commands to run the applications Substitute the appropriate pathname for my usr lib java lib classes zip java classpath tmcm jar usr lib java lib classes zip tmcm java classpath tmcm jar usr lib java lib classes zip tmcm java classpath tmcm jar usr lib java lib classes zip tmcm If you plan to use these commands often I would suggest making shell script or an alias David Eck Geneva NY 14456 USA Email eck hws e
315. tatements to be repeated followed by end loop One of the statements in the loop must be some sort of EXIT statement which causes the loop to terminate either unconditionally or conditionally and transfers control to the statement that follows the loop Statements can be nested An EXIT statement always exits from the innermost enclosing loop There are three forms of the EXIT statement EXIT EXIT IF lt condition gt EXIT UNLESS lt condition gt The plain EXIT statement exits the loop unconditionally and would ordinarily be used inside an IF statement that is nested inside the loop In the other two forms of the EXIT statement the lt condition gt is a logical expression as defined above An EXIT IF statement exits its loop if its condition is true an EXIT UNLESS statement exits its loop if its condition is false Here are two simple example programs that use loops DECLARE ct DECLARE length http math hws edu TMCM java xTurtle info html 8 of 13 3 26 2000 12 50 17 PM xTurtle Info ce s 0 LOOP LOOP EXIT IF 1 2 loop forever forward 1 length 7 random turn 45 0 lt length lt 7 CGE Ce 1 hsb random 1 1 EXIT IF ct 8 forward length END LOOP back length face 360 random END LOOP IF Statement An IF statement is used to choose one of several alternative courses of actions An IF statement always starts with a test of the form IF lt condition gt THEN and ends with END IF The end
316. tbook for that course but I will consider giving permission for other uses Again the applets including the informational page about each applet at the bottom of this page are free for any non commercial use including use in any course Note about software update in June 2004 The Java applets were written using the original version of Java While they have generally continued to work with more recent Java releases a few incompatibilities have crept in I June 2004 I fixed the known problems so that the applets should now work with all versions of Java at least for the time being I have also taken the opportunity to repackage the applets in executable jar files that can be run as stand alone applications outside of a web browser See the download page for more information The text for which I wrote the applets and labs is The Most Complex Machine A Survey of Computers and Computing It is an introductory survey of a big chunk of computer science You can learn more about it at its home page http math hws edu TMCM html For more information about me David Eck and my other projects see my home page at http math hws edu eck index html You can send me email at eck hws edu Later on this page after the labs you ll find links to more general information about each of the seven applets that are used in the labs For some of the applets a set of tutorial examples is included You don t need to read this material to do the la
317. tch and execute cycle More exactly it performs step operations until the value in the COUNT register is two At that point a new instruction has just been loaded into the IR register Clicking the Cycle button again will execute that instruction Click the Run button This makes the computer execute instructions continually like a real computer The Run button changes into a Stop button which you can use to stop the computer It will also stop if it executes a HLT instruction The speed at which the computer runs is determined by a pop up menu just below the run button At the Fastest Speed the register display is turned off so the computer can run as quickly as possible This speed is especially useful with the Graphics memory display Registers and Control Wires The xComputer has eight registers A register is a memory unit that holds one binary number Different registers holds different numbers of bits Each of the registers has a role to play in fetching and executing instructions Here is a short description of the purpose of each register http math hws ADDR register The address register is a 16 bit register that holds the address of a location in memory Whenever data is read from or written to memory this is the address that is used If you turn on the Autoscroll checkbox below the scrolling memory display then any time the value in ADDR changes the memory will be scrolled to show that address at the bottom
318. te a subroutine SUB SlowCircle radius that will draw a circle by drawing 60 arcs where each arc covers 6 degrees Then use your subroutine to slowly draw a picture like the following Exercise 4 Modify your subroutine from Exercise 3 so that it draws each of the arcs of the circle in a different color The color of an arc can be set to hsb hue 1 1 At the beginning the value of hue should be zero After drawing each arc it should be increased by 1 60 Exercise 5 A subroutine such as the one you wrote for Exercise 4 can be used in many different programs What did you have to know about those programs in order to write the subroutine What does this illustrate about black boxes Exercise 6 How many straight line segments are there in a Koch curve of complexity 2 You can use the TestKoch subroutine to draw the curve and them count the line segments You could do the same for complexity 3 and maybe for complexity 4 But what about complexity 10 or 100 There are two many line segments to count However it is possible to predict the number of segments for any complexity if you think about how Koch curves are created The question you should ask yourself is When the complexity is increased by one what happens to the number of line segments Try to figure out the pattern by looking at the number of line segments in curves of complexity 1 2 3 and 4 and by thinking about what happens as you go from one curve to the next Try to find a f
319. tem is colored black to indicate that it will not move again during the rest of the algorithm The black item divides the list into two parts each of these parts still has to be sorted This is done by applying QuickSortStep recursively to each part The great cleverness of QuickSortStep is in the efficient way in which it divides the list into smaller items and bigger items but that is easier seen than described The picture below shows QuickSortStep being applied to the original list of sixteen items An item has been removed from the list and placed in Temp A box encloses items that have not yet been compared to Temp as far as the program knows Temp could end up in any of the locations enclosed by the box Items to the left of the box are known to be smaller than Temp Items to the right are known to be larger Each step shrinks the box by one location moving an item from that location to the other side of the box if necessary In the end there is only one location left in the box and that is where Temp belongs oo Ef oe PT te la ie lS 16 Temp Using the Timed Sort Mode Now that you understand how some sorting algorithms work the next step is to investigate how efficiently lists of items can be sorted In this part of the lab you will use the Timed Sort mode of the xSortLab applet Select this mode from the pop up menu at the very top of the applet which you launched above In the Timed Sort mode the computer wo
320. tements and subroutines You should find that you are already familiar with the basic ideas because of your work in previous labs The xTurtle language also contains special purpose commands for doing turtle graphics These commands can be used to draw pictures on the computer screen In this lab you will learn about the basic xTurtle commands about loops and if statements and about variables Future labs will cover programming in more detail including the use of subroutines This lab covers some of the same material as Chapter 6 of The Most Complex Machine The lab is meant as a self contained introduction to this material but it would still be useful to read Chapter 6 before doing the lab This lab includes the following sections e Basic xTurtle Commands Color Writing xTurtle Programs Interacting with the User Exercises Start by clicking this button to launch xTurtle in its own window Sorry your browser doesn t do Java For a full list of labs and applets see the index page Basic xTurtle Commands When the xTurtle applet first starts up it displays a white drawing area on the left with a strip of controls on the right There is a turtle in the center of the drawing area represented as a small black triangle The turtle has a position and a heading Its heading is the direction it is facing given as a number of degrees between 180 and 180 The turtle has a heading of zero when it is facing to the right a headin
321. ten number corresponding to the byte For example the byte 00000111 which is equivalent to 7 in base ten is shown as lt 7 gt Pixels At the center of the applet you will see an 8 by 4 grid of little squares Each of these thirty two squares corresponds to one bit in the binary number You should think of these squares as being very big pixels Each pixel can be either black or white One bit specifies the color of one pixel 0 for white or 1 for black This is how two color graphical images can be represented by binary numbers Again see Section 1 1 of the text In the applet you can change the color of a pixel by clicking on it Exercises Exercise 1 For this exercise your goal is to use a search engine such as Alta Vista or WebCrawler to find an interesting page on the World Wide Web Pick a topic that interests you Think up some terms related to that topic and search for pages containing those terms Pick out one you find interesting Don t settle for some boring generic page like ESPN Sports or Apple Computer Inc Write a short paragraph saying what your topic was and how you went about doing the search Also include the URL for the page that you find Exercise 2 Search the Web to find the poem written by the Greek poet Sappho about her daughter Cleis How did you go about finding the poem Where did you find it Exercise 3 Starting from one of the links given above find the radius in kilometers of the planet Jupiter H
322. tes its argument by dropping any digits that follow http math hws edu TMCM java xTurtle info html 4 of 13 3 26 2000 12 50 17 PM xTurtle Info the decimal point e A random integer function randomInt x which returns a random integer in the range from to x inclusive e A random real number function random or just random without the parentheses which returns a random number in the range from 0 0 to 1 0 including 0 0 but not including 1 0 Note that the names of these predefined functions are reserved words There are a few reserved words in xTurtle that act like pre defined read only variables These read only variables contain information about the current state of the turtle You can inspect the values of these variables but you can t use assignment statements to change their values The read only variables are e forkNumber used to distinguish among multiple turtles when doing multitasking as described below e heading the direction in which the turtle is facing given in degrees between 180 and 180 where an angle of zero means that the turtle is facing to the right and positive angles are measured counterclockwise isDrawing has a value of 1 or 0 depending on whether the turtle s pen is down or up If the pen is up the turtle doesn t draw when it moves isVisible has a value of 1 or 0 depending on whether or not the turtle has been hidden with a HideTurtle command e xcoord gives the cur
323. that it was already in Step through the computation of the ChangeOltoX Y machine until it enters its halt state The machine moves along the tape changing any 0 it finds to an x and changing any to a y What makes it halt What would happen if there were no on the tape And by the way what happens when the machine encounters the edge of the applet window You should also try running the machine with the Run button Note that when a Turing machine halts it displays an h as its current state and the Step button changes to Reset Clicking Reset will reset the state to zero so the machine will be ready to start a new computation By convention a Turing machine always begins its computation in state zero Before you go on to the rest of the lab there are a few more things you should know about First you can use the mouse to drag the Turing machine to a new position on its tape You can also drag the tape If you want to drag the tape and the machine together use the right mouse button instead of the left button or hold down the Control key as you begin to drag Second and more important you should know how to change the state of the machine and the contents of its tape You can click on the Turing machine to hilite it You ll see a bright blue green outline and the blue rectangle below the machine will display a palette showing the possible states of the machine To change the state of the machine you can either type the
324. the differences that you have observed between two dimensional and three dimensional graphics Why is three D graphics harder What additional skills do you need in order to work in three dimensions Is it worth the extra effort This is one of a series of labs written to be used with The Most Complex Machine A Survey of Computers and Computing an introductory computer science textbook by David Eck For the most part the labs are also useful on their own and they can be freely used and distributed for private non commercial purposes However they should not be used as a formal part of a course unless The Most Complex Machine is also adopted for use in that course David Eck eck hws edu Summer 1997 http math hws edu TMCM java labs xModelsLab2 html 7 of 7 3 26 2000 12 50 26 PM Data Representations Applet Data Representations Applet What can you do with thirty two bits Computers use strings of bits to represent all the different types of data that they have to work with so the answer must be that you can do a lot of different things A given string of 32 bits can represent all kinds of things depending on the context in which it is used That is the same bits can encode different things depending on how they are interpreted This page contains an applet that lets you see different interpretations of the same 32 bit binary number The applet lets you type in a data value You can select the type of data you want to enter
325. the output to change in response Each gate does a simple computation Circuits that do complex computations can be built by connecting outputs of some gates to inputs of others In fact an entire computer can be built in this way http math hws edu TMCM java labs xLogicCircuitsLab1 html 1 of 10 3 26 2000 12 50 06 PM xLogicCircuits Lab 1 In the xLogicCircuits applet circuits are constructed from AND gates OR gates and NOT gates Each type of gate has a different rule for computing its output value Circuits are laid out on a circuit board Besides gates the circuit board can contain Inputs Outputs and Tacks Later we ll see that circuits can also contain other circuits All these components can be interconnected by wires To the left of the circuit board in the applet is a pallette The pallette contains components available to be used on the circuit board You can t usually see all the components at once but there is a scroll bar that allows you to scroll through all the components on the pallette The following illustration shows the part of the pallette that contains the six standard components along with some comments and a small sample circuit CF HOT Gate F OF Gate F AND Gate T Input i Output One thing you should note Wires cannot connect to each other except at Tacks Just because two wires cross each other on the circuit board does not mean that they are connected That is no signal will propagate from one of
326. the subroutine ends is called the return address Before jumping to the start of the subroutine the program must store the return address in a place where the subroutine can find it When the subroutine has finished performing its assigned task it ends with a jump back to the return address If for example the return address has been stored in a memory location labeled Ret Addr then the subroutine can finish with the statement JMP I RetAddr In the language of xComputer JMP TI is an indirect jump instruction which uses indirect addressing It tells the computer to jump to the location whose address is stored in Ret Addr In this case that will be the return address for the subroutine All of the subroutines that you will work with in this lab use return addresses in the same way A memory location in the subroutine is reserved for holding the return address Before jumping to the beginning of the subroutine the program will save the appropriate address in that memory location The subroutine ends with an indirect jump instruction to the return address As a first example look at the sample program MultiplyBySeven txt This program uses a very simple subroutine whose task is to multiply a number by seven The subroutine which is named Times7 is at the end of the program It begins with the lines RetAddr data The return address for the subroutine must be stored in this location before thesubroutine is called Times7 STO num
327. the user responds The display is not changed Here are some http math hws edu TMCM java xTurtle info html 7 of 13 3 26 2000 12 50 17 PM xTurtle Info examples of using these two subroutines AskUser What is the interest rate rate AskUser Enter a number less than max x YesOrNo Do you want to play again response Note that the strings used in these commands can include the values of variables just like the strings in TellUser and DrawText Logical Expressions LOOP statements and IF statements described below use logical expressions to test whether or not some specified condition is true A logical expression is a formula that can be either true or false Basic logical expressions are formed by comparing numerical values using the relational operators lt gt lt gt and lt gt The last three of these mean is less than or equal to is greater than or equal to and is not equal to respectively Basic logical expressions can be combined into more complex expressions using the logical operators and or and not These can also be written as single characters amp and In the absence of parenthethes the precedence ordering for operators in xTurtle from highest to lowest is NOT AND OR relational operators and and LOOP Statement To repeat a sequence of statements in xTurtle use a LOOP statement which consists of the reserved word loop followed by the s
328. the wires to another Wires can only carry signals between components such as gates Tacks Inputs and Outputs Click here to rotate a gate into one of four positions NOT gate turns its output ON when its input is OFF and vice versa A NOT gate reverses its input AND gate turns its output ON when both af its inputs are ON Otherwise the Sample circuit using output is OFF all six components The power ison The output at the bottom ane of the inputs and several wires are in the ON state OR gate turns its output ON when either of its inputs is on Cor when both are ON L Inputs can be placed around the edges of a circuit to provide input values for the circuit as a whole Outputs can be placed around the edges of a circuit to represent values computed by the circuit as a whole Tacks are simply connecting points for wires Which can be used to help make your circuits neater The applet that you launched above should start up showing a sample circuit called Basic http math hws edu TMCM java labs xLogicCircuitsLab1 html 2 of 10 3 26 2000 12 50 06 PM xLogicCircuits Lab 1 Gates At the top of the circuit board are an AND gate an OR gate and a NOT gate The gates are connected to some Inputs and Outputs A more complicated circuit built from several gates occupies the bottom of the circuit board To see how the circuit works you have to turn on the power Power to the circui
329. the y direction ztranslate A same as translate 0 0 A moves an object A units in the z direction xrotate A Rotates everything though an angle of A degrees about the x axis The x axis is fixed and everything else pivots around it The direction to use for positive angles is determined by the right hand rule Point the thumb of your right hand in the direction of the positive axis and the fingers of your right hand will curl in the direction of a positive angle yrotate A Rotates everything though an angle of A degrees about the y axis zrotate A Rotates everything though an angle of A degrees about the z axis rotate A same as zrotate A In the xy plane this looks like a rotation about the origin with positive angles representing counterclockwise rotation and negative angles clockwise rotation rotate A about B C Rotate through an angle of A degrees about the line that starts at the point B C 0 and extends in the same direction as the positive z axis In the xy plane this is just rotation about the point B C rotate A about line B C D Rotate by an angle of A degrees about the line that goes from the origin 0 0 0 to the point B C D The two words about line can also be written as a single word aboutline If B C D 0 0 0 nothing happens rotate A about line B C D EF G Rotate by an angle of A degrees about the line that goes from the point B C D to the point E F G xSkew A
330. ther a binary number a base ten integer a hexadecimal number a real number or as ASCII text In each case the input is represented differently as a different binary number How is it possible that five different binary numbers can all represent 1000 What is going on here How can the computer keep all the different meanings straight http math hws edu TMCM java labs DataRepsLab html 8 of 9 3 26 2000 12 50 04 PM Introductory Lab This is one of a series of labs written to be used with The Most Complex Machine A Survey of Computers and Computing an introductory computer science textbook by David Eck For the most part the labs are also useful on their own and they can be freely used and distributed for private non commercial purposes However they should not be used as a formal part of a course unless The Most Complex Machine is also adopted for use in that course David Eck eck hws edu Summer 1997 http math hws edu TMCM java labs DataRepsLab html 9 of 9 3 26 2000 12 50 04 PM xLogicCircuits Lab 1 Labs for The Most Complex Machine xLogicCircuits Lab 1 Logic Circuits Ir IS POSSIBLE IN THEORY to construct a computer entirely out of transistors although in practice other types of basic components are also used Of course in the process of assembling a computer individual transistors are first assembled into relatively simple circuits which are then assembled into more complex circuits and so on The
331. this exercise you are actually simulating the role of the xComputer s clock Each click has the same effect as one tick of the clock and you are driving the computation at your leisure in the same way as the ticking of the clock usually drives the computer with its regular ticking Count and Store For the last part of the lab consider the following program CountAndStore This program should have been automatically loaded by the xComputer applet so you won t have to type it in Just select it from the pop up menu at the top of the applet and click on the Translate button to store it in the xComputer s memory Note that in an xComputer program anything that comes after a semicolon on a line is a comment which is meant for human readers Comments are ignored by the computer lod c 1 Start with a 1 in location 12 sto 12 http math hws edu TMCM java labs xComputerLab1 html 7 of 10 3 26 2000 12 50 09 PM xComputer Lab 1 lod 12 This instruction is stored in location 2 inc sto 13 This instruction is stored in location 4 lod 2 Add 1 to the number in location 2 inc sto 2 lod 4 Add 1 to the number in location 4 inc sto 4 jmp 2 Go back to the instruction in location 2 This program is similar to the simple counting program that you looked at earlier in the lab except that the number for the second sto command has been changed and six new instructions have been inserted before the jmp command The instructions
332. this fact Exercise 10 Design your own animated scene using xModels Try to be creative and or aesthetic This is one of a series of labs written to be used with The Most Complex Machine A Survey of Computers and Computing an introductory computer science textbook by David Eck For the most part the labs are also useful on their own and they can be freely used and distributed for private non commercial purposes However they should not be used as a formal part of a course unless The Most Complex Machine is also adopted for use in that course David Eck eck hws edu Summer 1997 http math hws edu TMCM java labs xModelsLab1 html 10 of 10 3 26 2000 12 50 25 PM xModels Lab 2 Labs for The Most Complex Machine xModels Lab 2 Adding the Third Dimension REAL OBJECTS EXIST in three dimensions and realistic computer graphics must be able to deal with three dimensional objects In the previous lab you used the xModels applet to create two dimensional scenes and animations However the applet can also use three dimensional objects and three dimensional geometric transformations In this lab you will add the third dimension to your work with xModels Before starting this lab you should make sure that you are familiar with using the xModels applet to write programs and to view scenes You should understand the basics of the scene description language including the use of the define command to create new objects This materi
333. this form The same binary number can represent different values depending on how it is interpreted You can enter information in the data box in any of the following ways Integer any whole number in the range 32768 to 32767 e Unsigned integer any whole number in the range from 0 to 65535 Thus you can actually use any number from 32768 to 65535 However numbers from 32768 to 1 and from 32768 to 65535 are ambiguously represented by the same binary numbers e Assembly language instruction any legal assembly language instruction for xComputer such as LOD C 17 See the list below e ASCII characters a single quote followed by any typeable character or a pair of characters except for carriage return The quote just marks this as ASCII data For example DE e Hexadecimal number a dollar sign followed by from one to four hexadecimal digits For example A73D Binary number a B upper or lower case followed by from 1 to 16 zeros and ones For example B110010111010 When you type any of these things in the data box and press return it is translated into a http math hws edu TMCM java xComputer info html 2 of 8 3 26 2000 12 50 30 PM xComputer Info binary number and put into memory at the specified address If there is some error in what you type you ll get a small error message above the addr box So a binary number in memory can represent several different things The xComputer appl
334. tinues with subroutines in general and recursive subroutines in particular Recursion is used to produce nifty pictures xSortLab Lab Sorting and the Analysis of Algorithms Uses the xSortLab applet to investigate several different algorithms for sorting lists of numbers xTurtle Lab 4 Multiprocessing http math hws edu TMCM java index html 2 of 4 6 25 2004 11 48 41 AM TMCM Labs and Software Shows how multiprocessing can be used to divide a large problem into several subtasks that can be executed in parallel Some examples of communication between parallel processes are also given xModels Lab 1 Two D Graphics and Animation Introduces a scene description language for creating still images and multi frame animations Shows how hierarchical geometric models are used in computer graphics In this lab only two dimensional images are covered xModels Lab 2 Adding the Third Dimension Extends the ideas covered in the previous lab to three dimensions Also covers lathing and extrusion two operations for producing three dimensional objects The Applets DataReps A small applet that shows how the same 32 bits stored in the memory of a computer can represent different things depending on how they are interpreted It is related to material covered in Chapter 1 Section 1 of The Most Complex Machine xLogicCircuits Lets you create simulated logic circuits like those discussed in Chapter 2 by dragging AND gates OR gates
335. to make a nice colorful design either random or symmetric Hopefully it will be fun to watch as multiple turtles construct the picture Exercise 9 Is it really sometimes easier to write a program using parallel processing than to write a standard program to do the same task Write a short essay explaining and defending your opinion This is one of a series of labs written to be used with The Most Complex Machine A Survey of Computers and Computing an introductory computer science textbook by David Eck For the most part the labs are also useful on their own and they can be freely used and distributed for private non commercial purposes However they should not be used as a formal part of a course unless The Most Complex Machine is also adopted for use in that course David Eck eck hws edu Summer 1998 http math hws edu TMCM java labs xTurtleLab4 html 7 of 7 3 26 2000 12 50 23 PM xTurtleLab 4 Tiling Examples Labs for The Most Complex Machine Tiling Examples for xTurtle THE COPY OF xTurtle on this page has six sample programs written by Kevin Mitchell Each of these programs uses xTurtle s multitasking abilities to draw a tiling of the plane After launching xTurtle choose an example from the pop up menu at the top of the window and click the Run Program button Click this button to launch xTurtle in its own window Sorry your browser doesn t do Java Back to the Rest of the Lab http math hws edu TM
336. tton at first so that you can follow each step of the computation in detail To do one step in its computation the Turing machine considers the state that it is in and the symbol that it is reading in the cell where it is located Based on this information it will 1 write a new symbol in the current cell 2 move one cell to the left or to the right and 3 change to a new state Note however that the new symbol that the machine writes can actually be the same as the old symbol and that the new state can be the same as the old state The machine bases its action on the table of rules that is shown in the lower http math hws edu TMCM java labs xTuringMachineLab html 2 of 9 3 26 2000 12 50 12 PM xTuringMachine Lab right part of the applet For example look at the table of rules for the sample machine ChangeOl1toX Y The first row of the table says If the machine is in state O and if the symbol in the current square is that is a blank then the machine will write a in the square move one square to the right and change to state 0 All the rules for a Turing machine are of this general form Note that in this case the symbol it writes in the square is the same as the symbol that was already there this is just a fancy way of saying that it doesn t change the contents of the square Similarly when the machine changes to state 0 in this case it doesn t really change its state its new state is actually same state
337. tton makes the computer perform a single step in the fetch and execute cycle You have to click on it several times just to execute one instruction in the program Once again you should reset the PC to zero Then click through your program with the Step button until the HLT is executed Writing Programs for xComputer It should be clear that entering a long program into xComputer by typing it into the data box would be very tedious and error prone If you accidentally leave out one instruction for example you might have to retype most of the program Fortunately the xComputer applet lets you type a complete program in a separate text input area and then translate the whole program at once and store it in xComputer s memory This has three advantages You can edit the program in the window for example by inserting a new instruction You can if the configuration of your Web browser permits it save the program in a file so that you ll never have to retype it again And you can use labels in your program Labels are a powerful programming technique they are described in the Postscript to Chapter 3 in the text They are not covered in this lab but they will be an important part of the next lab If you want to type a new program just click on the New Program button in the Control area of the applet Alternatively you can select New from the pop up menu at the very top of the applet The computer display will disappear and will be replace
338. two control wires Turning on one of these will make it do an addition turning on the other will make it do a subtraction You should construct the circuit as specified by this illustration First four bit second four bit input goes here input goes here Ns If this control wire is ON the ALU should DE its two inputs z The four bit answer If this control wire ON the ALU should rae The fifth output is the carry its two inputs from an addition Fora subtraction it should be OFF Now an interesting thing about an ALU is that it actually performs all the computations that it knows how to do The control wires just control which of the answers get to the outputs of the ALU To make your Mini ALU you can start with the 4 Bit Adder and 4 Bit Minus circuits which were provided to you in the applet s palette The four bit subtraction circuit has only four outputs since for subtraction the carry bit from the leftmost adder does not provide any useful information You don t have to worry about how the Minus circuit works you don t even have to understand how negative numbers are represented in binary Start by placing a 4 Bit Adder and a 4 Bit Minus circuit on an empty circuit board along with the eight inputs at the top of the circuit These can be connected as shown http math hws edu TMCM java labs xLogicCircuitsLab1 html 9 of 10 3 26 2000 12 50 06 PM xLogicCircuits Lab 1 4 Bit Adder 4 Bit
339. two numbers The numbers that are to be multiplied are parameters to the subroutine and the product of the two numbers is its return value The memory locations labeled N1 N2 and Answer are used to hold the two parameter values and the return value These locations can be found at the beginning of the subroutine along with a memory location to hold the return address Before it calls the subroutine the main program must load the two numbers that it wants to multiply into N1 and N2 When the subroutine ends the main program can get the answer by loading the contents of memory location Answer You should read the program try it out and make sure that you understand all this The program contains a list of detailed instructions for using the subroutine Note that you don t have to understand the method that the subroutine uses for multiplying the numbers In fact it s a fairly complex procedure By the way when you read the Multiply subroutine you ll notice that it uses nine different labeled memory locations Five of these ret_addr N1 N2 Answer and Multiply are used for communication with the main program The other four are part of the internal working of the subroutine Ideally the main program wouldn t have to know about them at all because the main program is only interested in the task performed by the subroutine not in its internal workings These labels are called local names since they are meant to be used only locally in
340. uit also contains an OR gate in a feedback loop but now an AND gate has been inserted into the loop If you turn the input labeled Turn it ON on and then off the feedback loop and the output of the circuit will come ON If you turn the other input labeled Turn it OFF on and then off the loop and output will go OFF This circuit remembers which of its inputs was most recently turned on and off Since we want to work with binary numbers we think of ON as representing one and OFF as representing zero We say that we store one in the circuit by turning the top input on and off and that we store zero in the circuit by turning the lower input on and off The circuit stores the value zero or one You can check which value it is storing just by looking at its output You can set the value that it is storing by manipulating its inputs This simple memory circuit is the basic building block for most of what you will see in this lab In the previous lab you saw that it is often convenient to think of some inputs to a circuit of as carrying data into the circuit while other inputs are used to control the circuit The circuit itself doesn t really make any distinction between two different types of inputs but it useful for designers of circuits to distinguish between data inputs and control inputs depending on what functions the inputs serve in their circuit design All the circuits that you see in the rest of this lab follow the following convention e
341. uld be used that is as the data part of an instruction or as a stand alone item on a line by itself When the program is translated the label is replaced by the number it represents A label is given a value by using it to label one of the 16 bit items that make up the program The label name must be followed by a colon and the item that it labels The value of the label is the address of the location in memory that contains that item For example the following program adds up all the numbers from 1 to 50 next done sum number lod c 1 sto number lod c 0 sto sum lod sum add number sto sum lod number inc sto number sub c 51 jmz done jmp next hlt 0 0 J J 1 Initialize number to contain 1 Initialize sum to contain 0 Add current value of number to sum Add one to the value of number Subtract 51 from the number which is still in AC If the answer is zero jump to done Otherwise jump to next to continue the computation Halt The zeros are place holders to reserve memory locations for sum and number In this program next done sum and number are labels Next and sum refer to locations that hold instructions Sum and number refer to locations that hold data for the program The programmer can work with the instructions and data without having to work out the actual location numbers This program also illustrates comments Anything on a line after a semicolon is treated
342. umber in the list Change the name of the memory location Sum to Max As the program runs this memory location will hold the largest number seen so far in the list When the program ends and the whole list has been examined Max will hold the largest number in the entire list You can compare two numbers by subtracting one from the other and using a JMN instruction to test whether the answer is negative Exercise 7 Write another list processing program that makes a copy of a list You can model your program on ListSum txt However instead of adding up the numbers in the list it should copy them to another part of memory Use a label named Copy to indicate the location in memory where the copy of the list should begin Exercise 8 The CountAndStore program in Exercise 1 is a self modifying program That is the machine language instructions in locations 2 and 4 change as the program is executed Another way to write the program would be to use indirect addressing Use a memory location labeled Loc to keep track of which location the program is currently working on Use LOD I Loc and STO I Loc to load and store values in that memory location To move on to the next consecutive memory location add one to Loc Exercise 9 Write an essay explaining in detail how indirect addressing is used in the program you wrote for one of the exercises above Exercise 5 Exercise 6 or Exercise 7 Exercise 10 Write an essay explaining how labels a
343. ust click on it Any component on the circuit board can be moved around Just drag it by holding down the right mouse button Alternatively if you have a one button mouse for example you can hold down the control key to drag a component Whenever a wire or component is hilited you can delete it by clicking on the Delete button If you delete a component that has some wires attached those wires will also be deleted There is an Undo button that you can use to get back something that you delete by mistake Note that the Undo button can only undo one operation You can edit a circuit even while the power is on Subcircuits In addition to the six standard components the scrolling component pallette can also contain circuits that have been built from these basic components and iconified using the applet s Iconify button These iconified circuits can be used as components in building other more complex circuits You can drag them onto the circuit board just like other components The applet on this page should have loaded three such iconified circuits 4 Bit Adder Clock and One Bit Mem To see inside an iconified subcircuit hilite it and then click on the Enlarge button The circuit will expand to fill the circuit board You can also just double click on the subcircuit However not all browsers respond to double clicks When you expand a circuit icon from the pallette its icon is removed from the pallette The circuit
344. ut the origin Putting the transformations in the opposite order square rotate 30 xtranslate 5 gives a different result since the square is first rotated and then translated Here is a list of the transformations used in xModels where A B C D E F and G are numbers or in the case of an animation number ranges e scale A B C Scales by factors of A in the x direction B in the y direction and C in the z direction Scaling by a fractional amount makes an object smaller Scaling by a negative amount reflects the object through the corresponding coordinate plane The scaling is centered at the origin all other points move away from or towards the origin scale A B same as scale A B B scale A same as scale A A A xscale A same as scale A 1 1 scales in x direction only yscale A same as scale 1 A 1 scales in y direction only zscale A same as scale 1 1 A scales in z direction only http math hws edu TMCM java xModels info html 6 of 9 3 26 2000 12 50 33 PM xModels Info translate A B C Moves each point x y z to k A y B z C The effect is to move the object A units in the x direction B units in the y direction and C units in the z direction translate A B same as translate A B 0 translate A same as translate A 0 0 xtranslate A same as translate A 0 0 moves an object A units in the x direction ytranslate A same as translate 0 A 0 moves an object A units in
345. va About the Applet A pop up menu at the very top of the applet can be used to select machines that were loaded by the applet at start up or that have been created by the user Selecting New the first item in the menu will create a new empty machine Just below the applet is the machine itself sitting on an infinite tape The tape is divided into cells and each cell either contains a symbol or is blank The machine itself sits over one of the cells and displays its current state By convention the machine starts out in state zero When it is in the halt state it displays an h This area of the screen is also used to display messages the machine will be there when you dismiss the message http math hws edu TMCM java xTuringMachine index html 1 of 4 3 26 2000 12 50 31 PM The xTuringMachine Applet On the left side of the applet below the machine is a set of controls The first control is a pop up menu that controls the speed of the applet when it computes The Run button makes the machine start computing when you click it it changes into a Stop button The Step button makes the machine perform one step in its computation The Clear Tape button does just that The Delete Rule button can be used to delete one rule from the rule table It is only active when a rule has been selected The selected rule is shown in red you can select a rule by clicking on it The Load File and Save buttons are used to work with
346. value of one for x means that the color contains the maximum possible amount of red So rgb 0 0 0 represents black rgb 1 0 0 represents bright red and rgb 0 5 0 0 is a darker red Some other examples rgb 0 8 0 8 0 8 is a very light gray rgb 1 0 6 0 6 is pink and rgb 0 0 4 0 4 is a dark blue green The command hsb x y z uses an alternative method of specifying a color In this command X y and z represent hue saturation and brightness The hue is the basic color As x ranges from zero to one the hue ranges through the spectrum from red through orange yellow green blue violet and back to red The meaning of the brightness parameter is pretty clear with a value of one representing the brightest color of a given shade The saturation can be thought of as follows A saturation value of one gives the purest possible version of a color Decreasing the saturation from one towards zero is like mixing paint of that color with gray paint of equal brightness The basic color remains the same but it becomes diluted You ll find some examples of using the rgb and hsb commands later in the lab Writing xTurtle Programs The power of a computer comes from its ability to execute programs The xTurtle applet allows you to write and run programs Programs can include all the basic commands described above They can also include loops decisions subroutines and other features The applet can be configured to load one or more programs when it
347. variable Each process created in a fork command continues executing until either it reaches the end of the program or it executes a KillProcess command or it finishes the subroutine or function in which the fork command ocurred Note how forks in subroutines are handled Any processes that are created inside the subroutine end before the subroutine returns When the subroutine returns only the original process that called the subroutine is still running In fact the command fork N actually creates N child processes The original parent process goes to sleep until all the child processes have ended Then the original parent awakens The state of the turtle in the awakened parent process is the same as it was before the child processes were created That is the turtle still has the same heading position visibility pen state and drawing color as it did at the moment when the fork statement was executed If the fork command occurred inside a subroutine the subroutine does not return until all the child processes have ended and then it is actually the original parent process that returns The same sort of thing happens if you use a fork command in the xTurtle applet s command input box The processes that are created by a fork command are identical except for one thing Each process has a different value for the read only variable fork Number The fork numbers for the processes created by the command fork N range from 1 to N The different
348. ves trees Because binary trees are defined recursively they can be drawn by a recursive subroutine You should try to understand the definition of the Tree subroutine A second example of recursion is contained in the sample program KochCurves This example is also taken from Section 7 3 in The Most Complex Machine A Koch curve is a way of getting from one point to another with a lot of detours To help you understand this run the sample program KochCurves After you have run the program you can use the command TestKoch in the xTurtle applet s text input box When you do so you will be asked to specify a complexity level for the Koch curve You should try complexity levels of 0 1 2 3 and 4 A Koch curve of complexity 0 is defined to be a straight line segment A Koch curve of complexity is a line segment with a bump or detour The complexity one curve is made up of four line segments but you should think of each line segment a Koch curve of complexity zero A Koch curve of complexity 2 is obtained from the curve of complexity 1 by adding a detour to each line segment in the curve You should look at a Koch curve of complexity 2 as being made up of four smaller pieces where each piece is a Koch curve of complexity 1 More generally a Koch curve of complexity N is made up of four smaller Koch curves of complexity N 1 Once again this is a recursive definition and the subroutine that draws Koch curves is a recursive subroutine Tr
349. want to try out some other HTML features You will certainly want to add some graphics images to your page This is very easy to do in Composer since you can drag images from another page into the page you are creating I ve made a page of sample images that http math hws edu TMCM java labs WebPublishingLab html 5 of 7 3 26 2000 12 50 13 PM Web Publishing with Netscape Composer you can use You can get images from any page in the same way although you should of course try to be careful about copyright issues You can also drag images from one place to another on the page you are creating When you drag an image into your Web page it will appear wherever the blinking cursor is currently located Web browsers treat images much like big characters and you can have an image in the middle of a paragraph You can even include an image in a link someone viewing the page will be able to follow the link by clicking on the image There are several options for image placement and other image properties To see a dialog box containing these options just click on the image with the right mouse button When you publish your page the images on the page will be uploaded to the server along with the page itself Each image is stored in its own individual file not in the file that contains the HTML source The HTML source file just contains the name of the image file You can organize items on your page by using lists and tables Lists are fairl
350. will be stored in the variable betAmount and the program can then use that number by referring to the variable All of the input output commands have a nice feature that allows you to include the value of a variable in a string If a string includes the special character then that must be followed by the name of a variable When the string is displayed the and the name will be replaced by the value of the variable For example if betAmount and winnings are variables with the values 25 and 75 then TellUser You bet betAmount dollars you win S winnings would display the string You bet 25 dollars you win 75 All of this is illustrated in the sample program InputOutputExample You should select this program from the pop up menu read it run it and try to understand it Exercises Exercise 1 Find a sequence of xTurtle commands to draw each of the following a square with a circle inside it a pair of parallel lines connected by half circles at each end a plus sign The pictures should look something like this http math hws edu TMCM java labs xTurtleLab1 html 7 of 10 3 26 2000 12 50 15 PM xTurtle Lab 1 hard Exercise 2 Find a sequence of xTurtle commands that will draw your initials Draw each initial in a different color Exercise 3 For this exercise experiment with the Necklace sample program The original program draws a large circle of radius 5 made up of a sequence of 20 degree arcs Between ea
351. wn personal Web server Otherwise you can still hope to find a friendly Web server where you can locate your pages For students at Hobart and William Smith Colleges there are several Web servers where you can publish your Web pages The official Web pages of the Colleges are on a server called www hws edu If you want to be serious about maintaining a presence on the Web you should get an account on this server and publish your Web pages there See the Computer Services page for information You can also set up Web pages in your email account on the campus VAX hws3 hws edu I am not going to have you use this account for this lab as I would have liked because I can t get Netscape Composer to work properly with the VAX s somewhat out of fashion VMS operating system However for this lab I have set up a special account for you to use on one of the computers belonging to the Department of Mathematics and Computer Science The name of the machine is escher hws edu Your account on this machine will be deleted at the end of the Fall term so if you want to keep your Web pages around please talk to me about moving them to another machine before the end of the term You will have to configure Netscape Composer so that it knows about this account To do this choose the Preferences command from the Edit menu A dialog box will appear From the list on the left edge of this dialog box choose the item Publish which is listed under C
352. ws http math hws edu TMCM java download TMCM_Labs tar gz for Linux UNIX You can view the README file from the Labs archive for more information The Information Tutorial examples and applets from the The Applets section of the main page http math hws edu TMCM java download TMCM_Applet_Tutorials zip for Windows http math hws edu TMCM java download TMCM_Applet_Tutorials tar gz for Linux UNIX You can view the README file from this archive for more information PDF File for Printing The following PDF file contains copies of all the lab worksheets and applet information pages from http math hws edu TMCM java Except that where an applet should appear on a page you ll just see a note that Java is not available This file is provided primarily to make it easy to produce print outs You can read it using Adobe Acrobat Reader http math hws edu TMCM java DownloadingAndInfo html 2 of 3 6 25 2004 11 48 57 AM TMCM Java Downloading and Info http math hws edu TMCM java download tmcm java web site pdf If you click on the above link your browser might use a PDF plugin to let you see the contents of the file If it does not have the plugin it should let you download the file If you do have the plugin and still want to download the file try right clicking or Control clicking the link Java Source Code The Java source code for the applets can be browsed on line and is included in the complete web site
353. ws If the digit on the tape is a zero then simply change that digit to a one If the digit is a one change it to a zero move left and apply the same procedure at that position This is like carrying a one to the next column Finally to add one to a blank space simply change that blank to a one This can occur when a one is carried beyond the leftmost digit of the number the blank should be treated just like a zero For example 110_2 1_2 111_2 1011_2 1_2 1100_2 and 11_2 1_2 100_2 The sample Turing machine Increment is a simple Turing machine for incrementing a binary number This same machine can be found in Figure 4 2 of The Most Complex Machine The Increment machine should be started on the rightmost digit of a binary number It will add one to the number and then it will halt on the rightmost digit of the answer Try it out Every time you click the Run button the machine will add one to the number on its tape With somewhat more work it is possible to make a Turing machine that adds two binary numbers The sample machine AddBinaryNumbers does this in the ordinary way by adding corresponding digits in the numbers one by one starting at the right and working left The numbers to be added must be next to each other on the tape and they must be separated by a single blank space The machine must be started on the right end of the second number Try running this machine on the sample input and then try giving it sever
354. xTurtle For example you could compare the way loops are constructed in each language compare labels in assembly language to variables in xTurtle and compare the way computations are done in assembly language with the way they are done by assignment statements in xTurtle This is one of a series of labs written to be used with The Most Complex Machine A Survey of Computers and Computing an introductory computer science textbook by David Eck For the most part the labs are also useful on their own and they can be freely used and distributed for private non commercial purposes However they should not be used as a formal part of a course unless The Most Complex Machine is also adopted for use in that course David Eck eck hws edu Summer 1997 http math hws edu TMCM java labs xTurtleLab1 html 10 of 10 3 26 2000 12 50 15 PM xTurtle Info xTurtle Info The xTurtle Applet lets you program in a simple programming language which is also called xTurtle This page contains descriptions of the language and of the applet This is a rather long file about 42K Also available on separate pages are some tutorial examples I invented the xTurtle programming language to use as an example in The Most Complex Machine a book that surveys the field of computer science Since programming is only one of the topics in the book I wanted a reasonably simple language but one that would have the major features of a typical programming languag
355. xactly the same state with one small exception The xTurtle language has a predefined variable named ForkNumber This is a read only variable that is you can test the value of this variable but you can t change its value Each of the processes created by a fork statement gets its own value for ForkNumber For the first process the value of ForkNumber is 1 for the second the value is 2 and so forth To test this try executing the following commands Type them on a single line in the input box at the bottom of the xTurtle window and then click the Do It button fork 5 TellUser ForkNumber ForkNumber When the computer executes the TellUser command it substitutes the actual value of ForkNumber for ForkNumber Make sure you understand what happens You have to type both commands in the input box on one line If you execute fork 5 by itself two processes will be created but both processes will die before you get a chance to type in the next command In the sample program ParallelSpectrum txt the ForkNumber is used in the program in several calculations Each process does the same calculation but since different processes have different values for ForkNumber the result will be different in each process For example turn 4 ForkNumber will make Turtle 1 turn 4 degrees Turtle 2 turn 8 degrees Turtle 3 turn 12 degrees and so on The sample program TwoTasks txt shows how ForkNumber can be used to make several
356. y does the clock tick What process does the clock go through as it turns its output on then off then back on What is the role of the OR gate Note The Tacks in the feedback loop serve to slow the ticking down because in this simulated circuit it takes a bit of time for a signal to propagate from one Tack along a wire to the next Tack In a real circuit the length of the feedback loop could be used to control how long a signal takes to circle the loop Exercise 2 This is a continuation of Exercise 1 As an example of using the signal from a clock to drive another component build a circuit in which the output from a Clock circuit is connected to the control wire of a Count Reg circuit The circuit you build should have http math hws edu TMCM java labs xLogicCircuitsLab2 html 7 of 9 3 26 2000 12 50 07 PM xLogicCircuits Lab 2 three outputs which are connected to the outputs from the Count Register It should also have one control input which is connected to the Clock s control wire When you turn the power on the ticking of the Clock will make the Count Register count and it will do so as long as the control wire is turned off This circuit just counts up to 7 before it goes back to zero How would you make a circuit that counts up to 15 before it goes back to zero Exercise 3 One of the sample circuits 1 Bit Mem is capable of storing a one bit binary number Construct a four bit memory that can store a four bit binary
357. y simple A list consists of a sequence of indented items Generally the items are short often consisting of a single line Each item is preceded by a marker such as a bullet or a number An easy way to make a list is to type all the items pressing return after each one Then hilite the items and click on one of the two list creation buttons in the toolbar Tables are more complicated A table is made up of rows and columns By default tables are surrounded by a thin border The table can have a different background color from the rest of the page and in fact each row and each individual cell can have its own background color You can set one cell to span several rows and or several columns In this way you can make sophisticated layouts and there are still more options that I have not even mentioned here To insert a table into your page click the Table button in the toolbar You will see a dialog box that allows you to set several options such as the background color and the number of rows and columns You might want to set some of this but you can always go back and change the table s properties later When you click the Insert button a table is added to your page To type into a cell click in the cell to move the blinking cursor into it You can edit the text in tables just like you would any text You can also drag an image into a cell You can move the cursor from one cell to the next by pressing the tab key If the cursor is located
358. y to understand how the pictures you see are produced by the Koch subroutine The KochCurves program also defines a subroutine named Snowflake which draws Koch snowflakes A Koch snowflake is made by joining three Koch curves together at their endpoints producing a symmetric snowflake like picture Try it Exercises Exercise 1 Add the following lines to the end of the SymmetrySubs sample program after all the subroutines Run the program a few time to see what it does The write a short essay explaining exactly how the program works and why it produces the pictures that it does Try running this at fastest speed with the turtle turned off declare x x 0 loop face 360 random hsb x 1 1 multiforward 0 4 x x 0 005 if x gt 1 then x 0 http math hws edu TMCM java labs xTurtleLab3 html 3 of 6 3 26 2000 12 50 20 PM xTurtle Lab 3 end if exit if 1 2 end loop Exercise 2 The mathematics used in the subroutines defined in SymmetrySubs is not trivial How much did you need to know about this mathematics to use the subroutines What point about subroutines does this illustrate Exercise 3 The Speed pop up menu in the xTurtle applet works by inserting delays betweens commands Since circle is a single command a complete circle is drawn instantaneously no matter what the setting of the speed menu This disappointed one of my students who wanted to be able to watch the circles being drawn Wri
359. you see an enlarged part of it When you shrink the subcircuit back down to its original size the main circuit is still there In this case you ll see that an Adder circuit contains two Half Adder subcircuits which you can enlarge in their turn if you want Circuits and Arithmetic The 4 Bit Adder circuit is an example of a logic circuit that can work with binary numbers Circuits can work with binary numbers as soon as you think of ON as representing the binary value 1 one and OFF as representing the value 0 zero The 4 Bit Adder can add two 4 bit binary numbers to give a five digit result Here are some examples of adding 4 bit binary numbers 1011 tbe Let 1010 0111 0001 0110 0001 1111 0101 1010 0011 10001 10000 11110 01111 10001 00100 The answer has 5 bits because there can be a carry from the left most column Each of the four Adder circuits in the 4 Bit Adder handles one of the columns in the sum You should test the 4 Bit Adder to see that it gets the right answers for the above sums The two four bit numbers that are to be added are put on the eight Inputs at the top of 4 Bit Adder The sum appears on the outputs at the bottom with the fifth bit the final carry appearing on the output on the right You should observe that it takes some time after you set the inputs for the circuits to perform its computations http math hws edu TMCM java labs xLogicCircuitsLab1 html 6 of 10 3 26 2000 12 50 06 PM xLogi
360. ys of producing certain types of complicated objects The methods are called lathing and extrusion These are standard operations in three dimensional graphics The idea is similar in each case a specified figure is copied several times and the vertices of the copies are connected with line segments For lathing the copies are obtained by rotating the original around the y axis For extrusion the copies are obtained by translating the original in the z direction In xModels the commands for performing lathing and extrusion are lathe and extrude The lathe command takes a sequence of points in the xy plane and connects them with line segments It then takes the resulting figure and makes several copies of it by rotating it around the y axis The first parameter of the lathe command indicates the number of copies This is followed by a list of the x and y coordinates of the points in the xy plane This is easier to understand if you see an example The command lathe 12 3 3 7 3 says that the line from the point 3 3 to the point 7 3 is to be copied 12 times The copies are evenly spread out around the y axis With 12 copies they are spaced every 30 degrees The endpoints of the 12 lines are then connected giving an object that looks like a lampshade To see it type in the following scene description animate 60 lathe 12 3 3 17 3 yrotate 0 360 If you change the 12 to a 4 only 4 copies of the line will be made The resulting object look

TMCM Labs and Software - HWS Department of Mathematics and

Contents

Download Pdf Manuals

Related Search

Related Contents