Home

HP Solve: Issue 23 (April 2011)

1. EL minm EXEJEIEETEHE EIER OOOO i 1 2 3 4 pns 7 8 10 Fig 2 Plot of the limit of y 1 I n Values to eleven digits are given in table 1 below HP Solve 223 Page 44 Page 1015 Table 1 Example of e calculated limit values to 11 digits n J 1 l m Difference d 10 2 71828 046932 0 00000135914 6 _ n Difference d 1 2 J071828182846 1 2 225 046828182846 1 10 27182818 1487 0 00000001359 8 10 2 71828182 710 0 00000000136 9 Note d is the number of accurate digits The values of Table were calculated using the following RPL program lt lt DUP INV 1 OVER SWAP TAG 1 EXP OVER gt gt Key n run the program and level two will have the input value colon and the calculated value Level one will have the difference of the calculated value subtracted from e These values are the first three values in the table Here is how the program works The input n is copied to level 2 with DUP The reciprocal of n is calculated with INV One is added with 1 A copy of n from level two is brought to level one with OVER and Y calculates the function Remember that n is still on level two It is swapped to have the two values in the correct order for the command Next the value of e is calculated using 1 EXP The calculated value of the tagged function is still on level two and a copy is brought to level o
2. 00 We simplify the right side by introducing a new variable defining n r FV limit P 1 1 m m ca HP Solve 223 Page 46 Page 3 of 5 limit 1 I m In 00 The limit in the square brackets converges to The formula may be simplified and becomes FV 5 The difference between 4 and 5 15 that e5 is based on continuous compounding The principal at any instant in time 1s changing at a rate that equals the interest rate times the principal Does the discussion above give you a practical LC i 1 10 10 10 Divided Evenly sense for the value of e 2 5 25 40 3 3 33333 37 037 35 Peak 18 Ambigious ia 2 5 39 0625 ag a 32 1 66667 21 4335 1 42857 12 1427 20 Let s look at the value of e in a different way Compound interest is based on an interest rate for a 25 time period The time periods are all equal In 1 25 5 96046 15 mathematical terms the periods are integers The UU 10 amount of money involved is also a number This number is divided in to a specific number of EP REPE ROOM periods Fig 4 shows the number 10 divided into equal parts Along the horizontal axis Each part Fig 4 Ten divided into equal parts and multiplied has a Value This Value is multiplied by its self the number of times as its Part divisor See Fig 4 This is an analysis of the number ten Ten is divided by integer values 1 through
3. Unreleased version HP Solve 23 Page lt Page 1016 Functional consistency Despite all the added features the HP IObII4 still operates just like the HP 1061 Care was taken to ensure compatibility with existing valid keystroke sequences If pressing a series of keys is a valid key sequence and solves a problem on the HP 1061 it will solve the problem on the HP 1061 Any existing books or classroom materials will work as written with no changes needed Physical differences Two shift keys are now present The familiar yellow for functions written on the front of the keys and a new light blue for functions written above the keys The shift keys even show an arrow that actually indicates the up or down nature of the shifted functions The silver band around the key area is gone More display annunciators are present two shift indicators an indicator for the inverse key indicators for the 360 day calendar mode and semiannual coupons and an indicator for radians mode The STATS indicators now indicate whether an X or Y value is being displayed These X and Y indicators are also used in other circumstances such as when a function returns a primary value to the display and a secondary value in the SWAP position For example computing the Net Present Value NPV also computes the Net Future Value NEV and stores it in the SWAP position The X indicator is turned on when the NPV is being displayed Pressing will display the N
4. while memory 11 is accessed by HH for example Given the register the HP 10bII now has 21 addressable data memories Of course the memories for the five breakeven variables can be used as data memories 1f needed as well Simply press 3 bo AACS to store a value into the UNITS memory location and SeA to recall it Each of the breakeven locations is usable in that way That s an additional 5 HP Solve 23 Page 8 Page 5 of 6 memory locations Similar approaches can be used with the CST PRC MAR and MU locations as well as bond and even TVM locations if not used for other purposes A new clearing function has been added as the of the EX key It is labeled as and is one of three keys in reverse video where the other two are the and keys The reverse video means that these keys require an additional key press to execute a function and expect a subsequent P f1 or one of the trig functions to complete the desired operation as stated earlier The function is connected by a thin line to the 3 H 4 and H keys which all have a small vertical abbreviation next to them e Pressing and LU for example clears the cash flow data only leaving the rest of the calculator s memory intact e Pressing H clears the data e Pressing clears the breakeven data and e Pressing clears the bond data Since the existing HP 1061 and the earlier HP 10b allowed only the clearing of a digit with the key clearing a calculat
5. 180 Law of sines in various forms Law of cosines in various forms special case of a right triangle and the dreaded cases If you think about the possibilities you will find that there are 20 possible cases six combinations taken three at a time wherein you know three of the six unknowns and you want to calculate the remaining three Of these 20 possible cases the case of knowing all three angles is meaningless because there are an infinite number of possible triangles These cases are often grouped and described using three letters denoting S for side and A for angle 1 e AAA AAS side not between an angle ASA SAS SSS and SSA In order to solve a triangle problem you will need three knowns and one of them must be a side Why must I draw a triangle label it and look up the various equations in order to get the answer I need HP Solve tt 23 Page 30 Page 1 of 3 Why shouldn t the calculator do this work for me Since Triangle Solving is a common problem HP calculator users have addressed this automatic solution issue with programs The math method and solution has been programmed on the HP 97 HP 67 and HP 41C by John Kennedy See PPC Calculator Journal April 1980 V7N3P14 Also see similar programs in the PPC Calculator Journal May 1980 V7N4P30 Several others contributed ideas especially those of Keith Jarrett and George Donaldson John Kennedy s analysis is especially important because he used selected equat
6. Most of the commands allow both a logical address which is the 16 bit HP 41 address plus the bank select information or a physical address which is the native NEWT 24 bit address See Figure 2 for the requirements for the various commands Address format Four basic commands for dealing with memory are YMCLR PPPPPP DDDD or available The YMCLR command initializes a 4k block of LLLL B DDDD YMCPY PPPSPPP or memory to a specified value while the YMCPY command PPPSL B or copies from one 4k block of memory to another As I L B gt PPP or mentioned previously this command is handy for moving a L B gt L B module image to RAM for editing This copy command YPEEK amp YPOKE PPPPPP DDDD or accepts either logical what the CPU uses or physical RUM PE memory addresses for both source or destination These ERAGE DPBPED commands do not check for an attempt to write to Flash PPP PPP memory though so be careful Table 2 Command address format The YPEEK and YPOKE commands read or write a specific word to or from memory remember that the NEWT memory is 16 bits wide an on chip peripheral port The YPOKE command must be used with care however because the entire address space of the NEWT microprocessor is available This means that a user can write directly to a word in the X Y Z or T register or to the variables used by the operating system or directly to an MMU register The last two memory commands deal with the Flash memory and
7. Probably the most significant new feature provided by the 41CL is the wide range of module images available 1n the on board Flash memory These images can be plugged into a Port just as a physical module would be plugged into a Port First the four character module identifier 1s entered into the Alpha register and the appropriate PLUG command is executed from the keyboard Twelve PLUG commands are available PLUGI PLUGIL and PLUGIU control Port 1 on the calculator with corresponding commands for the other three ports The PLUG commands parse the module identifier and verify that the selection is valid for the Port selected Just like the original physical modules some module images can only be used in particular ports and if an invalid configuration is attempted a DATA ERROR message will result Once the selection 1s validated the software then automatically programs the MMU so that accesses for addresses in that Port will be redirected to the module image in the Flash memory At this point a Catalog will verify that the module is plugged into the Port and available for use No power down of the calculator is required While a module image 15 plugged into a port the physical port is not accessed by the CPU so physical modules may be present in the Port without any electrical conflict In addition to the module images in Flash memory blocks of RAM memory may also be plugged into a Port This allows the on board RAM memory to be used as HEPAX m
8. plus it would redefine the arithmetic and change sign keys as before In addition choosing HEXM would also activate the menu for hex input Finally choosing the LOGIC menu would activate the most recent base menu mode as well as turning on the LOGIC soft keys Tallying the Changes Overall the 5 955 function combinations had their keystroke totals reduced in the revised 42s from 32 104 to 29 515 causing a reduction in the average keystrokes per function from 5 392 to 4 956 or almost half a keystroke However digging a bit deeper reveals more significant differences A total of five soft key menus were able to be eliminated With the 39 additional commands added to the keyboard the number of function combinations accessible directly from the keyboard increased from 2 562 to 4 260 with a similar drop in the number of menu based functions Those new keyboard accessible functions averaged over 1 2 fewer keystrokes per function than when they were embedded in menus For the thirty HP Solve 23 Page 27 Page 8 of 9 commands which take no parameters the average keystrokes per function dropped by 2 1 In addition due to the new ALPHA entry method the commands whose most efficient access were through spelling out via ALPHA had their average keystrokes per function reduced from 12 694 to 10 618 or by around two keystrokes each With these changes a very worthy successor to the HP42S and higher powered companion to the HP355 coul
9. to have the machine run faster the NEWT 15 designed to run at up to fifty times normal speed using the Turbo mode But I couldn t just bump up the clock speed of the CPU without considering the rest of the HP 41 system For example anything plugged into a port has to see only the original 360 KHz clock and bus signals So while the NEWT is running faster than normal it continues to drive the Port signals at regular speed It also automatically throttles back to normal speed for operations that have timing requirements such as communicating with the display or driving the beeper The second area of improvement was the memory space available There are literally dozens of plug in modules that I might like to have available at a time but trying to carry them around with the calculator just isn t feasible So I designed a way for the NEWT to access a much larger memory while remaining 100 backwards compatible with the original HP 41 software by using a Memory Management Unit MMU As I soon found out designing the circuitry to do this was just a fraction of the effort that would be required to put together a replacement CPU board and it wasn t until 2010 that I actually had enough time to devote to complete the project HP Solve 23 Page 38 Page 1015 The replacement CPU board which I call the 41CL I assumed that the numbering from 41C to 41CV to 41CX was partly Roman numerals 1s finally ready for prime time This board which is
10. a drop in replacement for the CPU board in an HP 41C has the following features All of the features of an HP 41CX except for the timer If you need the time functionality you ll need a Time Module plugged into one of the Ports Full 600 register Extended Memory is built in Over 100 plug in module images are built in Turbo mode with 2X 5X 10X 20X and 50X speed options 56 empty pages 4K in length in non volatile Flash memory available for user programs 58 pages 4K in length of RAM available All RAM is continuously powered Full bus compatibility on the Ports allowing the use of any peripheral designed for the HP 41 system New built in functions to manage the expanded memory A full duplex serial port is available with an optional connector Clearly most of these new features are not supported by any existing software so in addition to the hardware design I also had to write a set of functions that will allow the typical user access to these new features These functions which I call Y Functions and which Catalog as YENS 1A aim to provide an intuitive way for the user to manage the module images present in the Flash memory on the new CPU board as well as control the new Turbo operating speed modes In addition for the advanced user there are functions to PEEK and POKE memory move entire 4k blocks of memory access the on chip peripheral registers and do PUT and GET operations with the on board serial port
11. be entered into your machine in a minute or less These programs were developed on the HP 4 but they will usually run on the HP 49 and HP 50 as well Note the HP48 byte count is for the program only Professor Ulam says this 1s not his idea but many math students have seen this conjecture It states that given any integer if you repeatedly apply one of two operations on the number and the result you will eventually reach one The operations are 1 If odd multiply by three and add one 2 If even divide by two Take the first interesting integer 3 The resultant values are 3 gt 10 5 16 8 4 2 I The Ulam process was applied seven times or completed seven operations or cycles Note that when a power of two is reached the sequence directly divides by two repeating operation 2 to reach one The two programs below provide the basic Ulam values ULAM applies the rules and returns the next value in the series ULM repeatedly applies ULAM until one is reached keeping count of how many times ULAM is applied ULAM lt lt IF DUP 2 MOD THEN 3 1 ELSE 2 END gt gt 13 commands 52 5 Bytes 2F47h Timing 27 gt 82 in 12 7 ms ULM lt lt 0 OVER DO ULAM SWAP 1 SWAP UNTIL DUP 1 SAME END DROP SWAP TAG 16 commands 55 0 Bytes FBE2h Timing 27 gt 111 in 2 78 sec Questions 1 12 amp 13 require 9 cycles 14 amp 15 require 17 cycles What are the first three consecutive n
12. 0 2500 12 8 33333 1 12 11 22 4 54545 2 92E 14 32 3 125 6 84E 15 3 33 3333 37037 13 7 6923 3 30 11 23 4 34782 4 78E 14 33 3 0303 7 74E 15 4 25 390625 14 7 14285 8 99E 11 24 4 16666 7 49E 14 34 2 94117 8 50E 15 5 20 3 20E 06 15 6 66666 2 28 12 25 4 1 12E 15 35 2 85714 9 07 15 6 16 6667 2 14 07 16 6 25 5 42 12 26 3 84615 1 62E 15 36 2 77777 9 39 15 7 14 2857 1 21E 08 17 5 88235 1 20E 13 27 3 7037 2 25E 15 37 2 7027 9 47E 15 8 12 5 5 96 08 18 5 55555 2 54E 13 28 3 57124 3 01 15 38 2 63157 9 29E 15 9 11 1111 2 58 09 19 5 26315 5 05E 13 29 3 44827 3 89EE15 39 2 5641 8 88E 15 10 10 L10E 10 20 5 9 53E 13 30 3 33333 4 85E 15 40 2 5 8 27E 15 HP Solve 23 Page 47 Page 4 of 5 Does this process provide another perspective of the value of e If you use ever larger values the Value in the tables approaches 2 71828 18284 59045 23536 02874 71352 66249 77572 47093 69995 95749 If you have an electrical background the number 36 should pop out This number is the complement of the time constant The Product peak value corresponds to the 37 value or 2 7027 Time constant T l l e 63 2120558829 e6 Is 100 63 2120558829 36 7879441171 the proportional value corresponding to e of the numbers in Fig 4 Fig 5 and Table 2 Let s evaluate a few Part and Product values for 1 000 367 2 7247 and 5 8553E159 368 2 7173 and 5 8614E159 Peak 369 2 7100 and 5 85154E159 Let s eva
13. 10 as indicated by the Part column Ten divided by the part value is listed in the value column The Product column is the Value column multiplied by itself by the Value of the Part Mathematically the Product column 1s the Value raised to the power of the Part or Value 10 divided by 3 is 3 3333 and the Product 3 3333 37 037 The number 10 is only used here to illustrate the process The Value and Product columns are plotted as shown in the red and blue plots Note that the Product and Value curves start Pat Vave Product ined together and end together Also note that the ae SEIEN product values reach a peak Fig 5isasimilar plot 99997 79775 son for the number 20 The point we are interested isin 5 4 1024 the peak of the product To better show the values I 2777 777 100 4 only plotted the first 14 of the 20 values I also 25 1525 87 plotted the vertical axis using a logarithmic scale T nur 1321 28 See 5 in Fundamentals of Applied Math Series in 11 1 81818 717 811 issue 22 By now you should notice the value of sat sagas 2 T ee Lean th i the 7 part Itis close to e 14 142857 147 444 Table 2 list the relevant values for the number 100 8 gt Twenty divided into equal parts Table 2 Table of the First 40 Equal Parts of 100 Part Value Product Part Value Product Part Value Product Part Value Product 1 100 100 11 9 0909 3 50 10 21 4 7619 1 71E 14 31 3 2258 5 85E 15 2 5
14. 23 page 3 Article The HP 10bII Financial Calculator Gene Wright What is it The HP 10bII is Hewlett Packard s revised entry level financial calculator It updates the functionality of the HP 1061 for the first time since the introduction of the original HP 10B back in January of 1989 These changes really increase the functionality provided on this entry level financial calculator so much so that calling it entry level just seems wrong The images below show the current HP 1061 on the left and the updated HP 10bII on the right Packing all these new features into the HP 1061 is incredible HP 10bll 2 Financial Calculator Financial Calculator ON paw 33805 50 SHIFT BEGIN DMY M DY 360 Act Sem INPUT MU l Fig 1 HP IObII current Fig 2 HP 10bII new release The four images below show previous versions of the HP 106 and HP 1061 family including a never released version on the far right ENS a HEWLETT HEWLETT O PACKARD BUSINESS po BUSINESS i i Bom ui ki uis cu o NN ie 0 0 Mie 1 t WR sooo oc 0 WA iG Y RCL CFj cSt MAR T CLEAR ALL INPUT a Ex Ey Exy tei ce ON ET E Fig 3 Early version Fig 4 Ugly version Fig 5 Early IOBII Fig 6
15. About the Author Gene Wright is the author of textbook Quantitative Analysis for Business a business math textbook using the 10 and HP 12C available from Amazon com is also a video lecturer for a CFA exam review course A former teacher at Lipscomb University in Nashville Tennessee he now works for a consumer electronics company Gene has written many articles on HP calculators and serves on the annual HHC committee HP Solve ft 23 Page 9 Page 6 of 6 From Editor HP Solve 23 page 10 Article From The Editor Issue 23 Winter is in full force with many areas getting lots of snow and ice HP Solve readers have spent more time indoors It seems that the RPN Tips Column has run its course Unless a reader provides an input the 22 previously published RPN tips will have to be it I am also saddened to report that I will discontinue the Math Problem Challenge series The reason for this 1s the Internet One of the most important skills anyone needs these days 1s the ability to find what you want to know on the Internet All you have to do is enter the problem into Google or other search engine and you get the answer That is no challenge Here is the content of this issue S01 HP 10bII Financial Calculator Gene Wright This new version of the HP 1061 is essentially a brand new machine While the foundation is the 1061 the feature and function set expansion is truly astounding Not s
16. FV and turn on the Y indicator The layout of the screen is shown below AMORT CFLO f STAT ERROR IL PER PRIN INT BALJL CF Y JLTVM FULL STAT FUNC AV Je n on vh Fig 7 HP annunciators Chain and algebraic mode The HP 10bII can be placed into either chain mode or an algebraic mode with hierarchy by the mode toggle 255 When pressed the display flashes a message to indicate which mode is active In chain mode H G EJES EHE returns a result of 9 while in algebraic mode it evaluates to 7 This will reduce the need for parentheses use in many problems Sadly RPN is not present on this model The operator stack has 13 locations available for a combination of operators and parentheses Trig and hyperbolic functions The HP 10bII includes trigonometric functions and their inverse functions as well as the corresponding hyperbolic functions with their inverses The angle mode can be set to degrees or radians using the mode Rad Deg toggle SAES The INV key is intelligent enough to know that if you just pressed FA S you intend to compute an inverse sine if you follow those two keypresses with the 3 key since the sine function is axa SIN above it This means that you do not have to press 1 just AESA Similarly the HYP key can be pressed without additional shift key presses To calculate the hyperbolic sine of 2 press SIN arcus MTM SIN HARAS To compute the inverse hyperbolic si
17. HESS ROM TOOL Circuit Analysis Pac TREK Clinical Lab Pac TRIH DYRK ___ PetroleumPaclA PETR ES41 Module 415 PlotterPacIA Table I Module images and mnemonics Control of the various Turbo modes is similar The TURBO2 TURBOS TURBOIO TURBO20 and commands select the corresponding Turbo clock speed The TURBOX command disables the Turbo mode and returns to 1x operation The TURBO command returns the current value of the Turbo mode in the X register All of the module images as well as the majority of the operating system HP Solve 23 Page 40 Page 3 of 5 software run at the selected speed However there are several timing loops in the operating system that will always automatically run at 1x The commands above will probably be sufficient for the vast majority of users and that s why I made them as simple as possible to use But advanced or adventurous users can take advantage of the remainder of the Y Functions and the features of the NEWT microprocessor itself Most of these advanced commands require one or more memory addresses and in designing the command operation I chose to use the Alpha register for the user to input this information because it 1s hexadecimal The command is then executed and if data is returned the value in the Alpha register 1s modified appropriately Some commands also return a status in the X register 0 for success and 1 for failure
18. HP Solve HP 10bll Financial Calculator Gene Wright Learn how HP has upgraded the HP 10bll with a host of new and useful functions Now business and financial students and professionals have a low cost machine suitable for all of their calculating needs Your articles Tweaking the HP42S Jake Schwartz Jake has spent a great deal of time analyzing HP calculators and his unique perspective on keyboard clutter and layout is applied to one of HP s more interesting machines the HP42S LE What Is FOCAL Hichard J Nelson What is FOCAL and how did the HP User Community learn of this HP announcement HP Solve asks you to provide any historical information that will help remove FOCAL from its urban legend status Fundamentals of Applied Math Series 6 a Problem Solving Part Il Richard J Nelson This second part explores the classic problem of Triangle solving and what is involved Why hasn t there ever been a good efficient Triangle Solver on a calculator Upgrading the HP 41 Monte J Dalrymple Read how Monte was able to redesign the Nut processor to utilize more modern technology for greater speed and greater memory with a project he calls NEWT Customer Corner Issue 23 April 2011 Welcome to the twenty third edition of the HP Solve newsletter Learn calculation concepts get advice to help you succeed in the off
19. I hesitated including them because they require even more care by the user Because they operate on the Flash memory the code must be relocated to RAM before the commands can be used Both commands check to make sure that they are running from RAM before executing and will return an error message without executing if they are located in the Flash memory Both commands will also return an error message without executing if the user attempts to erase or program the area of Flash that holds the operating system Allowing either operation on the operating system area would turn the 41CL into a brick The YFERASE command erases a 32kx16 block of Flash to the default state of OXFFFF for every word The YFWR copies a 4kx16 block of RAM to a 4kx16 block of Flash An attempt to copy from Flash will return an error message without executing because the only operation allowed during a Flash write 1s the writes themselves The final commands deal with the on board RS 232 port Currently I have commands to set the baud rate BAUD96 BAUD48 BAUD24 and BAUDI2 select 9600 4800 2400 and 1200 baud respectively There are also PUT and GET commands to transfer individual bytes as well as serial block transfer HP Solve tt 23 Page 41 Page 4 of 5 commands I plan to offer an optional serial connector that uses a blank Port cover to hold a 2 5mm stereo jack to bring the serial port signals out of the calculator Although it has taken forever the 41CL is almost read
20. ake my students do this such as HP Solve 23 Page 6 Page 3 of 6 shown in the formula below having these built in rather than computing them using the factorial key will be a big time saver since it is essentially three combination calculations in sequence N Xt Xt N X n n X N Xt o X X X X n N n Fig I0 Hypergeometric probability distribution formula In addition the factorial function will compute the gamma function if given a non integer argument The HP 10bII also has two probability distributions built in the normal and student s t distributions For the normal distribution enter a standardized z value and press 25 To find the inverse normal distribution enter the cumulative probability and press to compute the z value To find a probability using the student s t distribution enter the degrees of freedom press enter a t value and press EJ To compute an inverse student s t distribution calculation enter the degrees of freedom press C23 enter the probability and press EJ Both of these calculations can be done using E5 to separate the arguments as well by keying the first argument pressing then keying the second argument followed by EJ The student s t calculation can also be set up as a constant calculation using ES the constant key This is very useful for students as tables won t need to be referenced in the back of a textbook any longer You can almost hear the cheer
21. ard layout is applied to one of HP s more interesting machines the HP 42S The HP 42S was a follow on to the famous HP 41C series and it was designed to be compatible with it The HP 42S Pioneer case used for 11 different models is a thin convenient design that 1s always popular with HP calculator users Its soft key menus are analyzed by Jake with extensive images He even examines the user interfaces of other machines such as the HP 35s HP 1060 and the HP 17bII in order to suggest a more effective efficient way of laying out the machine S05 Better Problem Solving Part The basic idea of a calculator is that it is low cost simple to use and fast to solve problems Calculators are efficient problem solvers that are unique when compared to versions found on computers and cell phones Better Problem Solving Part II explores the classic problem of Triangle solving what is involved and asks the question Why hasn t there ever been a good efficient Triangle Solver on a calculator A suggested user interface is described for this most important calculator problem S06 What Is FOCAL 15 this HP 41 Programming Language an Urban Legend What is FOCAL and how did the HP User Community learn of this HP announcement HP Solve readers are asked to provide any historical information that will remove FOCAL from the urban legend category S07 Upgrading the HP 41 by Monte J Dalrymple The HP 41 was an astounding machine It was part of a system
22. ared Fig 1 Resistors along the edges of a cube before I checked the Internet See my additional challenge Find the equivalent resistance from a to 2 at the end across the internal diagonal of the cube Solving for the equivalent resistance across the internal diagonal corners of the equal valued resistors connected on the edges of a cube see Fig 2 is a messy series parallel equivalent resistance problem This problem doesn t have much practical value except to stimulate your basic understanding of resistors current flow and voltage drops Most importantly this problem requires that you understand Kirchhoff s laws eT amp Calculate Equivalent The two important characteristics of this circuit you Resistance A to B R1 R12 2 982 Ohms should observe 1s that all the resistors have the same value and that the circuit has complete symmetry Fig 2 Resistors connected on edges of cube The value of studying and solving this problem is to illustrate and understand an analytical approach The exact value of the resistors is not important if you imagine the following First let s make each resistor one ohm Next we will connect an unknown voltage across points A and B such that one ampere of current flows Let s assume that the resistors have an adequate power rating Assume that the current flows into point A It sees three identical paths See Fig 3 Path 1 is R1 R4 amp R5 and then RIO a
23. at the most commonly used log bases are 2 amp 10 The base for natural logarithms is e which is given to 56 digits below Fig 1 HP35s key e 2 71828 18284 59045 23536 02874 71352 66249 77572 47093 69995 95749 The 15D value of the number e may be easily called to memory if you can remember 1 It starts as 2 7 This 1s 0 3 less than three 2 The next four digits repeat twice 1828 What happened in 1828 The year Noah Webster copyrights the first edition of his dictionary and science fiction writer Jules Verne is born 3 Think of a symmetrical right triangle It has angles of 45 90 and 45 This memory aid sequence 2 7 1828 1828 45 90 45 will give you 15 decimal digits of e e is an irrational number whose decimal expansion never terminates and is never periodic 1 What is the number that doesn t belong in the list above It 15 the center one See Issue 20 p30 1 Defining is usually defined by e lim 1 el n gt curve of limit converging to is shown in Fig 2 below See example values in table one 3 a HHH HHE SSeS Oe ae JI ETE LI LEEEEEELEEEELEEEEEEEL P4055 SOS SS00 S000 S 000 2 HE EE EXE EE
24. d address that much depite HP s original decision to restrict it to 8K An image of the original and revised 425 is shown in figure 7 First let us discuss the HP17BII physical case and keys The keyboard arrangement and two line dot matrix LCD matches that of the older Pioneer series and thus would be a perfect enclosure for a 42S successor Also with its slanted front keys it would be a natural for two shifts and two shifted key planes In order to retain the up and down arrow keys originally in the lower left along with the two shift keys some relocation was required in order to maintain the column orientation of these two key pairs Since the locations of the shifts have traditionally been in that lower left hand position over the past many years it was decided to move the arrow keys up to the middle of the second and third rows Along with this since an additional key was needed for the second shift the roll down and x exchange y stack manipulation functions were combined onto the same key just below the ENTER The other shifted position on this key also became a convenient place to include the roll up function as well HP Solve 23 Page 25 Page 6 of 9 LA Bree 42s Scientific Calculator RPN SCIENTIFIC SIN COS ENTER LASI x Fig 7 The original HP42S left and a proposed HP42S right ported to the current HP17BII case Adding Common Functions to the Keyboard For the remainder of the new sec
25. d be realized Epilog For More Information A collection of comprehensive keyboard metrics collected on roughly forty HP non RPL calculators from the early 1970s through to the early 1990s may be found at http www pahhc org keyboards htm Additionally there are studies as to how clutter and keystroke counts would be affected by experimentally adjusting the number of keyboard keys the number of shift keys the number of soft key menus and the number of single row menu pages And finally there are detailed metrics for our fictitious 42S along with discussions of a few earlier wish list machines based on previously published articles in 2008 in Britain s Handheld and Portable Computer Club HPCC group s Datafile newsletter Copies of those articles are available at http www pahhc org For additional information on the HPCC group consult http www hpcc org By no means are these particular fantasy machines the only ones ever proposed in detail by the user community for instance one should seek out the great work done by Walter Bonin who has been proposing logical and exciting enhancements to HP machines for several years now and with Paul Dale is currently engaging in a serious repurposing project for the HP30b financial calculator which would transform it into a powerful RPN programmable scientific machine Additional information along with the latest version of the 50 plus page user manual may be obtained at http so
26. d pairs At that point the FULL indicator is turned on to alert the user that they have entered the maximum number of pairs for which the data values can be retained If another data value is entered the existing individual data values are discarded and HP 10bII reverts to register based statistics only This does change how some entries would behave between the two models On the HP 10bII it was possible to enter 1 2 and 3 into the statistics data but then to remove 4 and 5 from the data even though they had never been entered The HP IObII4 will not allow this while in list based statistics mode since the 4 and 5 would not be present in the list to remove The HP 10bII also allows the direct computation of values such as the coefficient of variation which is the standard deviation divided by the mean Just compute the standard deviation press EJ compute the mean and press the key On the earlier 10bII model the mean must be computed first and stored into a memory Why did it work that way I have no idea but it is much better now on the HP 10bII What are some other goodies included The HP 10bII gets a previous answer function whereby the value previously computed when EJ was pressed can be recalled at any point by pressing FUE This is very useful The HP 10bII also includes 10 extra memories 10 19 which are accessed using the old method of pressing the decimal point before the memory digit Memory 1 is accessed by
27. ded DSE FC ES C FC C EREG X lt gt and and their direct and indirect stack register number and flag number parameters This totals 1 223 function combinations requiring 13 646 keystrokes or an average of 9 52 keystrokes per function On the HP42S the only non menu ALPHA spelled functions with parameters were those corresponding to the X lt gt function a total of 210 function combinations requiring 2 730 keystrokes or an astronomical average of 13 00 keystrokes per function In both situations the HP42S scheme appears to have been inferior to that of the HP41 from the standpoint of minimizing keystroke counts It should be mentioned that an additional 13 HP42S no parameter functions not appearing in soft key menus could be accessed via the comprehensive 42 page CATALOG FCN menu using fewer keystrokes than their ALPHA spelling counterparts Nevertheless these 13 still required 84 keystrokes for an average of 6 46 keystrokes per function Despite the shortcomings of the HP42S ALPHA function system the remaining aspects of the machine allowed its overall 5 954 function combinations to require 32 104 keystrokes or an average of 5 39 keystrokes per function On the other hand the HP41 s 4 873 functions and 27 042 keystrokes represented a slightly higher average of 5 55 keystrokes per function Nevertheless had the 42S employed a second shift key and additional keyboard function plane the functi
28. e functions were made available via increasing the number of keyboard shift keys and shifted function key planes As aresult an increasingly cluttered keyboard was unavoidable and the HP 67 and HP 34C handhelds from 1976 and 1979 represented the peak with 3 shifts each permitting up to four functions per key Let us define keyboard clutter as the average number of functions per keyboard key Based on this definition the clutter value for the 35 key HP 67 would be 3 26 and for the 30 key HP 34C 3 40 It could also be argued that the HP48 49 50 series machines are equally complex with their left right and alpha shifts although the 50g clutter has a slightly lower value of 3 00 By having all functions visible on the keyboard however no command was more than two keystrokes away and the overall moral to the story of this article is that fewer keystrokes per function are always better ENTER 4 35 80 12C 67 34C 48SX 50g Fig 1 HP calculators and the progression of keyboard clutter Left to right HP35 unshifted key 80 key with a single shifted function HP12C key with two shifts and the HP67 HP34C 485 and HP50g each with three shifts The HP41 Changes the Game In 1979 Hewlett Packard released the HP41C which among many other things set a new standard in RPN calculator functionality and programming power As it appeared to the designers that adding still more shift keys and shifted functions beyond three would not be a g
29. ed in the mail from HP on July 31 1972 He remembered the HP 35A in a recent article that included previously unpublished information on this calcul ator http hhuc us 2007 Remembering 20The 20HP35A pdf He has also has an article published on HP s website on HP Calculator Firsts E See http h20331 www2 hp com Hpsub cache 392617 0 0 225 121 html HP Solve 23 Page 32 Page 3 of 3 What Is FOCAL HP Solve 23 page 33 Article What Is FOCAL Richard J Nelson One of the most popular calculators HP has ever made is the HP 41 introduced in 1979 see Issue 16 The HP 41 was programmable and many thousands of programs have been written for this machine The programming language was simple powerful easy to learn and a very high percentage of users wrote programs for their machines What was the programming language of the HP 41 called FOCAL is was a trademark of Digital Equipment Corporation and is referenced in http www bitsavers org pdf dec pdpl l rt1 1 v2c Jan76 DEC 11 ORDDA A D V2C DocDir pdf The above link is a PDF file to an RT 11 Document that is described with the following Abstract This document lists and describes the software manuals for the RT 11 Operating System Version 2C V2C including the Monitor system programs FORTRAN and BASIC A list of DEC Trademarks is provided in the front of the document and is shown below Copyright 1976 by Digital Equipment Corporation The
30. ed on Monte I think the 41CL project was big enough Although now that it s done I wouldn t mind reverse engineering the processor used the 71B and original RPL machines just for fun But I doubt I ll have time for that anytime soon Actually since the Voyager series used the same CPU as the 41C it would be possible to clone the 15C or 16C using the NEWT design but the electronics is only a small part of such a project so I ll probably leave that to someone else Having the CPU on a daughter board so that I could reuse the case display and keyboard is the only reason that the 41 CL project was possible 28 HP Solve Do you have any additional comments that may be of interest to HP Solve readers Monte Go to an HHC and meet people who know HP calculators inside and out Many of the early machines still have secrets to reveal and it s great seeing the ingenuity and engineering that went into their design 29 HP Solve Thank you for spending your time with us HP Solve 23 Page 18 Page 3 of 3 Tweaking the HP42S HP Solve 23 page 19 Article Tweaking the HP42S Jake Schwartz Introduction In 1972 the HP35 calculator appeared on the scene and its keyboard was a straightforward affair with basically one function assigned to each key with the exception of an arc key which served as a shift for the SIN COS and TAN keys in order to provide ASIN ACOS and ATAN functions In those early years to follow more and mor
31. eled on each key front no machines in the clamshell series 18C 19B 19BII financials or 28C 28S scientifics ever took advantage of them The Pioneer Series A year and a half later 1n January of 1988 a new line of vertical format machines dubbed the Pioneer series debuted with both scientific HP 275 and business HP 17B models containing 2 line dot matrix LCDs and continuing with a row of soft keys at the top being defined by the bottom row of the display However a new rounded key shape would only accommodate a primary function to be marked on each key effectively removing the possibility of any key front shifted key plane with a corresponding second shift key When later Pioneer HP 20S 21S and 32SII models with 1 line screens required the addition of a second shift key and key plane the function labels had to be crammed side by side above each key contributing significant clutter to the look of the keyboard However these units achieved reduced keystroke counts as a result Figure 3 compares the 27S and 325SII HP Solve 23 Page 21 Page 2 of 9 Enter the HP42S Toward the end of 1988 HP introduced the non expandable HP42S Pioneer model as a successor to the HP41 series Both appear in Figure 4 Both the functionality and programming features were significantly enhanced while still maintaining backward compatibility with HP41 programs However one handicap which the 425 shared with the 41 series was the concealment of the va
32. emory or MLDL memory for example An experienced user may want to copy a module image to RAM modify it and then plug this modified image into a Port I had to do this while debugging the design as I had some errors in several of the new functions that I had to patch before they could be used Unplugging a module image from a Port is just as simple There are twelve UNPLUG commands available UPLUGI UPLUGIL and UPLUGIU control Port 1 with corresponding commands for the HP Solve tt 23 Page 39 Page 2 of 5 other three ports Unlike the PLUG commands no checking for configuration is performed The software merely invalidates the appropriate MMU entries so that the CPU resumes access of the physical Port The user is responsible for not unplugging half of a module image Table 1 shows the module images available and the corresponding module identifiers Module Image Module Image Module Image Advantage Pac 1B 41 541 Module 415 Melbourne Advantage Apps AADV ESMLDL 7B ESML PPC Module PPCM ADVENTURE 1 ADVENTURE 2 AECROM AFDC1 ROM AFDC2 ROM Autofinance Astrology ROM ALPHA ROM AMC OSX ROM Assembler 4 Assembler 3 ASTRO 2010 ASTRO 2010 UI HP Autostart Beechcraft ROM Aviation Pac 1A Boeing B52 BCMW ROM Buffer ROM CCD Plus Module CCD Module 1B CCD OS X Chemistry User PRIQ RAMP REAL ROAM ROMS SANA SBOX SECY SGSG SIMM SIMP SKWD SMCH SMPL SMTS STAN STAT STRE STRU SUPR SURV THER TOMS C
33. er because I entered it and in fact also submitted FOCAL as a name which I suggested could be short for Forty One Contra Algebraic Language rather than the more straightforward Forty One Calculator Language that eventually won There was a protracted period when they said that they d picked a winner but were going through some legal checking before they could announce it and I guess it was because the name had been used before for a language and they were doing due diligence for trade marks or assessing the likelihood of being sued or something like that HP Solve tt 23 Page 35 Page 2 of 3 If you know of or have a reference to answer the question of when the name and who won the contest I would love hearing from you The big question to me is how did HP announce this to the world The news letter was defunct The Fig 5 newsletter text implies that the winner would be notified If that was the case how did the HP User Community find out about it Some HP enthusiasts I have asked even suggest that this could be an urban legend X lt gt Y Richard Email me at hp com HP Solve tt 23 Page 36 Page 3 of 3 Upgrading m HP Solve 23 page 37 Article Upgrading the HP 41 Monte J Dalrymple Early in 2004 I discovered that HP had at some point in the past released many of the internal specifications for the chips and software used in the HP 41 calculator I design microprocess
34. g expired HP Solve tt 23 Page 34 Page 1013 The acronym meaning of the DEC FOCAL computer language is FOrmula CALculator language FOCAL as the HP name for the HP 41 calculator programming 7 ME leu language is the result of a naming contest conducted by HP Key Notes you is going to win our contest to Name That L The rul editor Henry Horn published in HP s calculator newsletter in the July and everyone except Hewlett August 1982 V6 N3 issue on page 16 He mentioned the contest in the um employees and their families may enter context of a letter from a reader asking about the HP 41 programming i ia i The Language name must be a language See the last part of the text in Fig 3 The details of the issue clever acronym such as radar BASIC are shown in Fig 4 scuba FORTRAN sonar COBOL 2 The acronym must relate to the HP 41 3 The acronym must be onginal new HP Key Notes continued to be published for another year until the ner seraon ia normitted August 1983 Vol 7 No 2 issue This was the last issue and still the contest winning name was not announced The text is shown in Fig 5 Fig 5 FOCAL Contest Details HP KEY NOTES June August 1982 Vol 6 No 3 Programming and operating tipa answers to questions and information about new pro grams and developments concerning Hewlett Packard handheld computers Published quar terly See page 15 Reader c
35. hat thinking must be automated Just put in your unknowns and get all the answers The only inputs case information the user need be concerned with 1s 1 One of the inputs must be a side 2 The relative relationship of the sides and angles A a B b C c This 1s insured by the labeled input diagram and the menu key labels How a Calculator Triangles Solver Should Work The purpose of a modern calculator is to provide low cost fast and efficient answers to numerical problems If you need to solve a triangle problem at your computer connected to the internet you could use one of the many solvers that are on the web such as http www handymath com cgi bin irregangle8 cgi submitzEntry HP Solve tt 23 Page 31 Page 2 of 3 This program does not provide a high accuracy answer 5D but it does handle the ambiguous cases and it provides two sets of answers This website nicely illustrates how a Triangle Solver should work It does not include the area If you want to visualize the relationships of a triangle see http www geogebra org en upload files english fauxmanchu visualizetriangleinequalities9 html If however you want to use a Calculator Triangles Solver it must be as efficient and easy to use as possible 1 key press should open the triangle environment 2 Three numbers should then be entered Upon the termination of the third number the machine should immediately and automatically calculate the remaining t
36. he 41CL project actually working 23 HP Solve Do you have a calculator collection How extensive is your collection Monte I wouldn t really call it a collection I am more a user than a collector I would love to have an HP 35 and an HP 65 The HP 65 was announced just a few weeks after I got my HP 45 and I was crestfallen at the time But I couldn t have afforded it anyway I would like to get an HP 15C at some point 24 HP Solve Do you have any special HP calculators Monte Only to me personally My HP 45 will always hold a special place for me as it got me all the way through grad school at Berkeley Clearly my 41CV holds a special place given the amount of time I ve put into upgrading it to the 41CL 25 HP Solve What does your family think of your interest in calculators Monte I think they call it calculator derangement syndrome behind my back But three of my kids are engineers and the fourth has started on that path so they sort of understand the fascination with technology 26 HP Solve What kind of HP calculator would you like in the future Monte Well the 41CL is basically all that I ever wanted The HP 35S was so close to being ideal for a practicing engineer But the hexadecimal handling killed it for me Even though I know its quality I cringe to think of the day when my 16C might die I would buy a small pile of a redo of that machine 27 HP Solve What other HP calculator related projects have you work
37. hhuc us 79 He proposed and published the PPC ROM and actively contributed to the UK AANE HPCC book RCL 20 His primary calculator interest is the User Interface HP Solve 223 Page 48 Page 5 of 5
38. hree unknowns and the area Exactly how this 1s done will depend on the calculator and its features The angular mode would be the same as the calculator is set degrees radians or grads A A graphing calculator could display the triangle nomenclature such as a Area E A soft menu could be labeled to match the diagram and the appropriate key pressed after keying in the value When the third value is entered the program automatically solves When the answers are calculated they could put on the diagram The Area would also be indicated If a value 1s changed enter with a shift menu key and a new triangle 1s calculated in a similar manner as the solver works B Anentry level scientific calculator could not provide as nice a user efficient interface as a graphing calculator because of its limited display One solution could be to use data registers R1 R3 Sides A B amp C R4 R6 angles a b amp c RO could be the area Key strokes are important and the user should not have to enter place holder values such as zero How often could you use a Triangle Solver If you have ideas on improving calculator function efficiency email me at Email HP Solve at hpsolveQ hp com About the Author Richard J Nelson has written hundreds of articles on the subject of HP s calculators His first article was in the first issue of HP 65 Notes in June 1974 He became an RPN enthusiast with his first HP Calculator the HP 35A he receiv
39. ice or the classroom and be the first to find out about new HP calculating solutions and special offers Download the PDF version of newsletter articles Contact the editor From the Editor amp 8 TT E ER a m E zum Learn more about current articles and feedback from the latest Solve newsletter including RPN tips One Minute Marvels and Math problem challenges Learn more Meet an HP Calculator user Meet Monte Dalrymple an IC designer based out of California Read all about his past and present experiences as an HP calculator user Richard J Nelson Does e stand for earnings exceptional or exacting The sixth installment follows up on the previous article in this series which discussed Logs and pointed out that most commonly used log bases are 2 6 amp 10 EEE If you received this e mail from an associate and or would like to receive email of this type directly from HP please click here HP respects your privacy If you d like to discontinue receiving these type of e mails from HP please click here For more information regarding HP s privacy policy or to obtain contact information please visit our privacy statement or write to us at Privacy Mailbox 11445 Compaq Center Drive W Houston Texas 77070 ATTN HP Privacy Mailbox Hewlett Packard website Sign up for Driver and Support Alerts The HP Financial Calculator HP Solve
40. ince the HP 27s has an entry level machine had such a powerful mix of financial scientific and statistical functions Now the business financial student has a low cost machine that is suitable for all of his courses Gene has done a superb job in covering this latest HP accomplishment S02 This is collection of repeating regular columns From the editor This column provides feedback and commentary from the editor One Minute Marvels This OMM reverses explores the so called Ulam s Conjecture If you have any curiosity about numbers and how they are related you will find the two routines listed are fun to play with There are some interesting relationships that you may discover examining Ulam s Conjecture Math Problem Challenge 3 Solution Here is an equivalent resistance problem that is really very easy to solve IF you use the right approach You must think out of the box on this one aspects of the Cube Edge Resistor problem are explored in the solution to this last HP Solve Math Problem Challenge S03 Customer Corner Monte Dalrymple Monte is a California microprocessor designer who is also an HP calculator enthusiast His story is an interesting one and his biggest HP calculator project is also described in this issue S04 Tweaking the HP42S by Jake Schwartz Jake has spent a great deal of time analyzing HP calculators and his unique perspective on keyboard clutter and keybo
41. ion with the ES key clearing the stats with or clearing the entire calculator with ka these new clearing functions are very useful given the expanded data space on the calculator Compared to the competition The basic competitor for the HP 1ObII calculator is probably the Texas Instruments BAII calculator The TI engineers are probably not happy with this new HP entry since each of the functions shown below are present on the HP 10bII and are missing from the TI BAII calculator Perhaps TI should rename their model the TI BAII instead Functions on the HP 10bII not found on the TI BAI Plus Entry of a number in scientific notation Student s t distribution Gamma function Entry of a number with 12 digits Inverse Student s t distribution Markup calculations 11 extra storage memories Best fit regression choice Initial CF frequency other than one PI Exponent regression model No CPT compute key needed to solve Normal distribution Inverse 1 x regression model Inverse Normal distribution Weighted average That is quite a list Conclusion HP has upgraded the HP IObII with a host of useful functions If a primary market for the HP 1061 were university students they can now purchase an HP 1ObII which should have all the functions for their business and science mathematics classes At the suggested MSRP this 1s an incredible price performance point Now HP we re all still hoping and waiting for a new low end scientific model
42. ions to solve for the unknowns based on the knowns He never used a calculated value to calculate another unknown This maintained the highest possible accuracy The automated aspect is that the calculator identifies the 19 possible cases and selects the appropriate solution method based on the input knowns There are two additional considerations for an automated triangle solver 1 The Side Side Angle SAS case is special See Fig 1 This represents a solution that is C C ambiguous There are two possibilities forthis in p the 19 cases The answer is to calculate both b solutions John Kennedy investigated this and that is exactly what his programs do It should be A C B A C B obvious that the selection logic of which equations are used on the inputs is very important Fig 1 Two solutions for SSA case a b amp B known 2 In addition to calculating the various unknown angles and sides of the triangle you may also want to know the area At least one HP Calculator manual suggested the use of the Solver to solve triangles While this 1s a good approach is it not quite the ideal solution In years past it was the speed of the solver that was the primary issue Today s machines are fast enough Perhaps the ideal solution using today s technology is to wrap a triangle solver user interface around the solver When people keep talking about cases as if the user needs to be even aware of them they don t understand the problem All t
43. keystrokes The HP42 s 25 no parameter functions such as COSH or STR found neither on the keyboard nor in soft key menus required a total of 253 keystrokes via ALPHA Comparing these the HP41 averaged 7 03 keystrokes per function whereas the HP42 required a significantl y higher average of 10 12 keystrokes per HP Solve 23 Page 22 Page 3 of 9 O RPN SCIENTIFIC PRGM ALPHA 5008 ENG ALL RD ASN m K CATALOG ENTER N IR PN SCIENTIFIC RPN SCIENTIFIC RPN SCIENTIFIC RPN SCIENTIFIC Fig 5a 5e The HP42S ALPHA menu scheme Pressing shift ALPHA reveals the ALPHA register and also initiates the soft key menu in image a Pressing the down and up arrow keys toggle between the two menu pages in a and b From menu a pressing the ABCDE soft key reveals the submenu in image c whereby the individual A through E characters are accessed Again from a pressing the JKLM soft key reveals the submenu in image d to access the J through M characters Likewise from the menu page in image b pressing the soft key takes the user to the submenu in image e where the individual arrow characters may be selected As a result of this system each character with the exception of those corresponding to the numeric and arithmetic character primary keys requires two keystrokes HP Solve 23 Page 23 Page 4 of 9 function For ALPHA spelled functions requiring parameters the HP41 inclu
44. luate a few Part and Product values for 10 000 3677 2 719608 and Overflow 3678 2 718868 and Overflow 3679 2 718124 and Overflow We can t see the peak value of the Product because our calculator overflows Summary and Conclusion is an interesting and exciting number that is fundamental to nature and mathematics It is an irrational number and a member of an exclusive group of five numbers that make up Euler s famous Identity e 4 1 0 e has a decimal expansion that never terminates and is never periodic In this articled e is defined and it value accurate to 56 digits is provided Several plots are used to illustrate the nature of this exciting number e is the base of the natural logarithms and a vital part of interest calculations involving the time value of money TVM It is so interesting that there 1s a book dedicated to it e The Story of A Number Finally a memory aid given in this article helps the reader to memorize and remember 15 digits of e About the Editor Iw 4 Richard J Nelson is a long time HP Calculator enthusiast He was editor and OW publisher of HP 65 Notes The PPC Journal The PPC Calculator Journal and the CHHU Chronicle He has also had articles published in HP65 Key Note and HP Key Notes As an Electronics Engineer turned technical writer Richard has published hundreds of articles discussing all aspects of HP Calculators His work may be found on the Internet and the HCC websites at http
45. mp R11 HP Solve 23 Page 13 Page 3 of 4 Path 2 is R2 R6 amp R8 and then RIO amp R12 Path 3 is R3 R7 amp RY and then R11 amp R12 We don t know what voltage is being applied to A amp B but if we could calculate it the resistance could then be calculated I 1 and the problem is half solved Using A as a reference ground V1 V2 and V3 as shown in Fig 4 is obvious by inspection V1 is the same as the voltage across If 1 3 ampere and R3 one ohm V1 is 1 3 volt V2 is the sum of the voltage across R3 and R7 R7 has 1 6 volts across it V2 1 3 1 6 volts Caleulate Equivalent V3 is the sum of the voltage across R3 R7 and R11 RI R12 2 982 Ohms 1 3 1 6 1 3 2 6 1 3 2 6 5 6 volts Fig 3 Current division from A to B The equivalent resistance 5 6 volts divided by one ampere 0 8333333333 ohms The problem specified that each resistor 1s 2 982 ohms Scaling 2 982 x 0 8333333333 2 484 ohms Because of the symmetry there are only three different values you may measure across the eight resistor connection points of the cube 1 The internal diagonal is the problem as shown above x VI Calculate Equivalent There are two possibilities Both are the same value R12 2 982 Ohms Besist nce Ais 2 484 ohms Fig 4 Summing the voltages 2 Across each resistor All 12 values are the same no matter what resistor you measu
46. ne of the result press PA G5 CAC or Bond calculations The HP 10bII receives nice upgrade by providing functions to calculate bond price and yield A bond with a call provision is also handled nicely by changing the default value of 100 stored in the CALL register to the appropriate call value HP Solve 23 Page 5 Page 2 of 6 Date calculations The HP 10bII now does date calculations in actual 360 day calendar modes To compute the days between two dates key the first date press key the second date and press 8 bar For a date given a date and a number of days key the date press 9 key the number of days and press E98 xg Alternatively these two functions can also be inline operators where the first value 1s keyed the function accessed then the second value keyed followed by EJ This approach works for all two value functions other than arithmetic they can be done as inline or postfix operators Note that a date given a date and a number of days 1s always computed in actual days mode Dates may be entered in M DY or D MY formats depending on the mode setting The screen image below shows a date in the M DY format The last digit on the right indicates the day of the week lu Fig 8 Date as shown in the M DY format Breakeven calculations The breakeven relationship including a target profit 1s calculated using the third row of blue shifted functions as shown in the formula below FC is the fixed c
47. ne with over These are subtracted with the final and the program terminates The Story of a Number Now that we know the value of e and we can easily calculate it we will explore the number that even has a book published by Princeton University Press 41 William Street Princeton New Jersey 08540 4 e THE STORY OF NUMBER Ly LII tant TO PE i tele ts e V ul L 11 WOR C SL _ 4 me 4 Zr 8 Ta Or 3624 ie ler ELI cb EL XA A Q X Fig 5a 1994 Har o version Fig 3b 1998 paperback edition Fig 3c 2009 paperback edition HP Solve 23 Page 45 Page 2 of 5 dedicated to it This book has been translated into Spanish Greek Portuguese Brazil Korean Chinese traditional and Japanese See Fig 3 above is sometimes called Euler s constant and some writers have referred to it as 8 constant The name designation is often given as for Euler or for Exponent is also more easily p gt n 1 4 1 Fr e2 calculated by 21 3 4 Understanding A few numbers are especially important in mathematics Zero one and i are examples has to be added to this short list Combining these five numbers into one identity is one of Leonhard Euler s major accomplishments Where Ut e is Euler s number the base of natural logarithms i is the imaginary unit which satisfies 1 1 is pi the rati
48. ntinued to leave the majority of built in functions hidden but provided access via six at a time soft key menus using the top row of keys which were re definable and labeled in the bottom row of the LCD The clutter value for the HP 18C is only 1 43 functions per key and it would be even lower were it not for the left hand keyboard s numerous shifted alphanumeric characters Multiple soft key menus were reached starting with the MAIN menu and traversing the menu tree with keys leading to submenus named FIN BUS SUM TIME SOLVE and Furthermore many of those submenus contained menus at further lower levels as well Since a maximum of six functions could be displayed at once menus requiring additional functions had their sixth and rightmost key position labeled MORE or OTHER which when pressed revealed another HEWLEIT PACRAHLD TB Business Consultant ON USER PRGM ALPHA COS TAN po STO RCL DISP PRNT EXIT ENTER 4 CHS EEX INPUT 72 XEQ STO 557 K M Fig 2 The single line segmented HP41 LCD left permitted spelling out function names while the multi line dot matrix HP1ISC screen right on the right side of its clamshell case provided a method for labeling a menu of up to six soft keys in the top row row of functions Also despite the fact that the physical shape of the keys allowed for an additional function to be lab
49. o of the circumference of a circle to its diameter as the base of the natural logarithms and is frequently used in financial compound interest and natural growth calculations These calculations are part of the Time Value of Money TVM solver environment of HPs financial calculators The idea of adding the interest to the principal on each compounding time period raises the question of the length of the period The adage time is money is based on this relationship Interest and interest compounding associates the value of money on the time and the interest rate Most interest rates are annual interest rates expressed in percentage and usually specified as an APR Suppose the period is reduced from monthly to weekly If the interest rate remains the same the principal will grow faster because of compounding interest What happens when you reduce the interest time period to a day minute or a second Will your principle increase ever faster Is there a limit Yes there is and it is e This limit is called continuous compounding The formula to calculate the future value of a starting principal with interest compounded n times per year 15 FV 4 Where FV is the future value after Y years Y 1s the number of years P 1s the starting principal r is the annual interest rate n is the number of compounding periods To get to the continuous case we take the limit as the time slices get tiny FV limit P l r n
50. omments or contributions are welcomed Please send them An Internet search hasn t resolved the issue but the search has not been tooneof the following addresses completely exhaustive Fig 4 Issue Details of Fig 3 HP 41 Language Contest In V6N3 we initiated a contest to name the A search of the various user community newsletters should be made a used by mii ie by the way the contest was long ago closed so please The search should start after August 1983 do not submit more entries Since the end of the contest we ve tried to legally clear several The following references describe the HP 41 version of FOCAL you seemed to favor but they already were registered trademarks Also it is very difficult to do this on a worldwide basis http en wikipedia org wiki Focal We are o have a winner in process and we will notify http en wikipedia org wiki Focal_ HP 41 that person soon We haven t forgotten you http www absoluteastronomy com topics Focal_ HP 41 Fig 5 Last Issue contest report Here 1s an HP Museum reference to FOCAL Re FOCAL Message 12 Posted by Frank Wales on 15 Sept 2004 5 24 p m in response to message 11 by Mike Stgt FOCAL actually got associated with the HP 41 via a contest that Henry Horn ran through HP Key Notes to come up with a name for the 41 user code programming language around about 1982 I think I rememb
51. on keystroke counts would have been further reduced and machine ease of use further improved Back To the Future Flashing forward to 2007 2008 we saw the return of HP s usage of keys with slanted fronts permitting shifted key functions to be printed on the keys themselves Some examples of these are the HP35s which supported menus and the with no menus each with two shift keys along with the single shift menu plentiful HP17bII as shown in figure 6 Not only did this reduce the clutter around the keys but in the case of the HP35s keystroke counts were kept in check by filling all available shifted key positions with functions not otherwise occupied by menu access commands such as LOGIC CLEAR and BASE Another way that the HP35s managed clutter was to place its alphabetic key markings also on the key fronts just to the right of its blue shifted function names Compared to the HP325SII as shown in figure 3 with its alphabetic markings in the space to the lower right of each key the 35s appears less intimidating to this user Now returning to the present with the migration to a new much faster CPU as the basis for the HP20b HP30b and the latest incarnation of the HP12C it can only be imagined what a speed boost like this would do for the scientific machines Based on this possibility let us consider a revived HP42S with the speed of a modern CPU plus some additional tweaks 1 By function combinati
52. ond shifted key plane the goal was to bring out commonly used functions and programming aids many of which appeared on the HP41 s faceplate As a result virtually all of the functions in the FLAGS BASE PROB and CONVERT menus were able to be relocated onto the blue shifted positions along with the LBL RTN and ISG programming functions In addition keys to activate the x and zero and comparison test menus were promoted to the keyboard from originally having only been embedded as submenus inside the PGM FCN menu A total of 39 items were added representing 1 690 function combinations averaging 4 532 keystrokes per function in the new layout versus 5 736 for the embedded ones in the original 42S Of those 39 thirty are functions needing no parameters and they average 2 300 keystrokes per function for the new layout versus 4 433 for the original machine The only reason this no parameters average is not exactly 2 000 is due to the hyperbolic trig functions which require the blue shift HYP ahead of the trig keys themselves For these functions the advantage is not only the reduction in keystrokes but also that they are directly visible on the keyboard and thus may be located much more quickly Changing the ALPHA Scheme By bringing the alphabetic capital letters along with a few punctuation symbols out onto the keyboard Page 7 of 9 ALPHA entry returns to the HP41 method which averages one ke
53. ons we mean all the ways a function may be combined with its parameters For example the STO function may directly address the 100 numeric registers 00 through 99 or the 5 stack registers L X Y Z or T plus it may indirectly address values in those same 100 numeric or 5 stack registers This totals 210 possible parameters In addition the ALPHA variables may also be directly or indirectly addressed however the number of possible combinations of these are too numerous to count HP Solve 23 Page 24 Page 5 of 9 Financial Calculator HP 17bll Financial Calculator HP 35s fo Scientific Calculator E 821 X Y822 8 02 Ba22285 iso Ps Por re Por EBOGEDO ma 22 re a BDBoagsS 25 3 E Ed ES ON ENTER 4 44 Fig 6 HP35s scientific calculator left HP 1ObII financial machine center and the HP 17bII financial calc right all with keys which permit shifted functions to be printed on the front of the keys 1 Since the key arrangement and screen of the current 7 mimics that of the original 42S migrate the functionality into that physical case 2 Reduce keystroke counts for some commonly used functions by utilizing a second shift key and shifted key plane allowing for elimination of some menus 3 Adopt the HP41 HP35S ALPHA scheme with letters on each key front and 4 Increase the RAM capacity to 32K since the HP42S operating system coul
54. ood idea they changed the user interface philosophy with the HP41 whereby the majority of its function set was hidden from the user s view This machine with a single gold colored shift and shifted function key plane only barely began to reveal its built in capabilities In order to access functions which were not shown on the keyboard one would have to spell them out alphabetically in the single line segmented LCD from the new ALPHA key plane with its letters placed on each key front Counting both the gold and ALPHA shifted markings the clutter value for the HP41 was 2 64 functions per key Additionally as a spelling and reference aid the HP41 provided a CATALOG command which listed the name of every function one by one in alphabetical order Spelling out function names unfortunately increased many times over the number of keystrokes required for the average command For example the keyboard BEEP shifted function only required two keystrokes but the non keyboard ABS function needed ABS OF Six keystrokes Clamshells Soft Keys and Menu Trees In June of 1986 after the final iteration of the HP41 the 41CX was a couple of years old HP went in another direction by bringing out the first of a new line of clamshell case machines with multi line dot HP Solve 23 Page 20 Page of 9 matrix LCDs the HP18C Business Consultant With only a single shift key and corresponding sparsely filled right hand shifted key plane it co
55. ors for a living and it was fascinating to see how some relatively simple hardware combined with some very clever software could implement the marvel that is the HP 41 Just for fun I decided to try to create a clone of the NUT CPU which was the processor used in the HP 41 At the time my main goal was just to demonstrate that designing such a CPU using modern design tools wasn t really that difficult In fact 1t only took me about six weeks working in my spare time to finish the design But once the design was done I realized that the internal construction of the HP 41 might allow me to actually replace the brains of the calculator This is because in all but the last iteration of the HP 41 the CPU and Fig 1 Old and new CPU memory is contained on a small daughterboard that connects to the main calculator circuit board via a press fit connector This is how the NEWT which stands for Nut Extended With Turbo came to be I didn t want to just replace the CPU in the HP 41 I wanted to try to extend the design to take advantage of the advances in technology since the time of the HP 41 I targeted two areas for improvement The first area of improvement was the speed of the machine The CPU in the original HP 41 ran at just 360KHz which might seem ludicrous given the multi GHz clocks of today s computers but it was more than sufficient for most uses of the calculator However since there are some cases where it would be nice
56. ossibilities conversions Problems With Two Possibilities Function amp Inverse alternate Part I concluded with Better Problem Solving Part II will suggest a method of implementing a function that requires a single key press and three inputs The function then decides which of 19 solutions 1s the correct one and then calculates four outputs If this function 1s added to all mid range and high end scientific calculators it would save hundreds of hours of involved calculations for just about every technical user The problem is a very common everyday type problem Solving Triangles The problem I am referring to is what I call triangle solving Surveyors are probably the most well known triangle solvers but nearly every engineer technician contactor or hobbyist has had the need to solve usually for a side a triangle problem If you Google Solving Triangles you will get nearly 2 million hits Obviously this is an important problem Most HP calculator manuals will have Triangle solutions included Calculators with solvers will address the problem using the solver All of these fall short of a good efficient built in automatic Triangle Solving Environment to use an RPL term Why hasn t there ever been a good efficient Triangle Solver on a calculator Understanding the Problem The critical issue here is automatic If you research triangles you will find long discussions on triangle properties e g the sum of the angles
57. ost SP is the sales price per unit and VC is the variable cost per unit This is very handy for the student FC Profit SP VC Breakevenin units Depreciation calculations The HP 1061 handles depreciation calculations in the same way that the HP 12c models do The original cost is stored in E4 the salvage value is stored in ES while 28 is used to hold the declining balance factor and holds the expected life of the asset The user enters the year for which the depreciation 1s to be calculated and presses followed by the c or function to compute straight line sum of the year s digits or declining balance method The depreciation is returned to the display and the X and TVM indicators are turned on Pressing will display the remaining depreciable value and turn on the Y indicator The indicator 15 on to indicate a calculation 15 in progress and that TVM registers are being used Fig 9 Depreciation calculation in progress with TVM annunciator Enhanced statistics The HP 10bII now has a random number generator permutations and combinations built in The random number seed can be set by keying a value and pressing f Having two key positions dedicated to directly compute permutations and combinations may not seem like a big deal since the calculation using factorials isn t all that complicated However if a student is computing a hypergeometric probability calculation by hand and yes I used to m
58. ounced I had to have a 95L X and I still use it as a personal organizer I have one of most of the RPL models but never really use them The 4 level stack of the HP 45 is hard wired into my brain and I find myself cursing whenever I try to use the unlimited stack of an RPL machine I use my HP 16C quite frequently for hexadecimal calculations My desk always has my original 41CV and my 16C at hand I have an HP 33S and HP 35S but don t really use them regularly I really like the styling of the HP 35S but the handling of hexadecimal numbers is just too cumbersome 9 HP Solve What have you used your calculators for Monte Anything and everything I have copies of most of the HP modules for the 41CV and enjoy just exploring what they can do 11 HP Solve Have you noticed anything interesting about calculator usage during your travels Monte It s interesting that you can tell how old an engineer is by the calculator that he or she carries I still carry my 41CV which really dates me in meetings but I still see a lot of 32SIIs Many young engineers seem to view a calculator as almost disposable which is unfortunate Most programmers that I interact with are doing very low level programming and they usually have a 16C that is worth its weight in gold to them 12 HP Solve Does your calculator usage involve more than your profession Monte Yes I already mentioned the 95LX as a personal organizer and I also play chess on it TVM calculation
59. pectively This permitted direct 2 key access to the and pi characters in ALPHA mode as well without requiring any menus With the new 42S two changes required moving these functions elsewhere First since the RCL key now contains H as the primary ALPHA function ARCL as the gold shifted function and h as the blue shifted function no other position remains available in ALPHA mode Secondly function was moved off the next key to be replaced by the up arrow primary and BST gold shifted function It therefore became necessary to move and pi to keys which had an ALPHA function position open The spots chosen were above the decimal point and the since their primary ALPHA characters were not alphabetic leaving the blue shifted positions available Eliminating the BASE Menu On the original HP42S the six key BASE menu would activate the four base mode keys plus the A F submenu for the hex digits along with a LOGIC submenu key for bitwise logic functions in any base Also while the BASE menu was activated the arithmetic and change sign keys would perform the 36 bit BASEY BASE BASE BASE and BASE functions On our updated machine the four base mode functions plus the LOGIC menu were brought out on the blue shifted functions on the keyboard fourth and fifth row Pressing any of the four base mode keys would activate that particular base mode
60. postage prepaid READER S COMMENTS form on the last page of this document requests the user s critical evaluation to assist us in pre paring future documentation The following are trademarks of Digital Equipment Corporation DIGITAL DECsystem 10 MASSBUS DEC DECtape OMNIBUS PDP DIBOL 05 8 DECUS EDUSYSTEM PHA UNIBUS CHIP RSTS COMPUTER LABS L RSX COMTEX TYPESET B DDT TYPESET 10 DECCOMM TYPESET 11 Fig 1 List of Digital Equipment Trademarks related to their computer systems as listed by DEC A search of the USPTO found the following There are many other US and foreign FOCAL trademarks listed including several from FOCAL Corporation Use the Back button of the Internet Browser to return to TESS Typed Drawing Word Mark FOCAL Goods and EXPIRED IC 016 US 038 G amp 5 BOOKLETS AND MANUALS CONTAINING COMPUTER LANGUAGE AND INSTRUCTIONS FOR PROGRAMMING FIRST USE Services 19680216 FIRST USE IN COMMERCE 19680216 1 TYPED DRAWING Serial Number 72293484 Mark Drawing Code Filing Date March 18 1958 Current Filing 1A asis Original Filing 1A Basis eir 0879976 Registration Date November 4 1969 Owner REGISTRANT DIGITAL EQUIPMENT CORPORATION CORPORATION MASSACHUSETTS 146 MAIN ST MAYNARD MASSACHUSETTS 01754 Type of Mark TRADEMARK Register PRINCIPAL Affidavit Text SECT 15 Live Dead Indicator DEAD Fig 2 Digital Equipment Corporation registered FOCAL trademark details The trademark has lon
61. re 3 The diagonal of each cube face 12 total These are all the same Further investigation Can you now calculate the two values 2 amp 3 listed above See measured answers below How could you arrive at these answers peuseew 52 SUYO OFT C E SUYO T Cube Resistance Problem Solution Note 1 There are two basic laws i Around any closed circuit the algebraic sum of the voltage sources and IR drops must total zero ii At any junction of two or more conductors in a circuit the algebraic sum of the currents into a junction must equal the current out of the junction HP Solve 23 Page 14 Page 4 of 4 Customer Corner Meet Monte Dalrymple HP Solve Z23 page 15 Article Customer Corner Meet Monte Dalrymple Editor s note Customer Corner has appeared in past issues of HP Solve where we interviewed the worldwide users of HP s calculators Past interviews have been of users who live and work in the US UK Canada and Germany We now go to Liver more California for our next interview 1 HP Solve What is your background Monte I was born in a small town in Idaho but have lived in California since I was six I was always building things and discovered electronics in Junior High 2 HP Solve What did you study at school Monte I majored in Electrical Engineering at UC Berkeley Most of my coursework was in analog design and I didn t really do anything digital until my senior year My gradua
62. s are a snap on that machine too I use my 41CV whenever I am helping my kids with homework They had to have TI machines for school but for the life of me I can t use a machine with an equals sign 13 HP Solve What was the largest problem you have solved with an HP calculator Monte Well it wasn t one big calculation but I had to calculate the appropriate transistor size for each of the seventeen thousand transistors on my first chip Fortunately the computer does that work automat ically these days 14 HP Solve What are you currently using HP calculators for Monte I use the 16C for hexadecimal calculations almost daily Cost benefit calculations related to chip size and yield balancing the checkbook and so on for the 41CV 15 HP Solve What appeals to you about HP calculators Monte One word quality My HP 45 still works and I pull it out occasionally My 41CV is older than any of my children and I still use it daily 16 HP Solve Do you have a website Monte Yes http www systemyde com is where I advertise keep my resume and so on I have the rights to most of the designs that I have done recently so I use the website to give potential customers the information they need about these designs 17 HP Solve What are the important aspects of your website Monte If you go to http www systemyde com hp41 you ll see my work on the 41CL project in all its glory 18 HP Solve Do you write or post calculator articles on yo
63. s of students going up across classrooms even now Six regression models and best fit In addition to linear regression the HP 1061 can fit logarithm exponential power exponent and inverse REGR models to data by opening the regression environment by pressing C Number and Mode Description O Best Fit Automatically selects fit linear m x b 2 Logarithm m n x b 3 Exponential p elm x 4 Power b x 5 Exponent b m 6 Inverse m xb The presently selected model is displayed and and move up and down through the choices When the display indicates the model desired pressing will select that model The actual fit occurs when a regression function is executed Pressing will estimate an X value given a Y value and return the correlation in the SWAP position Pressing will estimate a Y value given an X value and return the slope the m coefficient for other models in the SWAP position Pressing will compute the weighted average X weighted by Y but also returns the slope the b coefficient for other models in the SWAP position When best fit is selected the HP IObII quickly selects the model with the best correlation and then displays Best fit for a moment followed a quick display of the model chosen New data editors The HP 10bII also includes the ability to review and edit statistics and cash flow data Pressing or opens up a data review editor where pressing moves you up or down through en
64. st majority of its functions under the hood This time around the user had the choice of either spelling them out in ALPHA mode like before or seeking the appropriate soft key menus containing the desired functions In both cases however the number of keystrokes required remained quite high as compared to a machine which was able to have all its functions visible out on the keyboard Also the ALPHA mode scheme on the 425 was very different with most of the characters embedded in a tree of soft key menus rather than being out on the keyboard With its single shift key and no ALPHA characters marked on the keyboard the 42S clutter value was only 1 95 functions per key versus 2 64 for the HP41 Despite access to many HEWLETT HEWLETT UJ PACKARD hp PACKARD SCIENTIFIC 3251 Figure 3 Two Pioneer series models the HP27S left from 1988 with its clutter value of 1 73 functions per key and HP32SII right from 1991 with its second shift key and higher clutter value of 2 73 With their rounded surface keys the provision for a function on each key front had been removed more available ALPHA characters than in the HP41 getting to the letters A through Z required two keystrokes each versus one on the HP41 Figure 5 shows examples of the HP42S ALPHA navigation scheme The HP41 had 37 functions requiring no parameters such as HMS or ABS which were not on the keyboard and therefore required spelling via ALPHA taking a total of 260
65. te work was about half analog and half digital When I started working I had to choose one way or the other and digital won 3 HP Solve What is your occupation Monte I have been an IC designer all of my career My first design was a serial communications controller and it s still in production today although in a much different technology I migrated to CPUS and have done more of those than I care to count The NEWT project was a refreshing change because the bit serial operation was fundamentally different from anything I had done before with a CPU And it was quite fun figuring out how to expand the capabilities of the machine in a backwards compatible fashion 4 HP Solve Do you do much traveling Monte Not really In fact for the past fifteen years I have telecommuted so I don t even have to deal with a daily commute Most of my interaction with customers is via email or teleconference these days although I still have to occasionally visit the customer site When projects involve people in half a dozen time zones teleconference 1s the only thing that makes sense 5 HP Solve When did you first see or use an HP calculator Monte I was in the library reading Scientific American when I saw the advertisement for the HP 35 I was so impressed that I bought a copy of the magazine I don t think I still have it though When Macy s started carrying the HP 35 I used to go to the store just to play with the display calculator This was m
66. tered X Y data values or cash flow values and cash flow frequencies As you move through them the X and Y annunciators come on and off to indicate whether you are viewing an X or Y value in the statistics editor and the CF and N annunciators do the same as you view cash flow data HP Solve 23 Page 7 Page 4 of 6 R E 500 600 Fig 11 Examples of annunciators during the new data editing mode Values can be changed by keying a new value and pressing Pressing the inserts a blank entry into the data area and the EJ key removes the presently displayed pair of values Pressing erases the presently displayed value and replaces it with a zero which can be kept or overwritten by keying another value and pressing These abilities a welcome addition to the HP 10bII s functionality There is now dedicated space for 15 cash flows and 15 statistics data points In addition there 1s a shared data space for any combination of up to 30 additional cash flows or statistics data points So it 1s possible to have 15 cash flows and 45 statistics data points 30 cash flows and 30 statistics data points 45 cash flows and 15 statistics data points or any other valid combination This is another big change from the existing HP 1061 which only used register accumulations for statistics The HP 10bII actually stores the data values entered unless you try entering more than the maximum of 45 allowe
67. that included bar code reading of programs interfacing to all aspects of the instrument and computer HP Solve 23 Page 11 Page 1 of 4 world and using disc drives printers and a long list of other peripherals Well over a hundred plug in modules provided an extensive array of applications programs that extend from complex math to medicine Monte has re designed the Nut processor to utilize more modern technology for greater speed 50x and greater memory all 41 modules with a project he calls NEWT Nut Extended With Turbo After many years of part time work he is not able to offer an HP 41 replacement board for your treasured HP 41 to enhance its performance beyond your dreams The most popular programming machine ever in terms of being programmed is described in this article Check Monte s website at http systemyde com hp41 S08 6 in the Fundamentals of Applied Math Series e Does e stand for earnings exceptional or exacting This 6 installment of the Applied Math series is a 5 Logs follow on e 1s often elusive and this review should help eliminate some of its easily enabled episodes That is it for this issue I hope you enjoy it If not tell me Also tell me what you liked and what you would like to read about XY Richard Email me at hpsolve hp com HP 48 One Minute Marvel No 10 Ulam s Conjecture Joseph Horn One Minute Marvels OMMs are short efficient unusual and fun HP 48 programs that may
68. umbers that require the same number of cycles 2 Three requires 7 cycles The ratio of cycles to the number is 2 333 What is the next number that exceeds this ratio HP Solve 23 Page 12 Page 2 of 4 3 What is the lowest number in which the number of cycles exceeds 100 4 Five requires 5 cycles What 15 the next number that 15 the same as the number of cycles HP Solve Math Problem Challenge 3 Solution This problem solution is the third in a series of real world practical or teaching problems offered as a challenge to HP Solve readers This problem is an equivalent resistance problem The math involved is not very complex but if you have any basic electrical experience you will understand Ohms law and equivalent resistance Here is the problem Twelve equal resistors are connected together as if they were R10 the edges of acube The equivalent resistance to be calculated is across the internal corners of the cube 1 e from ato gin Fig 1 The value of each resistor is 2 982 ohms The best solution idea 15 one that gives a clear step by step explanation of the solution The best solution is based on the guidelines listed in Issue 22 When I proposed this problem I did so remembering when I first encountered it long before the Internet If you Goggle Resistor cube problem you will get 222 000 hits Obviously the problem isn t a very difficult one to even think about under these conditions Here is my solution prep
69. ur website Monte Not really but I did keep a running status update for the 41CL project and the manuals for the NEWT processor and the 41CL are available there too I did do an article about the 41 CL design for Circuit Cellar magazine It was in the October 2010 issue 19 HP Solve Can you explain in more detail Monte The 41CL is a project that replaces the processor in my 41CV with an upgraded version that I designed myself It runs up to fifty times faster and contains images of over a hundred ROMs on board HP Solve 23 Page 17 Page 2 of 3 It s fully compatible with all of the 41 peripherals With this upgrade I expect that my 41CV now CL will outlive me 20 HP Solve Have you had contact with HHC Monte I first presented the idea of a replacement processor for the 41C series at HHC2004 I am pretty sure that everyone there thought yeah right Since my day job got in the way it has taken a long time to come to fruition but I actually do have a 41CL now and have sent some out for testing by people I met at HHC 21 HP Solve How many HHCs have you attended Monte Only two mainly because I don t travel much Since 2004 I have tried to contribute a paper though 22 HP Solve What have you gained from the HHCs Monte Mostly an appreciation that there are still people who are passionate about the technology in HP calculators Lots of people from HHC have answered dumb questions or provided feedback that helped me get t
70. urceforge net projects wp34s About the Author Jake Schwartz has been an HP calculator fan since 1971 after first trying the HP9810A desktop RPN machine at a co op job at RCA in New Jersey He has owned most of the scientific top of the line handhelds since the HP35A in the early 1973 joined PPC Calculator Club in 1977 and contributed to many of the clubs since including serving as Peripheral Routines coordinator for the PPC ROM project for the HP41 in 1980 Currently working at Lockheed Martin as a software engineer Jake has been presenting at and videotaping the annual U S HP calculator conferences for more than two decades HP Solve 23 Page 28 Page 9 of 9 Better Problem Solving Part Il HP Solve 23 page 29 Article Better Problem Solving Part II Richard J Nelson Introduction In the last issue of HP Solve I suggested that I am convinced that it 18 still possible to improve the common functions that we use with our calculators The premise is that calculators still survive in the market place amongst so many other devices such as smart phones and mini laptops because of their convenience and low cost The calculator must continually improve or become obsolete Ever increasing problem solving efficiency is vital for an advanced calculator Four improved functions were discussed in Part I Problems with Two Possibilities A Problems With Two Possibilities Function amp Inverse Problems with Two P
71. y senior year in high school and I barely knew what trigonometric functions were but I found it incredible that a machine that fit in my hand could do that 6 HP Solve So when did you buy your first HP Monte I started college with a slide rule because the 395 price of an HP 35 was more than tuition for one quarter at Berkeley But by the time of my first finals it was obvious that to be a Berkeley engineer you had to have an HP calculator At the time my uncle worked for HP and employees were able to buy one calculator per year at cost The first year he bought one for himself but the second year I didn t ask him in time to take advantage of the deal By then the HP 45 was out so that was what I had to have Given the size of the investment I carried it in the hard belt case Final exams were three hours so you also had to carry a fully charged spare battery pack for a final And heaven forbid you had back to back finals 7 HP Solve What machine did you buy after your first Monte My HP 45 was all I ever needed in college and when I first started my working career But when I found myself doing repetitive calculations figuring transistor sizes for my first chip I got my HP 4 CV Keystroke programming made the programs as easy as entering the number of fanouts a guess for their size and a guess at the wire length HP Solve 23 Page 16 Page 1 of 3 8 HP Solve What HP calculators have you used since Monte When it was first ann
72. y for prime time In retrospect I underestimated the effort required to both design the PC board and write the software to control the new features on the NEWT microprocessor But I think that the result has been worth the effort and wait The project has given me a much greater appreciation for the engineering that went into the design of the original HP 41 series References 1 See http www hp41 org for examples of the original HP documentation 2 The technically inclined can find the specification for the NEWT microprocessor at http www systemyde com pdf newt pdf 3 See http www systemyde com pdf sy4lcl pdf for the manual for the new 41CL calculator About the Author Monte Dalrymple has been designing integrated circuits for over 30 years He holds a BSEE and MSEE from the University of California at Berkeley and has fifteen patents Monte uses an HP 16C 41 and HP 41CL routinely Not limited to things digital he holds both amateur and commercial radio licenses Email Monte at monted systemyde com HP Solve 23 Page 42 Page 5 of 5 6 in Fundamentals of Applied Math Series HP Solve 23 page 43 Article 6 in Fundamentals of Applied Math Series Richard 0 Melson Introduction What is the excitement over 2432 Which number does not belong 3 m m 1 o golden rati Hint What kind of number is 43 The previous article in this series discussed Logs and it pointed out th
73. ystroke per character not counting keystrokes for entering and exiting ALPHA mode itself On the HP41 the numeric and arithmetic symbols plus the ASTO ARCL and CLA functions were reached via shifted key presses and the same would go for our revised 42s calculator with the gold shift The blue shifted key plane would produce the lower case letters pi and AVIEW on the appropriate keys Also where in the original 42S entering ALPHA mode turned on the A Z soft key menu the new method would directly activate the original second ALPHA menu page the top level symbols menu with brackets braces math punct uation and other miscellaneous characters However since the top key row has A to F and a to f in its primary and blue shifted positions the gold shifted keys would select the menu soft keys Pressing gold shift followed by a top row key therefore activates the selected lower level individual symbols menu and associates it with the primary top row key presses switching capital A F to the gold shifted plane and leaving the lower case a f to the blue shifted plane Then when a key for a symbol was pressed it would revert the top row back to having A F as primary and the top level symbols menu returned as gold shifted with lower case a f remaining blue shifted Moving Pi and Percent On the original HP42S the and pi functions were gold shifted on the second row of keys above RCL res

HP Solve: Issue 23 (April 2011)

Contents

Download Pdf Manuals

Related Search

Related Contents