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HP 32sII Calculator

1. Transmitter Antenna E x Keys Display Description ES OG Sets Degrees mode R value 7 3 1 value Starts rectangular input display routine 15 7 7 value Sets X equal to 7 3 Sets Y equal to 15 7 76 R717 3308 Sets Z equal to 0 76 and calculates R the radius T765 0631 Calculates T the angle in the x y plane P 92 51234 Calculates P the angle from the Z AXIS Mathematics Programs 15 9 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Example 2 What is the moment at the origin of the lever shown below What is the component of force along the lever What is the angle between the resultant of the force vectors and the lever Pa ie 22155 P 17 L Fo 23 a807 Peg Y X First add the force vectors Keys Display Description P E value Starts polar input routine 17 T value Sets radius equal to 17 215 P value Sets T equal to 215 17 R 717T m amp Sets P equal to 17 E R 17 888 Enters vector by copying it into v2 23 T 145 6888 Sets radius of v1 equal to 23 80 P 17 6868 Sets T equal to 80 15 10 Mathematics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 74 F723 ABA Sets P equal to 74 A R 29 4741 Adds the vectors and displays the resultant R T7960 7032 Displays T of resultant vector P739 9445 Displays P of resultant vector E R 29 4741 Enters resultant vector Since the momen
2. EJ MAR PGM JLI GTO LJ label nn EQN FDISP Errors and program entry Switching Digit entry binary windows Except when used like Clx gt Including all operations performed while the catalog is displayed except MAR and FGM XEQ which enable stack lift User Memory and the Stack B 5 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm The Status of the LAST X Register The following operations save x in the LAST X register X SQRT x2 eX 10x LN LOG yx Xy x x y SIN COS TAN ASIN ACOS ATAN SINH COSH TANH ASINH ACOSH IP FP RND ABS ATANH S CHG IH RCL x y x gt 6 r HR 2HMS DEG gt RAD 0 r y x Cn r x CMPLX Pn r CMPLX x CMPLX ex LN y CMPLX SIN COS 1 x TAN kg lb 3 C gt F cm gt in gt gt gal Notice that c does riot affect the LAST X register The recall arithmetic sequence x variable stores a different value in the LAST X register than the sequence x variable does The former stores x in LAST X the latter stores the recalled number in LAST X B 6 User Memory and the Stack File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm C More about Solving This appendix provides information about the SOLVE operation beyond that given in chapter 7 How SOLVE Finds a Root SOLVE is an iterative operation that is it repetitively executes the specified eq
3. The number displayed depends on the display format Because m is a function it doesn t need to be separated from another number by ENTER Note that calculator cannot exactly represent m since m is an irrational number Setting the Angular Mode The angular rode specifies which unit of measure do assume for angles used in trigonometric functions The mode does not convert numbers already present see Conversion Functions later in this chapter 360 degrees 2r radians 400 grads To set an angular mode press EV MODES A menu will be displayed from which you can select an option Gp Deeipion Annunciato Sets Degrees mode DEG Uses decimal degrees not degrees minutes and seconds Sets Radians mode RAD Sets Grads mode GRAD Real Number Functions 4 3 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm u Trigonometric Functions With x in the display To Calculate Press Sine of x Cosine of x Tangent of x Arc sine of x Arc cosine of x Arc tangent of x COS TAN EJ EJ EJ Note Calculations with the irrational number x cannot be expressed ance exactly by the 12 digit internal precision of the calculator This is particularly noticeable in trigonometry For example the calculated sin x radians is not zero but 2 0676 x 10 13 a very small number close to zero Example Show that cosine 5 7 x radians and cosine 128 57 a
4. During program entry ALL is replaced by FGM If you select FGM a new menu CL PGMS H is displayed so you can verity your decision before erasing all your programs During equation entry either keyboard equations or equations in program lines the CLR EGH Y H menu is displayed so you can verity your decision before erasing the equation If you are viewing a completed equation the equation is deleted with no verification Using Menus There is a lot more power to the HP 32SIl than what you see on the keyboard This is because 12 of the keys with a shifted function name printed on a dark colored background above them are menu keys There are 14 menus in all which provide many more functions or more options for more functions Pressing a menu key shifted produces a menu in the display a series of choices 1 5 PICTURE 1 4 Getting Started File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm E 1 Menu choices 2 Keys matched to menu choices 3 Menu keys HP 321l Menus Menu Chapter Description Numeric Functions IF FF ABS Number altering functions integer part fractional part and absolute value Loner Por S0 EK Probability functions combinations permutations seed and random number x vrmb Linear regression curve fitting and linear estimation xXx ow KM Arithmetic mean of statistical x and y values weighted mean of statistical
5. If no message appears but A does you have pressed an inactive key a key that has no meaning in the current situation such as L3 in Binary mode All displayed messages are explained in appendix E Messages Getting Started 1 19 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 2 Calculator Memory The HP 32SIl has 384 bytes of memory in which you can store any combination of data variables equations or program lines The memory requirements of specific activities are given under Managing Calculator Memory in appendix B Checking Available Memory Pressing EX displays the following menu zi VAR FGH Where 216 8 is the number of bytes of memory available Pressing the AF menu key displays the catalog of variables see Reviewing Variables in the VAR Catalog in chapter 3 Pressing the FGM menu key displays the catalog of programs 1 To enter the catalog of variables press WARF to enter the catalog of programs press PGM 2 To review the catalogs press EM or EX Lt 3 To delete a variable or a program press EX while viewing it in its catalog 4 To exit the catalog press LC Clearing All of Memory Clearing all of memory erases all numbers equations and programs you ve stored It does not affect mode and format settings To clear settings as well as data see Clearing Memory in appendix B To clear all of memory 1 Press EX ALL You wi
6. J FH ACTIVE JFH gt J SOLVE gt ALL VRRS H CALCULATING CLR EGH YH CLR PGMS YH DIVIDE BY OUPLICAT LBL EWM LIST TOP File name 32sii Manual E 0424 Printed Date 2003 4 24 A running program attempted t select a program label FH abel while an integration calculation was running A running program attempted to integrate a program FH a variable while another integration calculation was running A running program attempted to solve a program while an integration calculation was running The catalog of variables EX V RR indicates no values stored The calculator is executing a function that might take a while Allows you to verily clearing the equation you are editing Occurs only in Equation entry mode Allows you to verify clearing all program in memory Occurs only in Program entry mode Attempted to divide by zero Includes if Y register contains zero Attempted to enter a program label that already exists for another program routine Indicates the top of equation memory The memory scheme is circular so EH LIST TOF is also the equation after the last equation in equation memory Messages X E 1 Size 17 7 x 25 2 cm i IHTEGRATING INTERRUPTED IHVRL ID DATA IHVRL ID EGH INVALID x INVALIDO v INVALID cia LOUGCHa LOUGCHEGS MEMORY CLEAR MEMORY FULL ML E 2 Messages File name 32sii Manual E 0424 Printed Date 2003 4 24 The calculator is calculat
7. Oe D gt De WAS DOSER gt 00 Hic GTO H Wii EQ X If current value lt final value exit loop Wei LEL H HAS ISG A Wik GTO H Hii SEG If current value gt final value exit loop For example the loop control number 0 050 for ISG means start counting at zero count up to 50 and increase the number by 1 each loop The following program uses ISG to loop 10 times The loop counter 0000001 01000 is stored in the variable Z Leading and trailing zeros can be left off Li LEL LHe 1 81 LHS STH Z Hai LEL A Ha2 ISG 2 Has GTO Had ETH Press F Z to see that the loop control number is now 11 0100 File name 32sii Manual E 0424 Printed Date 2003 4 24 Programming Techniques 13 19 Size 177 x 25 2 cm Indirectly Addressing Variables and Labels Indirect addressing is a technique used in advanced programming to specity a variable or label without specifying beforehand exactly which one This is determined when the program runs so it depends on the intermediate results or input of the program Indirect addressing uses two different keys with LJ and with The variable has nothing to do with or the variable i These keys are active for many functions that take A through Z as variables or labels B jis a variable whose contents can refer to another variable or label It holds a number just like any other variable A through Z m is a programming function that directs Use the
8. Returns log e x EX Common logarithm Returns log 10 x Displays menu for linear regression x L amp n Returns the slope of the regression line xi X Jyr Y X xi x 2 Displays the amount of available memory and the catalog menu Begins catalog of programs Begins catalog of variables Operation Index F 9 Size 177 x 25 2 cm u Ev MODES OCT ER or E PARTS Pn r T PROB PSE Displays menu to set Angular modes and the radix or EA SUNS n Returns the number of sets of data points EN BASE nc Selects Octal base 8 mode Turns the calculator off Displays the menu for selecting parts of numbers E PROB Pn r Permutations of n items taken r at a time Returns nla n r Activates or cancels toggles Program entry mode Displays the menu for probability functions Wes Pause Halts program execution briefly to display x variable or equation then resumes Used only in programs T fe Returns the correlation coefficient between the x and y values x xJ y y Y x XY xty y Et RD Selects Radians angular mode EX Degrees to radians Returns 21 360 x Ex Selects the comma as the radix mark decimal point EA MODES F 10 Operation Index File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm u RANDOM RCL variable RCL varia
9. can have two solutions for t You can direct the answer to the only meaningful one f gt 0 by entering appropriate guesses The example using this equation earlier in this chapter didn t require you Solving Equations 7 7 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm u u to enter guesses before solving for T because in the first part of that example you stored a value for T and solved for D The value that was left in T was a good realistic one so it was used as a guess when solving for T E f an equation does not allow certain values for the unknown guesses can prevent these values from occurring For example y t log x results in an error if x lt O messages LOGS or LOGCHEG In the following example the equation has more than one root but guesses help find the desired root Example Using Guesses to Find a Root Using a rectangular piece of sheet metal 40 cm by 80 cm form an open top box having a volume of 7500 cm You need to find the height of the box that is the amount to be folded up along each of the tour sides that gives the specified volume A taller box is preferred to a shorter one 7 8 Solving Equations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm E It H is the height then the length of the box is 80 2H and the width is 40 2H The volume V is V2 80 2H x 40 2H x H which you can simplify and enter
10. 1x Ex Exits Program entry mode Try running this program to find the area of a circle with a radius of 5 Keys Display Description Ex J This sets the program to its beginning 5 78 5398 The answer We will continue using the above program for the area of a circle to illustrate programming concepts and methods Designing a Program The following topics show what instructions you can put in a program What you put in a program affects how it appears when you view it and how it works when you run it 12 2 Simple Programming File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Program Boundaries LBL and RTN If you want more than one program stored in program memory then a program needs a label to mark its beginning such as Ai LBL A and a return to mark its end such as ABS RTH Notice that the line numbers acquire an A to match their label Program Labels Programs and segments of programs called routines should start with a label To record a label press Ex letter key The label is a single letter from A through Z The letter keys are used as they are for variables as discussed in chapter 3 You cannot assign the same label more than once this causes the message DUPLICAT LBL but a label can use the same letter that a variable uses It is possible to have one program the top one in memory without any label However adjacent programs need a label between them to keep th
11. 7760 4326 3432 Result 1008 58 100 5 14 Integer part of result 5AO016 100110022 al HX 5A0 SAG Set base 16 HEX Base Conversions and Arithmetic 10 3 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm annunciator on al BH 1001100 1481188 Changes to base 2 BIN annunciator on This terminates digit entry so no ENTER is needed between the numbers 14111161168 Result in binary base Ez HX SEC Result in hexadecimal base ER DEC 1 516 0000 Restores decimal base The Representation of Numbers Although the display of a number is converted when the base is changed its stored form is not modified so decimal numbers are not truncated until they are used in arithmetic calculations When a number appears in hexadecimal octal or binary base it is shown as a right justitied integer with up to 36 bits 12 octal digits or 9 hexadecimal digits Leading zeros are riot displayed but they are important because they indicate a positive number For example the binary representation of 12510 is displayed as 11111101 which is the same as these 36 digits 000000000000000000000000000001111101 Negative Numbers The leftmost most significant or highest bit of a number s binary representation is the sign bit it is set 1 for negative numbers If there are undisplayed leading zeros then the sign bit is O positive A negative number is the 2 s complement of its p
12. EJ HR Hours minutes seconds to hours Converts x from hours minutes seconds format to a decimal fraction i or i Value of variable i Indirect Value of variable whose letter corresponds to the numeric value stored in variable i gt N F3 Converts centimeters to inches INPUT variable EX variable Recalls the variable to the X register displays the variable s name and value and halts program execution Pressing to resume program execution or EX to execute the current proaram line stores your F 8 Operation Index File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm u INV IP ISG variable LBL label ET MEM EN PEM EN VAR File name 32sii Manual E 0424 Printed Date 2003 4 24 Keys and Description input in the variable Used only in programs Reciprocal of argument Wed PARTS IF Integer part of x EX variable Increment Skip if Greater For control number ccccccc fffii stored in variable adds ii increment value to ccccccc counter value and it the result gt fff final value skips the next program line Ex Converts pounds to kilograms ER Converts gallons to liters EJ Returns number stored in the LAST X register ra Converts kilograms to pounds EJ label Labels a program with a single letter for reference by the XEQ GTO or FN operations Used only in programs Natural logarithm
13. Entering and Evaluating Equations 6 15 File name 32sii Manual E O424 Printed Date 2003 4 24 Size 177 x 25 2 cm Ode Operon Bem 1 Functions and Parentheses SIMCX 12 CK12 Unary Minus Czz R 3 Power S 4 Multiply and Divide xx A B 5 Add and Subtract P A E 6 Equality B C So for example all operations inside parentheses are performed before operations outside the parentheses Examples RHxB z2C ax b c CAxBI 3 C ax b S c A B C 12 a b c 12 CHrB o C 12 a b c2 12 CHG T iz H 65 2 CHG t 12 a 6 You can t use parentheses for implied multiplication For example the expression p 1 f must be entered as Px amp 1 F with the x operator inserted between P and the left parenthesis 6 16 Entering and Evaluating Equations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm E Equation Function The following table lists the functions that are valid in equations Appendix F Operation Index also gives this information LN LOG EXP ALOG SQ SQRT INV IP FP RND ABS x SIN COS TAN ASIN ACOS ATAN SINH COSH TANH ASINH ACOSH ATANH bEG RAD HR HMS CHG XROOT Cn r Pn r KG LB C F CM IN gt L gt GAL RANDOM m x 2 SX sy Ox Oy X y Xw X y r m b n AX Ay Xx YXx y XY For convenience prefix type functions which require one or two arguments display a left parenthesis when you enter them The pr
14. W 19 242 255 88 in cubic millimeters stores the result in V and displays V 6 E 19 2423 Changes cubic millimeters to liters but doesn t change V Entering and Evaluating Equations 6 13 File name 32sii Manual E O424 Printed Date 2003 4 24 Size 177 x 25 2 cm Using XEQ for Evaluation If an equation is displayed in the equation list you can press to evaluate the equation The entire equation is evaluated regardless of the type of equation The result is returned to the X register Example Evaluating an Equation with XEQ Use the results from the previous example to tind out how much the volume of the pipe changes if the diameter is changes to 35 5 millimeters Keys Display Description Wes WHA 25xqxO2x Displays the desired equation XEQ W 19 242 255 88 Starts evaluating the equation to tind its value Prompts for all variables 0735 000G Keeps the same V prompts for D 99 L720 006 HAHA store new D Prompts for L 553 765 7051 Keeps the same L calculates the value of the equation the imbalance between the left and right sides E 6 5 6 5537 Changes cubic millimeters to liters The value of the equation is the old volume from V minus the new volume calculated using the new D value so the old volume is smaller by the amount shown Responding to Equation Prompts When you evaluate an equation you re prompted for a value for each variable that s needed The prompt gives the vari
15. and key in Z and press R S 5 To key in a second vector press E for enter then go to step 2 6 Perform desired vector operation a Add vectors by pressing A b Subtract vector one trom vector two by pressing S c Compute the cross product by pressing C d Compute the dot product by pressing D and the angle between vectors by pressing R S 7 Optional to review v1 in polar form press P then press repeatedly to see the individual elements 8 Optional to review v1 in rectangular form press R then press repeatedly to see the individual elements 9 If you added subtracted or computed the cross product v has been replaced by the result v2 is not altered To continue calculations based on the result remember to press E before keying in a new vector 10 Go to step 2 to continue vector calculations Variables Used X YZ The rectangular components of v1 U V W The rectangular components of v2 R TP The radius the angle in the x y plane 0 and the angle from the Z axis of v1 U D The dot product G The angle between vector y Example 1 A microwave antenna is to be pointed at a transmitter which is 15 7 kilometers North 7 3 kilometers East and 0 76 kilometers below Use the 15 8 Mathematics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm u rectangular to polar conversion capability to find the total distance and the direction to the transmitter
16. va xX x C d Function Whose Roots Can Be Found In most situations the calculated root is an accurate estimate of the theoretical infinitely precise root of the equation An ideal solution is one for which f x 0 However a very small non zero value for f x is often acceptable because it might result from approximating numbers with limited 12 digit precision C 2 More about Solving File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm Interpreting Results The SOLVE operation will produce a solution under either of the following conditions mit it finds an estimate for which f x equals zero See figure a below W if it finds an estimate where f x is not equal to zero but the calculated root is a 12 digit number adjacent to the place where the function s graph crosses the x axis see figure b below This occurs when the two tinal estimates are neighbors that is they differ by 1 in the 12th digit and the function s value is positive for one estimate and negative for the other Or they are 0 10 477 or 0 10 4 In most cases f x will be relatively close to zero f x f x on 0 Ney Ne a b Cases Where a Root Is Found To obtain additional information about the result press see the previous estimate of the root x which was left in the Y register Press again to see the value of f x which was left in the Z register If f x equals zero or is relatively small it
17. E t No execution Occurs 4 The program pointer moves to the next line Repeat step 3 until you find an error an incorrect result occurs or reach the end of the program If Program entry mode is active then EX or EX simply changes the programs pointer without executing lines Holding down an arrow key during program entry makes the lines roll by automatically Example Testing a Program Step through the execution of the program labeled A Use a radius of 5 for the test data Check that Program entry mode is nof active before you start Keys Display Description 5 Ex A 3 8886 Moves program counter to label A EX hold R81 LEL A release 5 Bmaa8 EN hold Abe x2 Squares input release 25 8686 EX hold ABS x Value of z release 3 1416 ER hold R amp 4 x 257 release ra 5395 E hold ABS RTH End of program Result is correct release r3 5395 12 10 Simple Programming File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Entering and Displaying Data The calculator s variables are used to store data input intermediate results and final results Variables as explained in chapter 3 are identified by a letter trom A through Z or i but the variable names have nothing to do with program labels In a program you can get data in these ways WB From an INPUT instruction which prompts for the value of a variable This is the most handy technique E From
18. Enters the equation 1 X 2 6 a 1 AT OAS 2 Ba r3 CK CFFC 818 8 Checksum and length Cancels Equation mode Now solve to find the root Keys Display Description 2 3 X2 7 27 Your initial guesses for the root Wes sT 0xR 2 623 1 Selects Equation mode displays the equation a X SOLVING Calculates the root using guesses 4 2 4495 that bracket 6 681 649 658 692 x is relatively large There is a pole between the final estimates The initial guesses yielded opposite signs for f x and the interval between successive estimates was narrowed until two neighbors were found Unfortunately these neighbors made x approach a pole instead of the x axis The function does have roots at 2 and 3 which can be found by entering better guesses When SOLVE Cannot Find Root Sometimes SOLVE fails to find a root The following conditions cause the message H ROOT FHD WI The search terminates near a local minimum or maximum see figure a below If the ending value of f x stored in the Z register is relatively close to zero it is possible that a root has been found the number stored in the unknown variable might be a 12 digit number very close to a theoretical root C 8 More about Solving File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm W The search halts because SOLVE is working on a horizontal asymptote an area where f x is essentially constant for a wide range of x see figure b be
19. Evaluates the displayed equation If the equation is an assignment evaluates the right hand side and stores the result in the variable on the left hand side If the equation is an equality or expression calculates its value like XEQ See Types of Equations later in this chapter Evaluates the displayed equation Calculates its value replacing with if an is present Solves the displayed equation for the unknown variable you specify See chapter 7 Integrates the displayed equation with respect to the variable you specify See chapter 8 Begins editing the displayed equation subsequent presses delete the rightmost function or variable Deletes the displayed equation from the equation list Steps up or down through the equation list Shows the displayed equation s checksum verification value and length bytes of memory Leaves Equation mode You can also use equations in programs this is discussed in chapter 12 Entering Equations into the Equation List The equation list is a collection of equations you enter The list is saved in the calculator s memory Each equation you enter is automatically saved in the equation list 6 4 Entering and Evaluating Equations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm To enter an equation 1 Make sure the calculator is in its normal operating mode usually with a number in the display For example you can t be
20. File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Function Names in Programs Then name of function that is used in a program line is not necessarily the same as the function s name on its key in its menu or in an equation The name that is used in a program is usually a tuller abbreviation than that which can fit on a key or in a menu This fuller name appears briefly in the display whenever you execute a function as long as you hold down the key the name is displayed Example Entering a Labeled Program The following keystrokes delete the previous program for the area of a circle and enter a new one that includes a label and a return instruction If you make a mistake during entry press to delete the current program line then reenter the line correctly Keys Display Description ER Activates Program entry mode PRGM on a PGM Y PRGM TOP Clears all of program memory EX A Agi LEL A Labels this program routine A for area EX ABS xe Enters the three program lines Wea ABZ y R84 x r3 Ras ETH Ends the program Ez FGM LEL A Bar 5 Displays label A and the length of the program in bytes T CK EB2C B r 5I Checksum and length of program Cancels program entry PRGM annunciator off Simple Programming 12 7 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm A different checksum means the program was not entered exactly as gi
21. HHAH R S I 1 Bbb Example 2 Description Starts the polynomial root finder prompts for order Stores 5 its F prompts for E Stores 1 in E prompts for D Store 101 in D prompts for C Stores 101 in C prompts for B Stores 100 in B prompts for A Stores 100 in A calculates the tirst root Calculates the second root Displays the third root Displays the fourth root Displays the fifth root Find the roots of 4x4 8x 13x 10x 22 0 Because the coefficient of the highest order term must be 1 divide that coefficient into each of the other coefficients Keys Display P F value 4 OF value 8 4 Es LU value 13 4 Lx Evalue 15 30 Mathematics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Description Starts the polynomial root finder prompts for order Stores 4 its F prompts for D Stores 8 4 in D prompts for C Store 13 4 in C prompts for B Size 17 7 x 25 2 cm 22 A value 4G 8 8828 d 1156 R S i BBB R S i BBB R S i BBB I 1 H Stores 10 4 in B prompts for A Stores 22 4 in A calculates the first root Calculates the second root Displays the real part of the third root Displays the imaginary part of the third root Displays the real part of the fourth root Displays the imaginary part of the fourth root The third and fourth roots are 1 00 1 00 i Example 3 Find the roots of the following
22. Numbers are always shown using ALL display format which displays up to 12 characters Entering and Evaluating Equations 6 5 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm To enter a number in an equation you can use the standard number entry keys including LJ Cz and LE Press only after you type one or more digits Don t use for subtraction When you start entering the number the cursor changes from E to to show numeric entry The cursor changes back when you press a nonnumeric key Functions in Equations You can enter many HP 32SII functions in an equation A complete list is given tinder Equation Functions later in this chapter Appendix F Operation Index also gives this information When you enter an equation you enter functions in about the same way you put them in ordinary algebraic equations WB In an equation certain functions are normally shown between its arguments such as and For such infix operators enter them in an equation in the same order WI Other functions normally have one or more arguments affer the function name such as COS and LN For such prefix functions enter them in an equation where the function occurs the key you press puts a left parenthesis after the function name so you can enter its arguments If the function has two or more arguments press SPACE on the key to separate them If the function is followed by oth
23. Q12 CF a Q13 x87 Q14 SF ao 15 ABS 16 SORT Gi STOG Q18 FS 19 RTH a26 STO F G21 RV Q22 ST0 G Q23 RTH Description a 2 a1 2 Saves aj 2 Stores real part if complex root a1 2 ao a1 2 ao Initializes flag O Discriminant d lt O Sets flag O if d O complex roots d d Stores imaginary part if complex root Complex roots Returns if complex roots Calculates ai 2 d Calculates a1 2 Jidl Checksum and length E454 034 5 Bai LEL B BAS RCL B BAS RCL A BAS GTO T Starts second order solution routine Gets L Gets M Calculates and displays two roots Checksum and length 52B9 006 0 CHi LBL C Che 3 CAS AEG S Cad RV File name 32sii Manual E 0424 Printed Date 2003 4 24 Starts third order solution routine Indicates cubic polynomial to be solved Solves for one real root and puts ag and a1 for second order polynomial on stack Discards polynomial function value Mathematics Programs 15 23 Size 17 7 x 25 2 cm i Program Lines CAS SE D CHE VIEW amp Car GTO H Description Solves remaining second order polynomial and stores roots Displays real root of cubic Displays remaining roots Checksum and length CCF5 010 5 EH LEL E EHS 5 EHS AEM S EB4 RV EHS STO A EBE RV EHP STO B EBS RV EHS STO LC Fil RCL E Eii RCL amp Fie STOOD Fils VIEH amp Starts fifth order solution routine Indicates fifth order polynomial to be solved
24. Tangent Returns tan x EX Hyperbolic tangent Returns tanh x r3 variable Displays the labeled contents of variable without recalling the value to the stack Evaluates the displayed equation label Executes the program identified by label EX Square of x EX The x root of y Ex 37 X Returns the mean of x values X Xi 4 n a LE 4 Given a y value in the X register Operation Index F 13 Size 177 x 25 2 cm i Wea x lt gt variable x lt gt y Ex 2 X y x lt y x lt y a 270 Keys and Description returns the x estimate based on the regression line X y b m Ex Factorial or gamma Returns x x 1 2 1 or T x 1 EX The argument root of 2 argument2 Returns weighted mean of x values Lyixi Lyi Displays the mean arithmetic average menu Wes x exchange Exchanges x with a variable x exchange y Moves x to the Y register and y to the X register Displays the x y comparison tests menu EX If x y executes next program line if x y skips the next program line EN 377 3 It x lt y executes next program line if x gt y skips next program line EN 32 4 It x y executes next program line if xzy skips next program line Ex 377 p If x gt y executes next program line if x lt y skips next program line E 327 o It xzy executes next program line it x y skips the next
25. To enter a program into memory 1 Press EX to activate Program entry mode 2 Press EX CJ LJ to display PRGM TOF This sets the program pointer to a known spot before any other programs As you enter program lines they are inserted before all other program lines If you don t need any other programs that might be in memory clear program memory by pressing EX FGM To confirm that you want all programs deleted press t after the message CL FGM Y H 3 Give the program a label a single letter A through Z Press EX letter Choose a letter that will remind you of the program such as A for area If the message DUPLICAT LBL is displayed use a different letter You can clear the existing program instead press EN FGM use EX or Ex to find the label and press EX and C 4 To record calculator operations as program instructions press the same keys you would to do an operation manually Remember that many functions don t appear on the keyboard but must be accessed using menus To enter an equation in a progran line see the instructions below Simple Programming 12 5 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 5 End the program with a return instruction which sets the program pointer back to PRGM TOP after the program runs Press fea RIN 6 Press or Ex to cancel program entry Numbers in program lines are stored as precisely as you entered them and th
26. base affects display 10 5 arithmetic 10 3 converting 10 1 default B 5 programs 2 25 setting 10 1 14 10 BASE menu 10 1 base mode default B 5 equations 6 6 6 13 1225 fractions 5 2 programming 12 25 setting 12 25 14 10 batteries 1 1 A2 Bessel function 8 3 best fit regression 11 8 16 1 BIN annunciator 10 1 binary numbers See numbers arithmetic 10 3 Index 2 File name 32sii Manual E 0424 Printed Date 2003 4 24 converting to 10 1 range of 10 6 scrolling 10 7 typing 10 1 viewing all digits 3 4 10 7 borrower finance 17 1 branching 13 2 13 15 14 6 C adjusting contrast 1 1 canceling prompts 1 3 6 16 12 14 canceling VIEW 3 4 clearing messages 1 3 E 1 clearing X register 2 2 2 8 interrupting programs 12 19 leaving catalogs 1 3 3 4 leaving Equation mode 6 4 6 5 leaving menus 1 3 1 8 leaving Program mode 12 6 127 on and off 1 1 operation 1 3 stopping integration 8 2 14 7 stopping SOLVE 77 14 1 calculator adjusting contrast 1 11 default settings B 5 environmental limits A 2 questions about A 1 repair service A resetting A 4 B 3 self test A 5 shorting contacts A 4 testing operation A 4 A 5 turning on and off 1 1 warranty A 6 Size 17 7 x 25 2 cm cash flows 17 1 catalogs leaving 1 3 program 1 21 1222 using 1 21 variable 1 21 3 4 chain calculations 2 13 change percentage function 4 6 chan
27. in A Keys Display Description 6 0225 E 23 J amp a225E23 Avogadro s numbers STO Prompts for variable A HOLD key STOA Displays function as long as key is held down release amp B225E23 Stores a copy of Avogadro s numbers in A This also terminates digit entry no cursor present G 8686 Clears the number in the display RCL Prompts for variable A 6 4225623 Copies Avogadro s numbers from A the display Viewing a Variable without Recalling It The Wea tunction shows you the contents of a variable without putting that number in the X register The display is labeled for the variable such as H 1234 56 38 If the number is too large to fit completely in the display with its label it is rounded and the rightmost digits are dropped An exponent is displayed in full To see the full mantissa press F SHOW In Fraction display mode EX EDISP part of the integer may be dropped This will be indicated by at the left end of the integer To see the full mantissa press P The integer part is the portion to the left of the radix or Wes is most often used in programming but it is useful anytime you want to view a variable s value without affecting the contents of the stack 3 2 Storing Data into Variables File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm To cancel the VIEW display press or LC once Reviewing Variables in the VAR Catalog The
28. into the unknown variable and into the X register before executing the SOLVE variable instruction The two instructions for solving an equation for an unknown variable appear in programs as FH label SOLVE variable The programmed SOLVE instruction does not produce a labeled display variable value since this might not be the significant output for your program that is you might wart to do further calculations with this number Solving and Integrating Programs 14 5 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm before displaying it If you do want this result displayed add a VIEW variable instruction after the SOLVE instruction If no solution is found for the unknown variable then the next program line is skipped in accordance with the Do if True rule explained in chapter 13 The program should then handle the case of not finding a root such as by choosing new initial estimates or changing an input value Example SOLVE in a Program The following excerpt is from a program that allows you to solve for x or y by pressing X or Y Program Lines Description B1 LBL X Setup for X BZ 24 Index for X 83 GTOL Branches to main routine Checksum and length CCEC 004 5 YB1 LBL v Setup for Y Ya 25 Index for Y TH4GTOL Branches to main routine Checksum and length 2E48 004 5 Lai LBL L Main routine Lag STO i Stores index in i Laz FH F Defines program to solve La
29. press EX or EN until you see the desired program label and size For example LEL F 812 3 Optional Press Wea to see the checksum hexadecimal and length in bytes of the program For example CK SDER 012 0 for program F To see the memory requirements of an equation in a program B 2 User Memory and the Stack File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 1 Display the program line containing the equation 2 Press Wea to see the checksum and length For example LE fF 43 49 4 To manually deallocate the memory allocated for a SOLVE or J FN calculation that has been interrupted press zl RIN This deallocation is done automatically whenever you execute a program or another SOLVE or FN calculation Resetting the Calculator If the calculator doesn t respond to keystrokes or if it is otherwise behaving unusually attempt to reset it Resetting the calculator halts the current calculation and cancels program entry digit entry a running program a SOLVE calculation an J FN calculation a VIEW display or an INPUT display Stored data usually remain intact To reset the calculator hold down the key and press LN If you are unable to reset the calculator try installing fresh batteries If the calculator cannot be reset or if it still fails to operate properly you should attempt to clear memory using the special procedure described in the next section The calculator
30. the total impedance is 77 8 ohms and voltage lags current by 36 5 What a re the values of resistance R and capacitive reactance Xc in the circuit Use a vector diagram as shown with impedance equal to the polar magnitude r and voltage lag equal to the angle 0 in degrees When the values are converted to rectangular coordinates the x value yields R in ohms the y value yields Xc in ohms R C 77 8 ohms Keys Display Description E3 OG Sets Degrees mode 36 5 36 5888 Enters 0 degrees of voltage lag 77 8 Tres Enters r ohms of total impedance r3 62 5481 Calculates x ohms resistance R 46 2772 Displays y ohms reactance XC For more sophisticated operations with vectors addition subtraction cross product and dot product refer to the Vector Operations program in chapter 15 Mathematics Programs Time Conversions Values for time in hours H or angles in degrees D can be converted between a decimal fraction form H h or D d and a minutes seconds form H MMSSss or D MMSSss using the EX or Wz keys Real Number Functions 4 9 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm To convert between decimal fractions and minutes seconds 1 Key in the time or angle in decimal form or minutes seconds form that you want to convert 2 Press 3 or EX HR The result is displayed Example Converting Time Formats How many minutes and seconds are ther
31. trig 4 4 9 3 A 2 single step execution 12 10 slope curve tit 11 8 16 1 SOLVE asymptotes C 9 base mode 12 25 14 10 checking results 7 6 C 3 discontinuity C 6 evaluating equations 7 1 7 6 evaluating programs 14 1 flat regions C 9 how it works 7 6 C 1 initial guesses 7 2 7 6 7 7 7 10 14 5 in programs 14 5 interrupting 8 3 memory usage 1222 B2 B 3 minimum or maximum C 9 multiple roots 7 8 no restrictions 14 10 no root found 7 7 14 6 C 9 pole C purpose 7 1 real numbers 14 2 results on stack 72 7 6 C 3 resuming 14 round off C 16 stopping 2 7 7 undertlow C 16 using 2 File name 32sii Manual E 0424 Printed Date 2003 4 24 SPACE 6 6 6 18 square function 1 14 4 2 square root function 1 14 stack See stack litt affected by prompts 6 16 12 13 complex numbers 9 2 effect of ENTER 2 6 equation usage 6 13 exchanging with variables 3 8 exchanging X and Y 2 4 tilling with constant 2 7 long calculations 2 13 operation 2 1 2 5 9 2 program calculations 12 13 program input 12 12 program output 12 12 purpose 2 1 22 registers 2 reviewing 2 3 rolling 2 3 separate from variables 3 2 size limit 2 4 9 2 unaffected by VIEW 12 15 stack lift See stack default state B 5 disabling B 6 enabling B 6 not affecting B 7 operation 2 5 standard deviation menu 11 6 11 7 standard deviations calculating 11 6 11 7 grouped data 16 19 n
32. 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm The Automatic Memory Stack 2 17 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 3 Storing Data into Variables The HP 32II has 384 bytes of user memory memory that you can use to store numbers equations and program lines Numbers are stored in locations called variables each named with a letter trom A through Z You can choose the letter to remind you of what is stored there such as B for bank balance and C for the speed of light 3 1 Picture 1 Cursor prompts for variable 2 Indicates letter keys are active 3 letter keys Each white letter is associated with a key and a unique variable The letter keys are automatically active when needed The A Z annunciator in the display confirms this Note that the variables X Y Z and T are different storage locations from the X register Y register Z register and T register in the stack Storing and Recalling Numbers Numbers are stored into and recalled from lettered variables with the store and RCL recll functions To store a copy of a displayed number X register to a variable Press letter key To recall a copy of a number from a variable to the display Press letter key Storing Data into Variables 3 1 File name 32sii Manual E O424 Printed Date 2003 4 24 Size 177 x 25 2 cm Example Storing Numbers Store Avogadro s number approximately 6 0225 x 1023
33. 15 16 Mathematics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm Program Lines Description Checksum and length 4E79 012 0 D i LBL D This routine calculates the determinant Owe ECL A DHS ECL E Cad RCL x I Calculates A x E x I OHS ECL O AE ECL H Oar ECL C DAS Calculates A x E x I D x H x C OHS ECL G Dif ECL F Hii ECL B Diz Calculates A x Ex I Dx Hx C Gx F x B Dis ECL Did ECL E Dis ECL C Di Ax Ex l Dx Hx C Gx Fx B GxEx C Dir ECL A DiS RCLx F DiS RCL H O26 Ax Exl Dx Hx C Gx Fx B Gx Ex C Ax Fx H D21 REL DO D22 RCLx E D23 ECLx I O24 Ax Ex l Dx Hx C Gx Fx B Gx Ex B Ax Fx H Dx Bx I 025 RTH Returns to the calling program or to PRGM TOP Checksum and length 44B2 037 5 Mathematics Programs 15 17 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i Flags Used None Memory Required 348 bytes 212 for program 136 for variables Program Instructions l 2 3 8 Key in the program routines press when done Press A to input coefficients of matrix and column vector Key in coefficient or vector value A through L at each prompt and press R S Optional press D to compute determinant of 3 x 3 system Press to compute inverse of 3 x 3 matrix Optional press A and repeatedly press to review the values of the in
34. 16 4 Statistics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm Program Lines Description RAGS FS i It flag 1 is seta takes the natural antilog of b Rar e Ras STO E Stores b in B FAS VIEW B Displays value Rig m Calculates coefficient m kii STO M Stores m in M Riz VIEW M Displays value Checksum aril length EBF3 018 0 Y i LBL Y Defines the beginning of the estimation projection loop 82 INPUT X Displays prompts for and if changed stores x value in X YO SEC i gt Calls subroutine to compute Y v84 STO Y Stores Y value in Y Yag IHPUT Y Displays prompts for and if changed stores y value in Y THE YO STO i Adjusts index value to address the appropriate subroutine YOS KEGCi3 Calls subroutine to compute x Yao STO Stores x in X for next loop Yia GTO v Loops for another estimate Checksum and length BAO7 015 Ai LEL A This subroutine calculates Y for the straight line model Haz ECL M HHS RCLx 8 R84 RCL B Calculates Y MX B Aas RTH Returns to the calling routine Checksum and length 2FDA 007 5 Gai LEL G This subroutine calculates x for the straight line model Statistics Programs 16 5 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i Program Lines Description Gaz STO i Restores index value to its original value Gas ECL Y bGa4 ECL B GAS RCL M Calculates x Y B M GHE RTH Re
35. 16 as the c value Displays message then the decimal number Message indicates the fraction format denominator is no greater than 16 then shows the fraction v indicates that the numerator is a little below 8 Message indicates the fraction Programming Techniques 13 15 Printed Date 2003 4 24 Size 177 x 25 2 cm Keys Display Description A2 1 2 format denominator is factor of 16 then shows the fraction FIXED DEHOM Message indicates the fraction A2 8 16 format denominator is 16 then shows the fraction Wes 2 5386 Stops the program and clears flag cF Jo 10 Loops Branching backwards that is to a label in a previous line makes it possible to execute part of a program more than once This is called looping i81 LBL L i82 IHPUT H DAS IHPUT H Da4 IHPUT T DAS GTO D This routine taken from the Coordinate Transformations program on page 15 31 in chapter 15 is an example of an infinite loop It is used to collect the initial data prior to the coordinate transformation After entering the three values it is up to the user to manually interrupt this loop by selecting the transformation to be performed pressing N for the old to new system or O for the new to old system Conditional Loops GTO When you want to perform an operation until a certain condition is met but you don t know how many times the loop needs to repeat itself you can create a loop with a conditional test and a GTO ins
36. 17 7 x 25 2 cm E Program Listing Program Lines sHi LBL sH21 SHS CF H saHd CF 1 S65 GTO Z Description This routine set the status for the straight line model Enters index value for later storage in i for indirect addressing Clears flag O the indicator for In X Clears flag 1 the indicator for In Y Branches to common entry point Z Checksum and length EBD2 007 5 Lai LBL L LHe 2 LHS SF HB LH4 CF 1 LH3 GTO Z This routine sets the status fog the logarithmic model Enters index value for later storage in i for indirect addressing Sets flag O the indicator for In X Clears flag 1 the indicator In Y Branches to common entry point Z Checksum and length 7462 007 5 EH LEL E EHS 3 EHS CF HB EH4 SF 1 EHS GTO Z This routine sets the status for the exponential model Enters index value for later storage in i for indirect addressing Clears flag O the indicator for In X Sets flag 1 the indicator for In Y Branches to common entry point Z Checksum and length DCEA 007 5 F i LBL F PHS 4 F s SF HB PH4 SF 1 This routine sets the status for the power model Enters index value for later storage in i for indirect addressing Sets flag O the indicator for In X Sets flag 1 the indicator for In Y Checksum and length F399 006 0 zai LBL z He CLE File name 32sii Manual E 0424 Printed Date 2003 4 24 Defines common entry point for all models Clears t
37. 2 cm L R Linear Regression Menu Menu Label Description Estimates predicts x for a given hypothetical value of y based on the line calculated to fit the data Estimates predicts y tor a given hypothetical value of x based on the line calculated to fit the data Correlation coefficient for the x y data The correlation coefficient is a number in the range 1 through 1 that measures how closely the calculated line fits the data Slope of the calculated line y intercept of the calculated line WI To find an estimated value for x or y key in a given hypothetical value for y or x then press a 32 or za 2 mE To find the values that define the line that best fits your data press P followed by r m or b Example Curve Fitting The yield of a new variety of rice depends on its rate of fertilization with nitrogen For the following data determine the linear relationship the correlation coefficient the slope and the y intercept X Nitrogen Applied 0 00 20 00 40 00 60 00 80 00 kg per hectare Y Grain Yield 4 63 5 78 6 61 2 7 8 metric tons per hectare Keys Display Description al Clears all previous statistical 11 8 Statistical Operations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm data 4 63 O 1 8808 Enters data displays n 5 78 20 2 6808 6 61 40 3 4686 7 21 60 4 6808 7 78 80 5 00H Five data pairs entered W
38. 283 H 35 BH FH BE Bo 756 B6 SOLV IHG I H 2565 Daira Description Displays the leftmost hart of the TVM equation Selects l prompts for P Rounds the payment to two decimal places Calculates new payment Stores 176 89 in P prompts for N Retains 36 in N prompts for F Retains O in F prompts for B Retains 5750 in B calculates monthly interest rate Calculates annual interest rate Part 3 Using the calculated interest rate 6 75 assume that you sell the car after 2 years What balance will you still owe In other words what is the future balance in 2 years File name 32sii Manual E 0424 Printed Date 2003 4 24 Miscellaneous Programs and Equations 17 5 Size 17 7 x 25 2 cm Note that the interest rate I from part 2 is not zero so you won t get a DIVIDE BY amp error when you calculate the new l Keys Display Description Fes Px1 x 1 1 Displays leftmost part of the TVM equation r3 F P 176 89 Selects F prompts for P 178 56 Retains P prompts for I H736 06 Retains 0 56 in l prompts for N 24 E75 756 06 Stores 24 in N prompts for B SOLVING Retains 5750 in B calculates F the F 2 847 85 future balance Again the sign is negative indicating that you must pay out this money ER Fx 4 Sets FIX 4 display format Prime Number Generator This program accepts any positive integer greater than 3 If the number is a prime number not evenly divisible by integ
39. 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm E Storing Data into Variables Storing and Recalling Numbers seeeessss 3 1 Viewing a Variable without Recalling It 3 2 Reviewing Variables in the VAR Catalog 3 3 Clearing VelrialbleSu isst estere d I ORE tU bea RID VERRE EON 3 3 Arithmetic with Stored Variables ssesssseessss 3 4 Storage Arithmetic cccccscccceeeceeeeeeceeeeceeueeeene essen 3 4 Recall EHE BEEN sata osstucunmoidncs ducatus dtum A Ea canteen 3 5 Exchanging x with Any Variable eessssess 3 6 LETS fo olo SM UNI RERO 3 7 Real Number Functions Exponential and Logarithmic Functions 4 HONWEPEUDIGIIOPIS obese docui aao tinc duisi M Lou bid arcana 4 2 TRIG OM OIMENY etc 4 3 ENCINO PNE EE E 4 3 Setting the Angular Mode cccscccceneceeeeeeeeneeeeaes 4 3 Trigonometric FUNCHIONS cecceececeeceeeeceeeeeneeneneenes 4 4 Hyperbolic Functions aiacisasanisraaiguadiataianeniearauneamaaiennnts 4 5 Percentage FUNCTIONS 214s iececataciiasvanateiaaeaenees E 4 5 Conversion FUNCHONS a PT 4 Coordinate Conversions ccccccccceeecceeeeceeeeeeeeeeeeeans 4 7 TME CONVEISIONS T 4 9 Angle Conversions visa csansasiavvesengiiadiasncesmenesavesduboaedes 4 10 S al CONVE ONS PR 4 1 Probability Functions cccccccceeccceeeeeee
40. 4 24 Size 17 7 x 25 2 cm Program Listing Program Lines Description D22 RV D23 Divides previous result by the magnitude D24 ACOS Calculates angle D025 STU G D26 VIEW G Displays angle D27 GTO FP Loops back for polar display input Checksum and length 1DFC 040 5 Flags Used None Memory Required 270 bytes 182 for program 88 for variables Remarks The length of routine S can be shortened by 6 5 bytes The value 1 as shown uses 9 5 bytes If it appears as 1 followed by it will require only 3 bytes To do this you can press 1 Wa uz The terms polar and rectangular which refer to two dimensional systems are used instead of the proper three dimensional terms of spherical and Cartesian This stretch of terminology allows the labels to be associated with their function without confusing conflicts For instance if LBL C had been associated with Cartesian coordinate input it would not have been available for cross product Program Instructions 1 Key in the program routines press LC when done 2 If your vector is in rectangular form press R and go to step 4 If your vector is in polar form press P and continue with step 3 Mathematics Programs 15 7 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 3 Key in Rand press R S key in T and press R S then key in P and press Continue at step 5 4 Key in Xand press R S key in Y and press R S
41. ADAH Prompts for the new third fi Statistics Programs 16 21 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i Keys 15 R S 43 R S 22 R S 73 R S 37 R S 115 R S XEQ G Display H 3 nid Aris BREE Fay BREE H 4 HHH riS BREE F434 BREE H 3 Bid rod ARES Fr BREE H amp Hn 5 11 4118 H 23 4654 24 4854 16 22 Statistics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Description Displays the counter Prompts for the fourth xi Prompts for the fourth fi Displays the counter Prompts for the fifth x1 Prompts for the fifth fi Displays the counter Prompts for the sixth xi Prompts for the sixth fi Displays the counter Calculates and displays the grouped standard deviation sx of the six data points Calculates and displays weighted mean X Clears VIEW Size 177 x 25 2 cm 17 Miscellaneous Programs and Equations Time Value of Money Given any four of the five values in the Time Value of Money equation TVM you can solve for the fifth value This equation is useful in a wide variety of financial applications such as consumer and home loans and savings accounts The TVM equation is N ie 00 100 109 B 0 Balance B Payments P Future Value F The signs of the cash values balance B payment P and future balance F correspond to the direction of the cash flow Money that you
42. Clearing One or More Programs in chapter 12 Clear the statistics registers press EX 3 Clear all of user memory press EX ALL User Memory and the Stack B 1 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i Memory Requirements Variables 8 bytes per non zero value No bytes for zero values Instructions in program lines 1 5 bytes Numbers in program lines Integers O through 254 1 5 bytes All other numbers 9 5 bytes Operations in equations 1 5 bytes Numbers in equations Integers O through 254 1 5 bytes All other numbers 9 5 bytes Statistics data 48 bytes maximum 8 bytes for each non zero summation register SOLVE calculations 33 5 bytes J FN integration calculations 140 bytes To see how much memory is available press E MEM The display shows the number of bytes available To see the memory requirements of specific equations in the equation list 1 Press fe to activate Equation mode EGH LIST TOP or the left end of the current equation will be displayed 2 f necessary scroll through the equation list press EM or EX until you see the desired equation 3 Press fz to see the checksum hexadecimal and length in bytes of the equation For example CK 7F49 889 a To see the total memory requirements of specific programs 1 Press EX FGM to display the first label in the program list 2 Scroll through the program list
43. Date 2003 4 24 Size 17 7 x 25 2 cm Parentheses in Equations cccccsecceseeceeesceeeeceeneees 6 7 Displaying and Selecting Equations sssssssss 6 7 Editing and Clearing Equations cccccceseecceeeeeseeene ees 6 9 lyp s of EQUGIIONS essi a tare anal sates 6 10 Evaluating Equations 335i 6 nnisievieeanats DERIT ert DARE 6 11 Using ENTER for Evaluation ccccccsecccceeeeeeeeee ees 6 12 Using XEQ for Evaluation 6 14 Responding to Equation Prompts s0ccceseeeeeenees 6 14 The Syntax of Equations ha euo renis s denapicueacctideenudiissageons 6 15 Operator Precedence esseesseeeeee 6 15 ze tfo To E FUNCHON asc tcc TT TT 6 17 SVDICDOE fe eee eee ee eee eee eee 6 20 Verifying Equations cccccccsecccesseeceeeeeeceeaneeeesaneeeees 6 20 7 Solving Equations Solving an Equation NE TE DU 7 1 Understanding and Controlling SOLVE 7 5 Verifying the Result 7 6 Interrupting a SOLVE Calculation 7 7 Choosing Initial Guesses for SOIVE 7 7 For More Information s5sinccdatsosnasoctaseidaskonsntaaavacteeiabernns 7 11 8 Integrating Equations Integrating Equations FN 8 2 Accuracy of Integration csse 9 6 Specifying Accuracy essssesseeeneeeenene 8 6 Interprelilig ACCURACY cescnssccccnnemacriervesueen R 8 Contents 5 File name 32si
44. Enters y value of data pair 38 6 1 7184 5888 Enters x value of data pair 102 473 608 Enters y value of data pair Now intentionally enter 379 instead of 37 9 so that you can see how to correct incorrect entries Keys Display Description 379 Y71602 0006 Enters wrong x value of data pair Statistics Programs 16 9 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm u XEQ U 37 9 100 36 2 97 5 35 1 95 5 34 6 94 R 37 R S 101 Example 2 74 GRRE 74 BBB T 182 6688 74 GRRE YT 168 6688 ERE BREE T797 SBE 76 ARR T795 580806 A ro BREE R H 992525 B 33 5271 M 1 681 a BREE T799 6326 A240 3436 Retrieves 7 prompt Deletes the last pair Now proceed with the correct data entry Enters correct x value of data pair Enters y value of data pair Enters x value of data pair Enters y value of data pair Enters x value of data pair Enters y value of data pair Enters x valise of data pair Enters y value of data pair Calculates the correlation coefficient Calculates regression coefficient B Calculates regression coefficient M Prompts for hypothetical x value Stores 37 in X and calculates y Stores 101 in Y and calculates x Repeat example 1 using the same data for logarithmic exponential and power curve fits The table below gives you the starting execution label and the results the correlation and regression coefficients and
45. F Z 7 411 Single No implied Division is done letter multiplication before addition name The next equation also obeys the syntax rules This equation uses the inverse function IHV amp SIHCT22 instead of the fractional form 17SIHXT2 Notice that the SIN function is nested inside the INV function INV is typed by Ua F H B HxctLIHMMVCSIHETOoocCcIHMVCSIHMCF 222 Example Area of a Polygon The equation for area of a regular polygon with n sides of length d is Area n d 2 cos n n 4 sin x n You can specily this equation as Entering and Evaluating Equations 6 19 File name 32sii Manual E O424 Printed Date 2003 4 24 Size 177 x 25 2 cm H 8 25xHx0 2xC05 q7HIFSIN Oath Notice how the operators and functions combine to give the desired equation You can enter the equation into the equation list using the following keystrokes Wed EQN RCL A fz3 25 x RCL N x RCL D eA 2 x COS Wea 7 RCL N ir U1 SIN Wea 7 3 RCL N ir D1 DE Syntax Errors The calculator doesn t check the syntax of an equation until you evaluate the equation and respond to all the prompts only when a value is actually being calculated If an error is detected IHVRL ID EGH is displayed You have to edit the equation to correct the error See Editing and Clearing Equations earlier in this chapter By not checking equation syntax until evaluation the HP 32SIl lets you create equations t
46. Fractions 5 9 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm When you re evaluating an equation and you re prompted for variable values you may enter fractions values are displayed using the current display format See chapter 6 for information about working with equations Fractions in Programs When you re typing a program you can type a number as a fraction but it s converted to its decimal value All numeric values in a program are shown as decimal values Fraction display mode is ignored When you re running a program displayed values are shown using Fraction display mode if it s active If you re prompted for Values by INPUT instructions you may enter fractions regardless of the display mode A program can control the fraction display using the c function and by setting and clearing flags 7 8 and 9 Setting flag 7 turns on Fraction display mode EX isn t programmable See Flags in chapter 13 See chapters 12 and 13 for information about working with programs 5 10 Fractions File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Entering and Evaluating Equations How You Can Use Equations You can use equations on the HP 32SIl in several way WI For specifying an equation to evaluate this chapter WI For specifying an equation to solve for unknown values chapter 7 E For specifying a function to integrate chapter 8 Exam
47. Press once only to start editing the equation The E equation entry cursor appears at the end of the equation Nothing is deleted from the equation 3 Use to edit the equation as described above 4 Press or to save the edited equation in the equation list replacing the previous version To clear an equation you re typing Press EX then press r The display goes back to the previous entry in the equation list Entering and Evaluating Equations 6 9 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm To clear a saved equation 1 Display the desired equation See Displaying and Selecting Equations above 2 Press EX CLEAR The display shows the previous entry in the equation list To clear all equations clear them one at a time scroll through the equation list until you come to ERN LIST TOF press EN Lt then press EX repeatedly as each equation is displayed until you see EGH LIST TOP Example Editing an Equation Remove the optional right parenthesis in the equation from the previous example Keys Display Description Wes R 2xCxCOS T Shows the current equation in the equation list xCxCOS T Aj Turns on Equation entry mode and shows the E cursor at the end of the equation 2xCxCO ScT HN Deletes the right parenthesis 2xCxCOS T A Shows the end of edited equation in the equation list Leaves Equation mode Types of Equations The HP 32SII
48. Resumes the inverse routine Statistics Programs 16 17 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm a 0 8 Wood 1232 Stores 0 8 100 percent minus 20 percent in Q X and calculates X Grouped Standard Deviation The standard deviation of grouped data Sxy is the standard deviation of data points x1 x2 Xn occurring at positive integer frequencies f1 f2 fn This program allows you to input data correct entries and calculate the standard deviation and weighted mean of the grouped data Program Lines Description Si LEL S Start grouped standard deviation program S 2 CLE Clears statistics registers 28 through 33 SH B Sa4 STO H Clears the count N Checksum and length 104F 006 0 I81 LBL I Input statistical data points I 2 INPUT X Stores data point in X IH IHPFUT F Stores data point frequency in F I84 i Enters increment for N I85 RCL F Recalls data point frequency fi Checksum and length 4060 007 5 Fai LBL F Accumulate summations Fie 22 Fas STO i Stores index for register 28 Fad RV 16 18 Statistics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Program Lines FHS S7O i2 FHE RCLx Far 29 FHS STO i Fad RV Fil S7TO j 3 Fii RCL amp Fiz 3i Fis STO Fid RV Fis S7O 3 Fl amp xiv Fir STO H FiS RCL H FiS VIEW H Fea GTO I Description Updates gt f in register 28 xf i
49. SOLVE instructions l If your first TVM calculation is to solve for interest rate press 1 2 Press Wea EQN If necessary press ER or EX to scroll through the equation list until you come to the TVM equation 3 Do one of the following five operations b Press We N to calculate the number of compounding periods Press F SOLVE to calculate periodic interest For monthly payments the result returned for is the monthly interest rate i press 12 to see the annual interest rate Press fsa B to calculate initial balance of a loan or savings account Press Wz P to calculate periodic payment Press Wz F to calculate future value or balance of a loan 4 Key in the values of the four known variables as they are prompted for press after each value 5 When you press the last R S the value of the unknown variable is calculated and displayed 6 To calculate a new variable or recalculate the carne variable using different data go back to step 2 SOLVE works effectively in this application without initial guesses Miscellaneous Programs and Equations 17 3 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm u Variables Used N The number of compounding periods The periodic interest rate as a percentage For example if the annual interest rate is 15 and there are 12 payments per year the periodic interest rate i is 15 12 1 25 B The initial b
50. Selects Equation mode 7 2 Solving Equations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm E or current equation D F O xT E Starts the equation V T 5 G Tt 5xGxT 2 KON O WxT 8 5xGxT Terminates the equation and displays the left end r3 CK 6A92 829 48 Checksum end length g acceleration due to gravity is included as a variable so you can change it for different units 98 m s or 32 2 ft s Calculate hove ran meters an object falls in 5 seconds starting from rest Since Equation mode is turned on and the desired equation is turn on and the desired is already in the display you can start solving for D Keys Display Description F SOLVE _ Prompts for unknown known variable D V value Selects D prompts for V O T value Stores O in V prompts for T 5 G5 value Stores 5 in T prompts for G 9 8 SOLVING Stores 9 8 in G prompts for D D i 22 3088 Try another calculation using the same equation how long does it take are object to fall 500 meters from rest Keys Display Description Wes IU xT B B5xGXT Displays the equation F3 T D i22 588 Solves for T prompts for D 500 w B BB8Ba Stores 500 in D prompts for V G79 5006 Retains O in V prompts for G Solving Equations 7 3 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm SOLVING Retains 9 8 in G prompts for T T 186 1615 Example Solving the Ideal Gas Law Equation
51. Solves for one real root and puts three synthetic division coefficients for fourth order polynomial on stack Discards polynomial function value Stores coefficient Stores coefficient Stores coefficient Calculates a3 Stores a3 Displays real root of fifth order polynomial Checksum and length OFE9 019 5 i81 LBL L OHS 4 DAS ECL x C id ECL O DES xf DWE Dar ECL A DES RCL B DES xf Dik i11 STU E Die ROL C Starts fourth order solution routine 4a2 a3 a32 4a2 a32 ao 4a2 a3 a ay bo ao 4a0 a3 a12 Stores bo a2 15 24 Mathematics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm Program Lines DiS i14 STU G Dis RCL L Die RCL B Dir 4 Dis RCL A D13 i28 STU F Dei 4 Dee 3 O23 1 D24 D25 f D26 Der AEM S D28 RV D029 AE D DSH RCL amp O31 STU E 52 FS B O33 GIO F D034 ECL F Oss xiv 36 x2 Dar RCL G Das xiv 39 xi i48 STD E Description b2 a2 Stores b2 a3 330 Aao b1 aaa1 4a0 Stores b To enter lines D21 and D22 Press 4 fsa 2 Creates 7 004 as a pointer to the cubic coefficients Solves for real root and puts ag and a1 for second order polynomial on stack Discards polynomial function value Solves for remaining roots of cubic and stores roots Gets real root of cubic Stores real root Complex roots Calculate four roots of remainin
52. Tis RCL Ti amp VIEW X Displays the calculated value of X Line TO9 calculates the correction for Xguess Line T13 compares the absolute value of the calculated correction with 0 0001 If the value is less than 0 0001 Do If True the program executes line T14 if the value is equal to or greater than 0 0001 the program skips to line T15 Flags A flag is an indicator of status It is either set true or clear false Testing a flag is another conditional test that follows the Do if true rule program execution proceeds directly if the tested flag is set and skips one line if the flag is clear Meanings of Flags The HP 32SIl has 12 flags numbered O through 11 All flags can be set cleared and tested from the keyboard or by a program instruction The default state of all 12 flags is clear The three key memory clearing operation described in appendix B clears all flags Flags are not affected by EX ALL B Flags O 1 2 3 and 4 have no preassigned meanings That is their states will mean whatever you define it to mean in a given program See the example below mE Flag 5 when set will interrupt a program when an overflow occurs within the program displaying OWERFLOW and A An overflow occurs when a result exceeds the largest number that the calculator can handle The largest possible number is substituted for the overflow result If flag 5 is clear a program with an overflow is not interrupted though OVE
53. VIEW i operations label the display with the name of the indirectly addressed variable or register The SUMS menu enables you to recall values trom the statistics registers However you must use indirect addressing to do other operations such as STO VIEW and INPUT The functions listed below can use i as an address For GTO XEQ and FN i refers to a label for all other functions i refers to a variable or register Programming Techniques 13 21 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm STO i INPUT i RCL i VIEW i STO x i DSE i RCL 2x i ISG i XEQ i SOLVE i GTO i J FN d i X lt gt i FN i Program Control with i Since the contents of i can change each time a program runs or even in different parts of the same program a program instruction such as GTO lt i gt can branch to a different label at different times This maintains flexibility by leaving open until the program runs exactly which variable or program label will be needed See the first example below Indirect addressing is very useful for counting and controlling loops The variable i serves as an index holding the address of the variable that contains the loop control number for the functions DSE and ISG See the second example below Example Choosing Subroutines With i The Curve Fitting program in chapter 16 uses indirect addressing to determine which model to use t
54. X and Y Registers in the Stack Another key that manipulates the stack contents is x exchange y This key swaps the contents of the X and Y registers without affecting the rest of the stack Pressing twice restores the original order of the X and Y register contents The function is used primarily for two purposes B To view the contents of the Y register and then return them to y press twice Some functions yield two results one in the X register and one in the Y register For example EN converts rectangular coordinates in the X and Y registers into polar coordinates in the X and Y registers B To swap the order of numbers in a calculation For example one way to calculate 9 13 x 8 Press 13 ENTER 8 x 9 ke x The keystrokes to calculate this expression from left to right are 9 ENTER 13 ENTER 8 X 3 Note Always make sure that there are no more than four numbers in ance the stack at any given time the contents of the T register the e top register will be lost whenever a fifth number is entered Arithmetic How the Stack Does It The contents of the stack move up and down automatically as new numbers enter the X register lifting the stack and as operators combine two numbers in the X and Y registers to produce one new number in the X register dropping the stack Suppose the stack is filled with the numbers 1 2 3 and 4 See how the stack drops and lifts its contents while calculating 2 4
55. Y Vj Z Wk v2 v1 U X i V Yj W Dk Cross product vixv2 YW ZV i ZU XWj XV YU k Dot Product D XU YV ZW Angle between vectors y D Qrccos R x R where vi Xit Yj Zk and va2 Ui Vi Wk The vector displayed by the input routines LBL P and LBL R is V7 Program Listing 15 2 Mathematics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Program Lines RAI LEL R RAS IHPUT amp RAS IHPUT Y rad IHPUT Description Detines the beginning of the rectangular input display routine Displays or accepts input of X Displays or accepts input of Y Displays or accepts input of Z Checksum and length F8AB 006 0 WHI LBL t Hee ECL Y 35 3 ECL A aea vax Quer WAS xz He STO T Hay RV HHS RCL Z GAD vax DQer HiH STOR Hii xzw Hie STOP Defines beginning of rectangular to polar conversion process Calculates X Y and arctan Y X Saves T arctan Y X Gets J X Y2 back Calculates X Y Z2 and P Saves R Saves P Checksum and length 3D28 018 0 F i LBL F Pas IHPL Pas INFU F 4 IHPLI Pas RCL T Fae ECL F Par ECL PHS 0 r2v x Fas STO Z Pia RV Pil r Ovex Fiz STO 2 File name 32sii Manual E 0424 Printed Date 2003 4 24 Detines the beginning of the polar input display routine Displays or accepts input of R Displays or accepts input of T Displays or accepts input of P Calcu
56. You don t have to remember the names of 1 6 Getting Started File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm the tunctions built into the calculator nor search through the names printed on its keyboard Exiting Menus Whenever you execute a menu function the menu automatically disappears as in the above example If you want to leave a menu without executing a function you have three options mM Pressing backs out of the 2 level CLEAR or MEM menu one level at a time Refer to EX in the table on page 1 4 WI Pressing or LC cancels any other menu Keys Display 123 123 Wed PROB Cn r Proar SD FR or 123 8888 WI Pressing another menu key replaces the old menu with the new one Keys Display 123 123 Wed PROB Cn r Poor SD F E CLEAR VARS ALL 23 880818 Annunciator The symbols along the top and bottom of the display shown in the following figure are called annunciators Each one has a special significance when it appears in the display picture 1 8 Getting Started 1 7 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm HP 32SIl Annunciator Upper Row The EX and EX keys are active for stepping through a list When in Fraction display mode press E FDISPJ only one of the A or V halves of the WA annunciator will be turned on to indicate whether the displayed numerator is slightly less than or slightly grea
57. Z by multiplying the result matrix by the inverse of the coefficient matrix A D old X B E AY K y Y C F yl Z Specifics regarding the inversion process are given in the comments for the inversion routine 15 12 Mathematics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm E Program Listing Program Lines Description A i LBL A Starting point for input of coefficients ABZ 1 12 Loop control value loops from to 12 one at a time nes STU Stores control value in index variable Checksum and length 9F76 012 5 Lai LBL L Starts the input loop Laz INPUTS i gt Prompts for and stores the variable addressed by i Laz ISG i Adds one to i La4 GTO L If i is less than 13 goes back to LBL L and gets the next value Las GTOAR Returns to LBL A to review values Checksum and length 8356 007 5 I i LBL I This routine inverts a 3 x 3 matrix IEZ 4EQ D Calculates determinant and saves value for the division loop J Ha STO M H4 RCL A Ha ECL I THe RCL C l r ECL G Ha lao STO Calculates E x determinant Al CG Tif ROL C Iii ECL OU I12 RCL H Tia RCL F I14 Tis STO Y Calculates F x determinant CD AF I16 ECL Tir RCLx G Mathematics Programs 15 13 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i Program Lines I12 RCL A 119 RCL x H I2H I21 10 Z I22 RCL A Iles RCLx E I24 RCL B I25 RCLx O
58. a 27th variables that you can access directlythe variable i The LJ key is labeled i and it means i whenever the A Z annunciator is on Although it stores numbers as other variables do i is special in that it can be used to refer to other variables including the statistics registers using the i function This is a programming technique called indirect addressing that is covered under Indirectly Addressing variables and labels in chapter 13 Storing Data into Variables 3 7 File name 32sii Manual E O424 Printed Date 2003 4 24 Size 177 x 25 2 cm 4 Real Number Functions This chapter covers most of the calculator s functions that perform computations on real numbers including some numeric functions used in programs such as ABS the absolute value function Exponential and logarithmic functions Power functions and Xv Trigonometric functions Hyperbolic functions Percentage functions Conversion functions for coordinates angles and units Probability functions Parts of numbers number altering functions Arithmetic functions and calculations were covered in chapters 1 and 2 Advanced numeric operations root tinding integrating complex numbers base conversions and statistics are described in later chapters All the numeric functions are on keys except for the probability and parts of numbers functions The probability functions En e Pn x SD and F are in the PROB menu press
59. also ensure that the VIEWed variable is in the X register as well except for the Polynomial Root Finder program Using Equations to Display Messages Equations aren t checked for valid syntax until they re evaluated This means you can enter almost any sequence of characters into a program as an equation you enter it just as you enter any equation On any program line 12 14 Simple Programming File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm press P to start the equation Press number and math keys to get numbers and symbols Press before each letter Press to end the equation It flag 10 is set equations are displayed instead of being evaluated This means you can display any message you enter as are equation Flags are discussed in detail in chapter 13 When the message is displayed the program stops press to resume execution If the displayed message is longer than 12 characters the and V annunciators turn on when the message is displayed You can then use and to scroll the display You can press W SCRL to turn off and make the top row keys perform their normal functions It you don t want the program to stop see Displaying Information without Stopping below Example INPUT VIEW and Messages in a Program Write an equation to find the surface area and volume of a cylinder given its radius and height Label the program C for cylinder and use the variable
60. and then recall then when needed for calculation then this prevents the stack s contents from being altered just before a calculation For example see the Coordinate Transformations program in chapter 15 Routine D collects all the necessary input for the variables M N and T lines DO2 through DOA that define the x and y coordinates and angle 0 of a new system To respond to a prompt Mien you run the program it will stop at each INPUT and prompt you for that variable such as k76 GG The value displayed and the contents of the X register will be the current contents of R To leave the number unchanged just press R S To change the number type the new number and press R S This new number writes over the old value in the X register You can enter a number as a traction if you want If you need to calculate a number use normal keyboard calculations then press R S For example you can press 2 5 PA R S To calculate with the displayed number press before typing another number To cancel the INPUT prompt press LC The current value for the variable remains in the X register If you press to resume the program the canceled INPUT prompt is repeated If you press during digit entry it clears the number to zero Press LC again to cancel the INPUT prompt To display digits hidden by the prompt press Fea SHOW If it is a binary number with more than 12 digits use the and and keys to see the rest Simple
61. annunciator doesn t indicate accuracy it means you can use Lf Jand lo move through the list of variables The accuracy isn t shown Sometimes an annunciator is lit when you wouldn t expect it to be For example if you enter 2 7 3 you see A 2 2 3 even though that s the exact number you entered The calculator always compares the fractional part of the internal value and the 12 digit value of just the fraction If the internal value has an integer part its fractional part contains less than 12 digits and it can t exactly match a fraction that uses all 12 digits Longer Fractions If the displayed fraction is too long to fit in the display it s shown with at the beginning The fraction part always fits the means the integer part isn t shown completely To see the integer part and the decimal fraction proms and hold fs You can t scroll a fraction in the display 5 4 Fractions File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm u Example Keys Display Description 14 84 88873125 Calculates e 4 3 1262664 28416 Shows all decimal digits A 4 88873125 Stores value in A Wes A A 888 3125 Views A B Clears x Changing the Fraction Display In its default condition the calculator displays a fractional number according to certain rules See Display Rules earlier in this chapter However you can change the rules according to how you want fractions displayed B You c
62. as V 40 H x 20 H xAxH Type in the equation Keys Display Description r3 Selects Equation mode and V fs v starts the equation We 40 H 3 u ca4Bn H N Wes CC 20 8 H xc28 H B H r 4 H xieB Hox4xHN W 4 Hi x i26 Terminates and displays the equation r3 CK B2HC 827 48 Checksum and length I seems reasonable that either a tall narrow box or a short flat box could be formed having the desired volume Because the taller box is preferred larger initial estimates of the height are reasonable However heights greater than 20 cm are not physically possible because the metal sheet is only 40 cm wide Initial estimates of 10 and 20 cm are therefore appropriate Keys Display Description Leaves Equation mode 10 H 20 28 Stores lower and upper limit guesses Solving Equations 7 9 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i r3 uUz iamn Hoxz Displays current equation Wes H V value Solves for H prompts for V 7500 H 15 8088 Stores 7500 in V solves for H Now check the quality of this solution that is whether it returned an exact root by looking at the value of the previous estimate of the root in the Y register and the value of the equation at the root in the Z register Keys Display Description 15 6886 This value from the Y register is the estimate made just prior to the final result Since it is the same as the solution
63. coefficient A equal to 25 Sets B equal to 8 Sets C equal to 4 Sets D equal to 15 Continues entry for E through L Returns to first coefficient entered Calculates the inverse and displays the determinant Multiplies by column vector to compute X Calculates and displays Y Calculates and displays Z Begins review of the inverted matrix Displays next value Displays next value Displays next value Displays next value Displays next value Mathematics Programs 15 19 Size 177 x 25 2 cm G 8 8682 Displays next value H76 B596 Displays next value 176 0289 Displays next value G BAZ Inverts inverse to produce original matrix A R 23 B888 Begins review of inverted matrix B 8 8888 Displays next value and so on Polynomial Root Finder This program finds the roots of a polynomial of order 2 through 5 with real coefficients It calculates both real and complex roots For this program a general polynomial has the form x ag 1x7 c aix a0 0 where n 2 3 4 or 5 The coefficient of the highest order term an is assumed to be 1 If the leading coefficient is not 1 you should make it by dividing all the coefficients in the equation by the leading coefficient See example 2 The routines for third and fifth order polynomials use SOLVE to find one real root of the equation since every odd order polynomial must have at least one real root After one root is found synthetic
64. division is performed to reduce the original polynomial to a second or fourth order polynomial To solve a fourth order polynomial it is first necessary to solve the resolvant cubic polynomial y boy b y bo 0 where b22 a2 b a3aj1 4ao 15 20 Mathematics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm bo ao 4a2 a3 a12 let yo be the largest real root of the above cubic Then the fourth order polynomial is reduced to two quadratic polynomials x J Dx K M 0 eU Dx K M 0 where J a3 2 K yo 2 L J a yo x the sign of JK a1 2 Roots of the fourth degree polynomial are found by solving these two quadratic polynomials A quadratic equation x a1x ag O is solved by the formula a a la Cy a 2 2 po m3 If the discriminant d a1 2 ao 2 O the roots are real if d O the roots are complex being ut iv 2 a 2 iV d Program Listing Program Lines Description Pa i LBL F Detines the beginning of the polynomial root tinder routine Paz INPUT F Prompts for and stores the order of the polynomial Pas STO i Uses order as loop counter Checksum and length 699F 004 5 I81 LBL I Starts prompting routine T 2 IHPUTCi Prompts for a coefficient I8 OSE i Counts down the input loop I84 GTO I Repeats until done IMs RCL F I8 amp STO i Uses order to select root finding routine Mathematics Progr
65. fea PROB The parts of numbers functions IP FP and ABS are in PARTS menu press Wed PARS Exponential and Logarithmic Functions Put the number in the display then execute the function there is no need to press ENTER Real Number Functions 4 1 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm To Calculate Press Natural logarithm base e Common logarithm base 10 ER Natural exponential Common exponential antilogarithm al Power Functions To calculate the square of a number x key in x and press EW x To calculate a power x of 10 key in x and press EX 10 To calculate a number y raised to a power x key in y x then press U For y gt 0 x can be any rational number for y lt O x must be are integer for y O x must be positive 15 Em 2 225 888 6 EX 107 i AGA AGG AAGA 5 ENTER 4 VA 625 0088 2 ENTER 1 404 BY a 3789 1 4 GZ ENTER 3 LA 2 7446 To calculate a root x of a number y the x root of y key in y x then press Em WY For y O x must be an integer To Calculate Press Result 3 155 125 GA ENTER 3 Ex GZ 5 B8B888 3 55 125 ENTER 3 EN GZ 5 BAGA 4 2 JReal Number Functions File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm M 27202 3 893 1 4 Ex 2 BEBE Trigonometry Entering x Press F to place the first 12 digits of x into the X register
66. for a comprehensive list of the functions that save x in the LAST X register Correcting Mistakes with LAST X Wrong One Number Function If you execute the wrong one number function use EX to retrieve the number so you can execute the correct function Press first if you want to clear the incorrect result from the stack Since Wz and fea CHG don t cause the stack to drop you can recover from these functions in the same manner as from one number functions Example Suppose that you had just computed In 4 7839 x 3 879 x 10 and wanted to find its square root but pressed by mistake You don t have to start over To find the correct result press EN Lx Mistakes with a Two number operation If you make a mistake with a two number operation LE LE J LE or you can correct it by using EX and inverse of the two number function or LE LE or L or 1 Press EN to recover the second number x just before the operation 2 Execute the inverse operation This returns the number that was originally first The second number is still in the LAST X register Then W f you had used the wrong function press ER again to restore the original stack contents Now execute the correct function W f you had used the wrong second number key in the correct one and execute the function If you had used the wrong first number key in the correct first number press Ex to recover the second number and exec
67. fractions to x If x 1 displays current c value ER Converts F to C ra CF n Clears flag n n O through 11 Displays menu to clear numbers or parts of memory clears indicated variable or program from a MEM catalog clears displayed equation Clears all stored data equations and programs Clears all programs calculator in Program mode F 4 Operation Index File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm 4 5 4 1 13 12 1 4 1 20 u Eat E amp H Clears the displayed equation calculator in Program mode CLE E 3 Clears statistics registers CLVARS E WARS Clears all variables to zero Clx fal x Clears x the X register to zero CM ER Converts inches to centimeters ER Displays the CMPLX_ prefix for complex functions CMPLX EX Complex change sign M zx i zy CMPLX EX Complex addition Returns Z1x i z1y z2x i z2y CMPLX EN Complex subtraction Returns z 1x i z1y Z2x i z2y CMPLX x EX Complex multiplication Returns Z1x i z1y x Z2x i Z2y CMPLX Ex Lx Complex division Returns Z1x i z1y z2x i Z2y CMPLX1 x EX Complex reciprocal Returns 1 zx i zy CMPLXCOS Ex Complex cosine Returns cos zx i zy CMPLXex EJ Complex natural exponential Returns e CMPLXLN EX Complex natural log Returns log zx i zy
68. in catalog moves Operation Index F 1 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i Keys and Description to next equation in equation list moves program pointer to next line during program entry executes the current program line not during program entry Reciprocal EX Common exponential Returns 10 raised to the x power za Percent Returns y x x 100 Wes Percent change Returns x y 100 y We Returns the approximation 3 14159265359 12 digits Accumulates y x into statistics registers Ex Removes y z from statistics registers 3 SUNS Returns the sum of x values 3 SUNS x2 Returns the sum of squares of x values 1 xv Returns the sum of products of x and y values 53 SUNS Returns the sum of y values 3 SUMS v Returns the sum of squares of y values FE 53 fox Returns population standard deviation of x values F 2 Operation Index File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm u 0 ry x J FN d variable A through Z ABS ACOS ACOSH ALOG ALL File name 32sii Manual E 0424 Printed Date 2003 4 24 Wea Sa ov Returns population standard deviation of y values My yr n Wea x Polar to rectangular coordinates Converts r 0 to x y r3 FH a _ variable Integrates the displayed equation or the
69. is explained in detail in chapter 2 under Exchanging the X and Y Registers in the Stack Controlling the Display Format Periods and Commas in Numbers To exchange the periods and commas used for the decimal point radix mark and digit separators in a number 1 Press EX to display the MODES menu 2 Specify the decimal point radix mark by pressing or For example the number one million looks like E 1 866 684 8646 if you press or E 1 466 886 6846 if you press 1 14 Getting Started File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm E Number of Decimal Places All numbers are stored with 12 digit precision but you can select the number of decimal places to be displayed by pressing EX the display menu During some complicated internal calculations the calculator uses 15 digit precision for intermediate results The displayed number is rounded according t the display format The DISP menu gives you four options Fa SC EH ALL Fixed Decimal Format F FIX format displays a number with up to 11 decimal places 11 digits to the right of the or radix mark if they fit After the prompt FIX type in the number of decimal places to be displayed For 10 or 11 places press LJ O or L 1 For example in the number 123 456 7089 the 7 0 8 and 9 are the decimal digits you see when the calculator is set to FIX 4 display mode Any number teat is too larg
70. is very likely that a solution has been found However if f x is relatively large you must use caution in interpreting the results Example An Equation With One Root Find the root of the equation 2x9 4x2 6x 8 0 Enter the equation as an expression More about Solving C 3 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Keys Display Wed EQN 2 Ez x RCL X eI 3 4 x RCL X UY 2 6 x RCL X 8 ZxW 3 4dW R za LEK Z LSH 8345 8 Now salve the equation to find the root Keys Display O X 10 T za 2xn7d4dtdxkR Z F X SOLVING A 1 6586 1 6586 4 HBHHWBHE 11 Description Select Equation mode Enters the equation Clecksum and length Cancels Equation mode Description Initial guesses for the root Selects Equation mode displays the left end of the equation Solves for X displays the result Final two estimates are the same to four decimal places f x is very small so the approximation is a good root Example An Equation with Two Roots Find the two roots of the parabolic equation x24 x 6 0 Enter the equation as an expression C 4 More about Solving File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm E Keys Display Description r3 Selects Equation mode X 2 Enters the equation X LE 6 MADEM OE r3 CK 6363 812 8 Checksum and length Cancels Equation mode Now solv
71. local population that meet the criteria Since your friend has been known to exaggerate from time to tame you decide to see how rare a 26 date might be Note that the program may be rerun simply by pressing R S Keys Display Description 16 16 Statistics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm u aT3 BAGG Resumes program 2 i B8 B227 Enters X value of 2 and calculates Q X 10000 227 4937 Multiplies by the population for the revised estimate Example 2 The mean of a set of test scores is 55 The standard deviation is 15 3 Assuming that the standard normal curve adequately models the distribution what is the probability that a randomly selected student scored 90 What is the score that only 10 percent of the students would be expected to have surpassed What would he the score that only 20 percent of the students would have failed to achieve Keys Display Description S M78 6608 Starts the initialization routine 55 S71 8088 Stores 55 for the mean 15 3 15 3888 Stores 15 3 for the standard deviation D 5 value Starts the distribution program and prompts for X 90 a Aiii Enters 90 for X and calculates Q X Thus we would expect that only about 1 percent of the students would do better than score 90 Keys Display Description 178 8111 Starts the inverse routine 0 01 4 74 6078 Stores 0 1 10 percent in Q X and calculates X O78 1688
72. lower limit and press ENTER then key in the upper limit 3 Display the equation Press P and if necessary scroll through the equation list press EX or EX to display the desired equation 4 Select the variable of integration Press P variable This starts the calculation uses far more memory than any other operation in the calculator If executing causes a MEMORY FULL message refer to appendix B You can halt a running integration calculation by pressing or R S However no information about the integration is available until the calculation finishes normally The display format setting affects the level of accuracy assumed for your function and used for the result The integration is more precise but takes much longer in the ALL and higher F SC and EH settings The uncertainty of the result ends up in the Y register pushing the limits of integration up into the T and Z registers For more information see Accuracy of Integration later in this chapter 8 2 Integrating Equations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm To integrate the same equation with different information If you use the same limits of integration press move them into the X and Y registers Then start at step 3 in the above list If you want to use different limits begin at step 2 To work another problem using a different equation start over from step 1 with an equation that define
73. number in i to determine which variable or label to address This is an indirect address A through Z are direct addresses Both and are used together to create an indirect address See the examples below By itself i is just another variable By itself is either undefined no number in i or uncontrolled using whatever number happens to be left over in i The Variable i Your can store recall and manipulate the contents of i just as you car the contents of other variables You can even solve for i and integrate using i The functions listed below can use variable STO i INPUT i DSE i RCL i VIEW i ISG i STO x i JFNdi x i RCL x i SOLVE i 13 20 Programming Techniques File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm The Indirect Address i Many functions that use A through Z as variables or labels can use to refer to A through Z variables or labels or statistics registers indirectly The function uses the value in variable i to determine which variable label or register to address The following table shows how Micontiin Then i will address variable A or label A variable Z or label Z variable i n register Xx register Xy register x register Ly register Yxy register 234 or lt 34 or O error INVALID lt i gt Only the absolute value of the integer portion of the number in i is used for addressing The INPUT i and
74. receive has a positive sign while money that you pay has a negative sign Note that any Miscellaneous Programs and Equations 17 1 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm problem can he viewed from two perspectives The lender and the borrower view the same problem with reversed signs Equation Entry Key in this equation FxlHHxicl cloeI liBWHo Ho ITFxtlc I liBB H B Keys Display Description r3 EGH LIST TOF Selects Equation mode or current equation P 100 Px 188 Starts entering equation x u1ct Pxif x i l x Wes LO I 188x 1 Ci l RCL 100 1 i 1 1098_ Wea LL LA t1 I 1882 B RCL N Wea C1 I 1883 H2N F X a Ho I FXN Wes LC 1 RCL H3 ISTFxC1 IB 100 Wea UJ Fxil I 1BB2N 23 RCL N 1 I 1882 HN RCL B I i8B83 H EN Pxi e x 1i it Terminates the equation ra hold CK 45C4 1854 8 Checksum and length Memory Required 94 bytes 54 bytes for the equation 40 bytes for variables 17 2 Miscellaneous Programs and Equations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm E Remarks The TVM equation requires that must be non zero to avoid a DIVIDE BY amp error If you re solving for and aren t sure of its current value press 1 before you begin the SOLVE calculation Wa The order in which you re prompted for values depends upon the variable you re solving for
75. self test again If you pressed the keys in order but got this message repeat the self test to verify the results If the calculator fails again it requires service see page A 7 Include a copy of the fail message with the calculator when you ship it for service 5 To exit the self test reset the calculator hold down and press LN Pressing and starts a continuous self test that is used at the factory You can halt this factory test by pressing any key Support Batteries and Service A 5 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm a Limited One Year Warranty What Is Covered The calculator except for the batteries or damage caused by the batteries is warranted by Hewlett Packard against defects in materials and workmanship for one year from the dale of original purchase If you sell your unit or give it as a gift the warranty is automatically transterred to the new owner and remains in effect for the original one year period During the warranty period we will repair or at our option replace at no charge a product that proves to be defective provided you return the product shipping prepaid to a Hewlett Packard service center Replacement may be with a newer model of equivalent or better functionality This warranty gives you specific legal rights and you may also have other rights that vary from state to state province to province or country to country What Is Not Cov
76. smaller interval Consequently several more iterations are required over the larger interval to achieve an approximation with the same accuracy and therefore calculating the integral requires considerably more time Because the calculation time depends on how soon a certain density of sample points is achieved in the region where the function is interesting the More about Integration D 9 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm calculation of the integral of any function will be prolonged if the interval of integration includes mostly regions where the function is not interesting Fortunately if you must calculate such an integral you can modity the problem so that the calculation time is considerably reduced Two such techniques are subdividing the interval of integration and transformation of variables These methods enable you to change the function or the limits of integration so that the integrand is better behaved over the intervals of integration D 10 More about Integration File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Messages The calculator responds to certain conditions or keystrokes by displaying a message The symbol comes on to call your attention to the message For signiticant conditions the message remains until you clear it Pressing or clears the message pressing am other key clears the message and executes that key s function
77. the display format To specify the accuracy of the integration set the display format so that the display shows no more than the number of digits that you consider accurate in the integrand s values This same level of accuracy and precision will be reflected in the result of integration If Fraction display mode is on flag 7 set the accuracy is specified by the previous display format 8 6 Integrating Equations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm Interpreting Accuracy Atter calculating the integral the calculator places the estimated uncertainty of that integral s result in the Y register Press to view the value of the uncertainty For example if the integral Si 2 is 1 6054 0 0001 then 0 0001 is its uncertainty Example Specifying Accuracy With the display format set to SCI 2 calculate the integral in the expression for Si 2 from the previous example Keys Display Description EN SC 2 1 61E8 Sets scientific notation with two decimal places specifying that the function is accurate to two decimal places 2 BBED Rolls down the limits of integration frown the Z and T registers into the X and Y registers r SIHCHI H Displays the current Equation a X INTEGRATING The integral approximated to two f 1 66E8 decimal places i 4E 3 The uncertainty of the approximation of the integral The integral is 1 61 0 00100 Since the uncertainty would not aff
78. the first 12 digits again EX DEC 9 471 6 Restores base 10 Arithmetic in Bases 2 8 and 16 You can perform arithmetic operations using 4 LE X and in any base The only function keys that are actually deactivated outside of Decimal mode are Vx Le LN LA and However you should realize that most operations other than arithmetic will not produce meaningful results since the fractional parts of numbers are truncated 10 2 Base Conversions and Arithmetic File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Arithmetic in bases 2 8 and 16 is in 2 s complement form and uses integers only E f a number has a fractional part only the integer part is used for an arithmetic calculation WI The result of an operation is always an integer any fractional portion is truncated Whereas conversions change only the displayed number and not the number in the X register arithmetic does alter the number in the X register It the result of an operation cannot be represented in 36 bits the display shows OWERFLOM and then shows the largest positive or negative number possible Example Here are some examples of arithmetic in Hexadecimal Octal and Binary modes 12F16 E9A16 Keys Display Description Ex He Sets base 16 HEX annunciator on 12F E9A FC3 Result 77608 432682 EX oc rr ii Sets base 8 OCT annunciator on Converts displayed number to octal
79. the lines of the program To see your checksum 1 Press EX FGM for the catalog of program labels 2 Display the appropriate label by using the arrow keys if necessary 3 Press and hold F to display CK value length For example to see the checksum for the current program the cylinder program Keys Display Description EX PGM LEL C 861 5 Displays label C which takes 61 5 bytes r3 CK 6647 861 5 Checksum and length 12 22 Simple Programming File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm hold If your checksum does not match this number then you have not entered this program correctly You will see that all of the application programs provided in chapters 15 through 17 include checksum values with each labeled routine so that you can verify the accuracy of your program entry In addition each equation in a program has a checksum See To enter an equation in a program line earlier in this chapter Nonprogrammable Functions The following functions of the HP 32 Il are not programmable EN CLEAR PGM Ex GTO L LJ E CLEAR ALL ES GTO L label nn E MEM E Ls Ex Lt Wea SHOW E PROM Wea EQN Ex FDISP Programming with BASE You can program instructions to change the base mode using EX BASE These settings work in programs just as they do as functions executed from the keyboard This allows you to write programs that accept
80. the solution is an exact root A BAGA This value from the Z register shows the equation equals zero at the root The dimensions of the desired box are 50 x 10 x 15 cm If you ignored the upper limit on the height 20 cm and used initial estimates of 30 and 40 cm you would obtain a height of 42 0256 cm a root that is physically meaningless If you used small initial estimates such as O and 10 cm you would obtain a height of 2 9774 cm producing an undesirably short flat box It you don t know what guesses to use you can use a graph to help the behavior of the equation Evaluate your equation for several values of the unknown For each point on the graph display the equation and press at the prompt for x enter the x coordinate and then obtain the corresponding value of the equation the y coordinate For the problem above you would always set V 7500 and vary the value of H to produce different values for the equation Remember that the value for this equation is the difference between the left and right sides of the equation The plot of the value of this equation looks like this 7 10 Solving Equations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm u 7500 40 H 20 H 4H 20 000 0801010 For More Information This chapter gives you instructions for solving for unknowns or roots over a wide range of applications Appendix C contains more detailed information about how the algo
81. to the new system continue with step 7 To translate from the new system to the old system skip to step 12 Press N to start the oldto new transformation routine Key in X and press R S Key in Y press R S and see the x coordinate U in the new system 10 Press and see the y coordinate V in the new system TI 12 For another old 4o new transformation press and go to step 8 For a new to old transformation continue with step 12 Press O to start the new to old transformation routine Mathematics Programs 15 35 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 13 Key in U the x coordinate in the new system and press R S 14 Key in V the y coordinate in the new system and press to see X 15 Press to see Y 16 For another new to old transformation press and go to step 13 For an old to new transformation go to step 7 Variables Used The x coordinate of the origin of the new system The y coordinate of the origin of the new system The rotation angle 0 between the old and new systems The x coordinate f a point in the old system The y coordinate of a point in the old system The x coordinate of a point in the new system lt C lt lt KAUZFe The y coordinate of a point in the new system Remark For translation only key in zero for T For rotation only key in zero for M and N Example For the coordinate stems shorn below convert points P1
82. type of equation If you want the equation to prompt for variable values instead of including INPUT instructions make sure flag 11 is set 4 End the program with a RTN Program execution should end with the value of the function in the X register Example Program Using Equation The sine integral function in the example in chapter 8 is sr Xa O x This function can be evaluated by integrating a program that defines the integrand saiLBL Defines the function S 2 SIHI H The function as an expression Checksum and length 4914 009 0 S63 RTH Ends the subroutine Checksum and length of program C62A 012 0 Enter this program and integrate the sine integral function with respect to x from O to 2 t 2 Keys Display Description 14 8 Solving and Integrating Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm EX RD Selects Radians mode F S Selects label S as the integrand O 2 2 Enters lower and upper limits of integration r3 X IHTEGERTIHG Integrates function from O to 2 1 6854 displays result al OG 1 6854 Restores Degrees mode Using Integration in a Program Integration can be executed from a program Remember to include or prompt for the limits of integration before executing the integration and remember that accuracy and execution time are controlled by the display format at the time the program runs The two integration instructions appear in the p
83. was not the same 4 608 Final value for f x is relatively large Example An Asymptote Find the root of the equation C 10 More about Solving File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm E Ibo edi X Enter the equation as an expression Keys Wea EQN 10 Ux REL X Wea O ENTER Wea SHOW c 005 STO X 5 Wea EQN E SOLVE x RV Wea SHOW Display B III LE ecel 82 6 IB INV Ca A 16006 H limi H BREE BEER Description Selects Equation mode Enters the equation Checksum and length Cancels Equation mode Your positive guesses for the root Selects Equation mode displays the equation Solves for x using guesses 0 005 and 5 Previous estimate is the same Watch what happens when you use negative values for guesses Keys 1 KZ STO X 2 UA m EQN Wed SOLVE X File name 32sii Manual E 0424 Printed Date 2003 4 24 Display 1 86688 IB INV Caw HO ROOT FHO Description Your negative guesses for the root Selects Equation mode displays the equation No root found for f x 46 666 666 692 1 Displays last estimate of x M rroaldEbio iB BBa Size 17 7 x 25 2 cm Previous estimate was much larger f x for last estimate is rather large More about Solving C 11 a It s apparent from inspecting the equation that if x is a negative number the smallest that f x can be i
84. works with three types of equations M Equalities The equation contains an and the left side contains more than just a single variable For example x y r is an equality Assignments The equation contains an and the left side contains just a single variable For example A 0 5 x b x his an assignment 6 10 Entering and Evaluating Equations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm u WB Expressions The equation does not contain an For example x lis an expression When you re calculating with an equation you might use any type of equation although the type can affect how it s evaluated When you re solving a problem for an unknown variable you ll probably use an equality or assignment When you re integrating a Function you ll probably use an expression Evaluating Equations One of the most useful characteristics of equations is their ability to be evaluated to generate numeric values This is what enables you to calculate result from an equation It also enables you to solve and integrate equations as described in chapters 7 and 8 Because many equations have two sides separated by the basic value of an equation is the difference between the values of the two sides For this calculation in an equation essentially treated as The value is a measure of lour well the equation balances The HP 32SII has two keys for evaluating equations a
85. x values Sx Sv OX OF Sample standard deviation population standard deviation Dx v xe ve ey Statistical data summations DEC Hx OC BH Base conversions decimal hexadecimal octal and binary Programming Instructions SF CF FS Functions to set clear and test flags S gt lt 25 Comparison tests of the X and Y registers S gt lt 2 Comparison tests of the X register and zero Getting Started 1 5 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 2 HP 32II Menus continued Menu Description Chapter The following example shows you how to use a menu function Example Other functions nnn n WAR POR Memory status bytes of memory available catalog of variables catalog of programs program labels UL REDO GR a o Angular modes and or radix decimal point convention Fe SC EH ALL Fix scientific engineering and ALL display formats Functions to clear different portions of memory refer to EX in the table on page 1 4 How many permutations n different arrangements are possible from 28 items taken four r at a time Keys Display 28 4 4 Wed PROB Cnr Pror SOR Fnr N 491 408 HHHH Displays r menu Description Displays the probability Displays the result Repeat the example for 28 items taken 2 at a time Result2756 Menus help you execute dozens of functions by guiding you to them with menu choices
86. you ve removed the batteries replace them within 2 minutes to avoid losing stored information Have the new batteries readily at hand before you open the battery compartment Use any brand of fresh I E C LR44 or manufacturer s equivalent button cell batteries Equivalent 1 5 volt button cell batteries you might find from various manufacturers are LR44 A76 V13GA KA76 357 SP357 V357 and SRAAW 1 Have three fresh button cell batteries at hand Avoid touching the battery terminals handle batteries only by their edges 2 Make sure the calculator is OFF Do not press ON again until the entire battery changing procedure is completed If the calculator is ON when the batteries are removed the contents of Continuous Memory will be erased 3 Remove the battery compartment door by pressing down and outward on it until the door slides off left illustration A 3 picture 4 Turn the calculator over and shake the batteries out Warning Do not mutilate puncture or dispose of batteries in fire The batteries can burst or explode releasing hazardous chemicals d 5 Insert the new batteries right illustration Stack them according to the diagram inside the battery compartment 6 Replace the battery compartment door slide the tab on the door back into the slot in the calculator case Support Batteries and Service A 3 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Testing Calcu
87. 0 13 Q The calculator has displayed the message MEMORY FULL What should do A You must clear a portion of memory before proceeding See appendix B Q Why does calculating the sine or tangent of x radians display a very small number instead of O A n cannot be represented exactly with the 12 digit precision of the calculator Q Why do get incorrect answers when use the trigonometric functions A You must make sure the calculator is using the correct angular mode EX DG RD or GR Q What does the symbol in the display mean A This is an annuncidor and it indicates something about the status of the calculator See Annunciators in chapter 1 Q Numbers show up as fractions How do get decimal numbers A Press EN FDISP Environmental Limits To maintain product reliability observe the following temperature and humidity limits B Operating temperature O to 45 C 32 to 113 F WI Storage temperature 20 to 65 C 4 to 149 F E Operating and storage humidity 90 relative humidity at 40 C 104 F maximum A 2 Support Batteries and Service File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Changing the Batteries Replace the batteries as soon as possible when the low battery annunciator 3 appears If the battery annunciator is on and the display dims you may lose data If data is lost the MEMORY CLEAR message is displayed Once
88. 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm E 14 15 16 17 The Indirect Address i eee 13 21 Program Control with 1 asinis de pee van UD Sa sup tutus 1 3 22 EQUGIIONS WIN Ul EE E D 13 24 Solving and Integrating Programs S ng a Progra essan ENEA 14 1 Using SOLVE im PFOGEFOfB diede Eon s E 14 5 miegrating a Program me aE EA A 14 7 Using Integration in a Program sss 14 9 Restrictions o Solving and Integrating 14 10 Mathematics Programs VECIOM loin c tenes 15 1 Solutions of Simultaneous Equations 15 12 Polynomial Root Finder sseee 15 20 Coordinate Transformations 0ccccsseeceeeeeceeeeeeeeeeees 15 31 Statistics Programs auci UU 16 1 Normal and Inverse Normal Distributions 16 11 Grouped Standard Deviation cccccceccceseeceeeeeeeeees 16 18 Miscellaneous Programs and Equations Time Value of Money essesem 17 Prime Number Generator cee eere 17 6 Contents 9 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Part 3 Appendixes and Regerence A Support Batteries and Service CGICUIGION SUD DOM reinir EnA E NEA A 1 Answers to Common Questions ceeceeeeeeeeeeee een ees A Environmental BImillsca queen ER edv a Nvidia esed esee A 2 Changing the Batteries cccccececc
89. 1 Reenter the incorrect data but instead of pressing press EXI L2 This deletes the value s and decrements n 2 Enter the correct value s using If the incorrect values were the ones just entered press EX to retrieve them then press EX to delete them The incorrect y value was still in the Y register and its T value was saved in the LAST X register Example Key in the x y values on the left these make the corrections shown on the right Initial x y Corrected x y 20 4 20 5 400 6 40 6 Keys Display Description al Clears existing statistical data 4 20 i PAGG Enters the first new data pair 6 400 2 6888 Display shows n the number of data pairs yon entered Ex 466 6886 Brings back last x value Last y is still in Y register Press twice to check y Ex 1 8888 Deletes the last data pair 6 40 2 8888 Reenters the last data pair Statistical Operations 11 3 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 4 20 EX i BAGA Deletes the first data pair 5 20 2 8888 Reenters the first data pair There is still a total of two data pairs in the statistics registers Statistical Calculations Once you have entered your data you can use the functions in the statistics menus Statistics Menus The linear regression menu linear estimation x and curve fitting r m B See Linear Regression later in this chapter Th
90. 12 25 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i Pld ENTER FAS EHTEER 5 PHE 25 Pay x 2 PHS 2 Pag Pill x Fil x Piz x F Fiz ETH al PGM LEL P 812 5 Ex CK 7FB4 819 5 Now evaluate this polynomial x 7 Keys Display P A value 7 R S 12 691 0606 5x 5x 2 5x 2 x 5x 2 5x 2 x3 Displays label P which takes 19 5 bytes Checksum and length Cancels program entry Description Prompts for x Result A more general form of this program for any equation Ax B x C x D x E would be F i LBL F Pae IHPUT PHS IHPUT PH4 ITHPUT PHO IHPUT Fide IHPLT PHY IHPUT PHS EHTEER PHS EHTEE M Of D 12 26 Simple Programming File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Pil EHTEE Fii ECL A Pie RCL E Pils x Pid ROL C Pils x Pie RCL D Pir x Pis RCL E FiS RTH Checksum and length E93F 028 5 Simple Programming 12 27 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 13 Programming Techniques Chapter 12 covered the basics of programming This chapter explores more sophisticated but useful techniques m Using subroutines to simplify programs by separating and labeling portions of the program that are dedicated to particular tasks The use of subroutines also shortens a program that must perform a series of steps more than once WI U
91. 24 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i HET variable A DSE instruction is like a FOR NEXT loop with a negative increment After pressing a shifted key for ISG or DSE EX or Wea you will be prompted for a variable that will contain the loop control number described below The Loop Control Number The specified variable should contain a loop control number ccccccc fHii where WI ccccccc is the current counter value 1 to 12 digits This value changes with loop execution W fff is the final counter value must be three digits This value does not change as the loop runs E ii is the interval for incrementing and decrementing must be two digits or unspecified This value does not change An unspecified value for ii is assumed to be O1 increment decrement by 1 Given the loop control number ccccccc fffii DSE decrements cccccce to ccccccc ii compares the new ccccccc with fff and makes program execution skip the next program line if this ccccccc x fff Given the loop control number ccccccc fffii ISG increments ccccccc to ccccccc ii compares the new cccccccc with fff and makes program execution skip the next program line if this ccccccc gt fff 13 18 Programming Techniques File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm D MHB8i LEL H IF current value gt final value continue loop IF current value lt final value continue loop
92. 2sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm SUMMAN SIONS NCS ere inan i E 11 11 The Statistics Registers in Calculator Memory 11 12 Access to the Statistics Registers cccccsseceeeneeees 11 13 Part 2 Programming 12 Simple Programming Designing a PrOGEFCIITI wseassarccs ido atn te PO T ae maedesneasanuesense 12 2 Program Boundaries LBL and RTN 12 3 Using RPN and Equations in Programs 12 4 Data Input and Output ssesesseeeee 12 4 E MISTING Gi dorso tt MEE OO TET 12 5 Keys That Clear 12 6 Function Names in Programs essen 12 7 RUN MING E Bererelrel RE EE OO OO 12 8 Executing a Program XEQ sss 12 9 lesing a Prograde e T T 12 9 Entering and Displaying Data ssseeeeeeees 12 11 Using INPUT for Entering Data sss 12 11 Using VIEW for Displaying Data 12 14 Using Equations to Display Messages 12 14 Displaying Information without Stopping 12 17 Stopping or Interrupting a Program ssessesse 12 18 Programming a Stop or Pause STOP PSE 12 18 Interrupting a Running Program ssssssse 12 18 Eid Aas OP NM 12 18 Eding role ro EET D E T 12 19 Contents 7 m File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 2
93. 3 4 24 Size 17 7 x 25 2 cm Service Agreements In the U S a support agreement is available for repair and service Refer to the form that was packaged with the manual For additional information contact the Calculator Service Center see the inside of the back cover Regulatory Information U S A The HP 32SIl generates and uses radio frequency energy and may interfere with radio and television reception The calculator complies with the limits for a Class B computing device as specified in Subpart J of Part 15 of FCC Rules which provide reasonable protection against such interference in a residential installation In the unlikely event that there is interference to radio or television reception which can be determined by turning the calculator off and on or by removing the batteries try mM Reorienting the receiving antenna B Relocating the calculator with respect to the receiver For more information consult your dealer an experienced radio or television technician or the following booklet prepared by the Federal Corrnunications Commission How to Identify and Resolve Radio TV Interference Problems This booklet is available from the U S Government Printing Office Washington D C 20402 Stock Number 004 000 00345 4 At the first printing of this manual the telephone number was 202 783 3238 West Germany The HP 32SIl complies with VFG 1046 84 VDE 0871B and similar non interference standards If you use
94. 4 SOLVECiO Solves for appropriate variable Las VIEWS i gt Displays solution La RTH Ends program Checksum and length E159 009 0 Fai LBL F Calculates f x y Include INPUT or equation prompting as required F16 RTN 14 6 Solving and Integrating Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Integrating a Program In chapter 8 you saw how you can enter an equation or expression it s added to the list of equations and then integrate it with respect to any variable You can also enter a program that calculates a function and then integrate it with respect to any variable This is especially useful if the function you re integrating changes for certain conditions or if it requires repeated calculations To integrate a programmed function 1 Enter a program that defines the integrand s function See To write a program for FN below 2 Select the program that defines the function to integrate press P label You can skip this step if you re reintegrating the same program 3 Enter the limits of integration key in the lower limit and press then key in the upper limit 4 Select the variable of integration and start the calculation press fs SOLVE variable Notice that FN is required if you re integrating a programmed function but riot if you re integrating an equation from the equation list You can halt a running integration calculation by pressing or
95. 4 Size 17 7 x 25 2 cm If a number entered in decimal base is outside the range given above then it produces the message TOO BIG in the other base modes Any operation using TOO BIG causes an overflow condition which substitutes the largest positive or negative number possible for the too big number Windows for Long Binary Numbers The longest binary number can have 36 digits three times as many digits as fit in the display Each 12 digit display of a long number is called a window 36 bit number 111111111111 BHinmnaanmnmimmgaii11111111111 Re Highest window Lowest window displayed When a binary number is larger than the 12 digits the or gt annunciator or both appears indicating in which direction the additional digits lie Press the indicated key or to view the obscured window 10 7B Picture SHOWing Partially Hidden Numbers The fz and EX functions work with non decimal numbers as they do with decimal numbers However if the Bali octal or binary number does not fit in the display the leftmost digits are replaced with an ellipsis 10 6 Base Conversions and Arithmetic File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm E Press za to view the digits obscured by the A or A label Keys Display Ez oc 23456712345 123456712345 A 123456712345 Wes A A 456712345 Wes hold 123456712245 Description Enters a large oc
96. 5 13 16 memory usage 1222 B2 messages in 12 15 1 2 18 moving through 12 11 not stopping 12 18 numbers in 12 6 pausing 12 19 prompting for data 12 12 purpose 12 1 resuming 1 2 15 return at end 12 4 routines 13 RPN operations 12 4 running 12 10 1222 showing long number 12 6 stepping through 12 10 stopping 12 14 12 16 12 19 techniques 13 1 testing 12 10 using integration 14 9 File name 32sii Manual E 0424 Printed Date 2003 4 24 using SOLVE 14 5 variables in 12 12 1 4 1 14 7 prompts attect stack 6 16 12 13 clearing 1 3 6 16 12 14 equations 6 15 INPUT 12 12 12 14 14 2 14 8 programmed equations 13 10 14 2 14 8 responding to 6 15 12 14 showing hidden digits 6 16 12 14 PSE pausing programs 12 12 12 19 14 9 preventing program stops 12 18 3 10 Q quadratic equations 15 22 questions R RV and R 2 3 radians angle units 4 3 A 2 converting to degrees 4 1 1 radix mark 1 16 A 1 random numbers 4 13 B 5 RCL 32 12 13 RCL arithmetic 3 6 B 8 real numbers integration with 8 1 operations 4 1 SOLVE with 14 2 Index 11 Size 17 7 x 25 2 cm real part complex numbers 9 1 9 2 recall arithmetic 3 6 B 8 rectangular to polar coordinate conversion 4 8 9 6 15 1 regression linear 11 8 16 1 repair service A resetting the calculator A 4 B 3 return program See programs Reverse Polish Notation See RPN rolling th
97. 5 2 cm i 13 8 Program MenO EE T o o and 12 20 Viewing Program Memory csccsececceeeeeeeeeeeees 12 20 Memory USGOe sosutescvue suia deti CUR eta Suv bison E YS F UEM 12 20 The Catalog of Programs MEM 12 21 Clearing One or More Programs ssesess 12 22 The C heekSUITiescnias Suae eb Pala sueta Rd ex tdbatid etate 12 22 Nonprogrammable Functions cccscccceeesceeneeeeeeeeees 12 23 Programming with BASE sessssseeeee 12 23 Selecting a Base Mode in a Program 12 24 Numbers Entered in Program Lines 12 24 Polynomial Expressions and Horner s Method 12 25 Programming Techniques ROUTINES Tho PrOGFOETIS eiecit ra Paese e A 13 1 Calling Subroutines XEQ RTN 13 2 Nested Subroutines esses 13 3 Branening CIO CES 13 5 A Programmed GIO Instruction sese 13 5 Using GTO from the Keyboard 13 6 Conditional Instructions cccccccceseccceseeeeeeeeeeaeeeeeaeees 13 7 Tests of Comparison x y XPO 13 8 Mec RE 13 9 LOODS eee ERU eee eee E meee eae ere 13 16 Conditional Loops GTO seeeeeeeees 13 16 Loops With Counters DSE ISG 13 17 Indirectly Addressing Variables and Labels 13 20 The Variable PET 13 20 Contents File name 32sii Manual E
98. 5 5 1 88808 Enters the first time 9 25 10 12 5 Enters the remaining data six 12 8 5 E BHAG data points entered 3 S 2 5888 Calculates the standard deviation time 11 6 Statistical Operations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Population Standard Deviation Population standard deviation is a measure of how dispersed the data values are about the mean Population standard deviation assumes the data constitutes the complete set of data and is calculated using n as a divisor m Press Wea ox for the population standard deviation of the x values m Press Wea ov for the population standard deviation of the y values Example Population Standard Deviation Grandma Tinkle has four grown sons with heights of 170 173 174 and 180 cm Find the population standard deviation of their heights Keys Display Description Ez Clears the statistics registers 170 173 174 Enters data 180 2 B88 Lol ox 4 8606 Four data points accumulated 3 5215 Calculates the population standard deviation Linear regression Linear regression L R also called linear estimation is a statistical method for finding a straight line that best fits a set of x y data Note To avoid a STAT ERROR message enter your data before u executing any of the functions in the L R menu Statistical Operations 11 7 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25
99. 5 6 Tr Gabe Then multiplies the intermediate answers together for the final answer Exercises Calculate 16 3805x5 WA 181 0000 0 05 Solution 16 3805 5 05 Calculate JI 2 3 x 4 5 J 6 7 x 84 9 2 21 5743 Solution 2 ENTER 3 4 4 ENTER 5 x L 6 ENTER 7 8 ENTER 9 Calculate 10 5 17 12 x 4 0 2500 Solution 17 ENTER 12 O 4 x 10 ENTER 5 Gy amp Or 10 ENTER 5 7 17 ENTER 12 h 4 x x 2 14 The Automatic Memory Stack File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Order of Calculation We recommend solving chain calculations by working from the innermost parentheses outward However you can also choose to work problems in a left to right order For example you have already calculated 4 14 7 x 3 2 by starting with the innermost parentheses 7 x 3 and working outward just as you would with pencil and paper The keystrokes were 7 3 142 2 214 EI It you work the problem from left to right press 4 ENTER 14 ENTER 7 ENTER 3 x O 2 o EJ This method takes one additional keystroke Notice that the first intermediate result is still the innermost parentheses 7 x 3 The advantage to working a problem left to right is that you don t have to use lo reposition operands for nomcommutaiive functions L and LE However the first method starting with the innermost parentheses is o
100. 6 Programming Techniques File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Conditional Instructions Another way to alter the sequence of program execution is by a conditional test a true false test that compares two numbers and skips the next program instruction if the proposition is false For instance if a conditional instruction on line AO5 is x that is is x equal to zero then the program compares the contents of the X register with zero If the X register does contain zero then the program goes on to the next line If the X register does nof contain zero then the program skips the next line thereby branching to line AO7 This rule is commonly known as Do if true AHi LEL A Do next if true ABS x u gt Skip next if false O e AGE GTOB Hay LH Has STOA O gt Bi LELE The above example points out a common technique used with conditional tests the line immediately after the test which is only executed in the true case is a branch to another label So the net effect of the test is to branch to a different routine under certain circumstances There are three categories of conditional instructions B Comparison tests These compare the X and Y registers or the X register and zero m Flag tests These check the status of flags which can be either set or clear WB loop counters These are usually used to loop a specified number of times Programming Techn
101. 9 5 1 5 3 setting maxim urn 5 5 digit entry cursor backspacing 1 3 6 9 12 7 in equations 6 6 in programs 2 7 meaning 1 12 discontinuities of functions C 6 display adjusting contrast 1 1 annunciators 1 8 function names in 4 15 X register shown 22 display format affects integration 8 2 8 6 8 8 affects numbers 1 16 affects rounding 4 15 default B 5 periods and commas in 1 16 A 1 setting 1 16 A 1 DISP menu 1 16 do if true 13 6 14 6 dot product 15 1 DSE 13 16 LE exponent 1 12 E in numbers 1 11 1 17 A 1 ENG format 1 17 See also display format ENTER clearing stack 2 6 copying viewed variable 12 15 Index 4 File name 32sii Manual E 0424 Printed Date 2003 4 24 duplicating numbers 2 6 ending equations 6 5 6 9 6 10 126 evaluating equations 6 12 6 13 separating numbers 1 13 1 15 2 6 stack operation 2 6 EQN annunciator in equation list 6 5 6 8 in Program mode 12 6 EQN LIST TOP 6 8 E 2 equality equations 6 11 6 12 7 1 equation entry cursor backspacing 1 3 6 9 12 21 operation 6 6 equation list adding to 6 5 displaying 6 8 editing 6 10 EQN annunciator 6 5 in Equation mode 6 4 operation summary 6 4 Equation mode backspacing 1 3 6 9 during program entry 12 6 leaving 1 3 6 4 shows equation list 6 4 starting 6 4 6 8 equations and fractions 5 10 as applications 17 1 base mode 6 6 6 13 12 25 checksums 6 21 12 7 1224 B2 compar
102. Checksum and length 0019 003 0 H amp 1 LBL H Starts routine to display two real roots or two roots Haz RCL F Gets the first real root Has STO x Stores the first real root Had VIEW Displays real root or real part of complex root HES RCL G Gets the second real root or imaginary part of complex root HAE FS G Were there any complex roots Ha GTO U Displays complex roots if any Has STO x Stores second real root Hao VIEW amp Displays second real root Hig RTH Returns to calling routine Checksum and length BE87 015 0 Wai LEL U Starts routine to display complex roots Uae STO i Stores the imaginary part of the first complex root Was VIEW i Displays the imaginary part of the first complex root Liga VIEW Displays the real part of the second complex root Was RCL i Gets the imaginary part of the complex roots Uae 7 Generates the imaginary part of the second complex root Ue STO i Stores the imaginary part of the second complex root Was VIEW i Displays the imaginary part of the second complex root Checksum and length OEE4 012 0 Mathematics Programs 15 27 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i Flags Used Flag O is used to remember if the root is real or complex that is to remember the sign of d If d is negative then flag O is set Flag O is tested later in the program to assure that both the real and imaginary parts are displayed if necessary Memor
103. EX memory function provides information about memory nnn n VAR FGM where nnn n is the number of bytes of available memory Pressing the AR menu key displays the catalog of variables Pressing the FGM menu key displays the catalog of programs To review the values at any or all non zero variables 1 Press EX VAR 2 Press EX or EX to move the list and display the desired variable Note the W A annunciator indicating that the left shifted and keys are active If Fraction display mode is active WA does not indicate accuracy To see all the significant digits of a number displayed in the VRR catalog press fea SHOW If it is a binary number with more than 12 digits use the and keys to see the rest 3 To copy a displayed variable from the catalog to the X register press ENTER 4 To clear a variable to zero press EX while it is displayed in the catalog 5 Press to cancel the catalog Clearing Variables Variables values are retained by Continuous Memory until you replace there or clear them Clearing a variable stores a zero there a value of zero takes no memory To clear a single variable Storing Data into Variables 3 3 File name 32sii Manual E O424 Printed Date 2003 4 24 Size 177 x 25 2 cm Store zero in it Press O variable To clear selected variables 1 Press EN VAR and use EX or EX to display the variable 2 Press EH CLEAR 3 Press LC to cancel the catalo
104. Functions for One Complex Number z Change sign z EV CMPLX Inverse 1 z EN CMPLX Natural log In z EM CMPLX Natural antilog e7 E Sin z E Cos z E Tan z E Operations with Comb Numbers 9 3 File name 32sii Manual E O424 Printed Date 2003 4 24 Size 177 x 25 2 cm To do an arithmetic operation with two complex numbers 1 Enter the first complex number z1 composed of x1 i y1 by keying in y1 x ENTER For Z 2 key in the base part z1 first 2 Enter the second complex number z2 by keying in y2 x2 For Z 2 key in the exponent z2 second 3 Select the arithmetic operation Arithmetic With Two Complex Numbers z and zz Addition z 1 z2 Ea Subtraction z z2 Ez Multiplication z1 x z2 EN CMPLX Division z 14 Z2 Ex CMPLX LE Power function Z4 aw CMPLX Examples Here are some examples of trigonometry and arithmetic with complex numbers Evaluate sin 2 i 3 Keys Display Description 3 2 Real part of result EX 3 1545 4 1689 Result is 9 1545 i 4 1689 Evaluate the expression z 1 z24z3 where z1 23 i 13 z2 2 i z2 4 i3 Since the stack can retain only two complex numbers at a time perform the calculation as 9 4 Operations with Comb Numbers File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm z x 1 z2 z3 Keys Display Description 1 ENTER 2 A ENTER Add z2 z3 displays rea
105. HP 32SIl RPN Scientific Calculator Owner s Manual G HEWLETT PACKARD HP Part No 00032 90068 Printed in Singapore Edition 5 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Notice This manual and any examples contained herein are provided as is and are subject to change without notice Hewlett Packard Company makes no warranty of any kind with regard to this manual including but not limited to the implied warranties of merchantability and fitness for a particular purpose Hewlett Packard Co shall not be liable for any errors or for incidental or consequential damages in connection with the furnishing performance or use of this manual or the examples contained herein Hewlett Packard Co 1990 1991 1992 1993 All rights reserved Reproduction adaptation or translation of this manual is prohibited without prior written permission of Hewlett Packard Company except as allowed under the copyright laws The programs that control your calculator are copyrighted and all rights are reserved Reproduction adaptation or translation of those programs without prior written permission of Hewlett Packard Co is also prohibited Hewlett Packard Company Corvallis Division 1000 N E Circle Blvd Corvallis OR 97330 U S A Printing History Edition 1 November 1990 Edition 2 March 1991 Edition 3 June 1992 Edition 4 April 1993 Edition 5 November 1994 File name 32sii Manual E 0424 Pri
106. HPLE File name 32sii Manual E 0424 Printed Date 2003 4 24 This routine converts from the new system to the old system Prompts for and stores U Prompts for and stores V Pushes V up and recalls U Pushes U and V up and recalls T Sets radius to 1 for the computation of sin T and cos T Calculates cos T and sin T Calculates U cos T V sin T and U sin T V cos T Pushes up previous results and recalls N Pushes up results and recalls M Completes calculation by adding M and N to previous results 15 34 Mathematics Programs Size 177 x 25 2 cm Program Lines Description O12 STO W Stores the x coordinate in variable X 013 siy Swaps the positions of the coordinates 014 STO v Stores the y coordinate in variable Y 015 x wv Swaps the positions of the coordinates back 016 VIEW X Halts the program to display X O17 VIEW Y Halts the program to display Y o1i8GToo Goes back for another calculation Checksum and length 7C14 027 0 Flags Used None Memory Required 119 bytes 63 for program 56 for variables Program Instructions 9 Key in the program routines press when done Press D to start the prompt sequence which defines the coordinate transformation Key in the x coordinate of the origin of the new system M and press R S Key in the y coordinate of the origin of the new system N and press Key in the rotation angle T and press R S To translate from the old system
107. I265 I2r STU I Iles ECL E 129 RCLx I I8 ECL F I1 RCL x H lsc I 3 3 STU H I4 ECL C I 35 RCL x H I5 ECL B Taf RCLx I lsc 139 ECL B I4 RCL F I41 ECL C Ide RCLx E I4 I44 STU LC I45 RV I45 STU EB I4 RCL F I42 RCLx G I43 ECL O L28 RCLx I I51 File name 32sii Manual E 0424 Printed Date 2003 4 24 Description Calculates H x determinant BG AH Calculates x determinant AE BD Calculates A x determinant El FH Calculates B x determinant CH Bl Calculates C x determinant BF CE Stores B Calculates D x determinant FG DI 15 14 Mathematics Programs Size 177 x 25 2 cm Program Lines I52 RCL O a3 RCL x H I54 ECL E aa RCLx G a6 I5r STOG I58 RV 129 STU L I5H RCL i I51 SIU I I52 RCL amp les STU E I543 RCL amp lea STOF lee RCL Z ler STU H I523 169 STU Ir RCL H Description Calculates G x determinant DH EG Stores D Stores I Stores E Stores F Stores H Sets index value to point to last element of matrix Recalls value of determinant Checksum and length 4C14 105 0 Jai LBL J Jaz S7T0 13 Tas DSE J 4 670 J TES RTH This routine completes inverse by dividing by determinant Divides element Decrements index value so it points closer to A Loops for next value Returns to the calling program or to PRGM TOP Checksum and length 9737 007 5 Mi LEL M Haz r Fil
108. J E LBL H J1 Wed EQN RCL P x RCL V Fea RCL N X RCL R X RCL T ENTER Wea RIN PEGM TOP H i LEL H r3 SF H 2 SF ii Hes PxVMzHxEXx Hid ETH H Hele Description Selects Program entry mode Moves program pointer to top of the list of programs Labels the program Enables equation prompting Evaluates the equation clearing flag 11 Checksum and length 13E3 015 0 Ends the program Cancels Program entry mode Checksum and length of program 8AD6 19 5 14 4 Solving and Integrating Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm Now calculate the change in pressure of the carbon dioxide if its temperature drops by 10 C from the previous example Keys Display Description L 4 618 Stores previous pressure r3 H A BELG Enters the limits of integration lower limit first ra P We 006G Selects variable P prompts for V H76 005G Retains 2 in V prompts for N k76 BEZI Retains 005 in N prompts for R T7297 1466 Retains 0821 in R prompts for T 10 k T 287 1G888 Calculates new T SOLVING Stores 287 1 in T solves for new P F H H3239 L 6 6821 Calculates pressure change of the gas when temperature drops from 297 1 K to 287 1 K negative result indicates drop in pressure Using SOLVE in Program You can use the SOLVE operation as part of a program If appropriate include or prompt for initial guesses
109. Operation Index F 5 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm u CMPLXSIN CMPLXTAN CMPLXy COS COSH DEC DEG DEG E DSE variable Keys and Description ER Complex sine Returns sin Zy i Zy E Complex tangent Returns tan zx i Zy E CMPLX Complex power z2 IZoy Returns Z IZ E PROB En r Combinations of n items taken rata time Returns n r n r Cosine Returns cos x Ex Hyperbolic cosine Returns cosh x E BASE DEC Selects Decimal mode Ex ps Selects Degrees angular mode ER Radians to degrees Returns 360 2nm x Displays menu to set the display format EX variable Decrement Skip if Equal or less For control number ccccccc fffii stored in a variable subtracts ii increment value from ccccccc counter value and if the result fff final value skips the next program line Be gins entry of exponents and adds E to the number being entered Indicates that a power of 10 follows EN ISP EN n Selects Engineering display with n F 6 Operation Index File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm u ENTER ex EXP F EJ EDISP FIX n Wea FLAGS FN label File name 32sii Manual E 0424 Printed Date 2003 4 24 Keys and Description digits following the first digit n O through 11
110. P2 and P3 which are currently in the X Y system to points in the X Y system Convert point P 4 which is lid the X Y system to the X Y system 15 36 Mathematics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm y P 6 8 P 79 7 e P 2 7 3 6 M N 7 4 T 27 Keys Display Description Ez OG Sets Degrees mode since Tis given in degrees D H7 value Starts the routine that defines the transformation H value Store 7 in M 4 T value Store 4 in N 27 M T BBaBBB Stores 27 in T N 37 value Starts the old to new routine Mathematics Programs 15 37 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i 9 1 value 7 U 9 2622 W 17 8649 47 9 BAGA 5 177 BAGA 4 CZ R S U 18 6921 W 5 4479 47 5 00A 6 17 4 088 8 U 4 5569 W 11 1461 O U 4 5569 2 7 R S W 11 1461 3 6 EZ R S 4 i1 8481 2 5 9818 15 38 Mathematics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Stores 9 in X Stores 7 in Y and calculates U Calculates V Resumes the old to new routine for next problem Stores 5 in X Stores 4 in Y Calculates V Resumes the old to new routine for next problem Stores 6 in X Stores 8 in Y and calculates U Calculates V Starts the new to old routine Stores 2 7 in U Stores 3 6 in Vand calculates X Calculates Y Size 177 x 25 2 cm 16 Sta
111. PUT instruction looks like this H amp 81 LEL A ARZ IHFUT F ABS xe Abd r ABS x Abe ETH To use the INPUT function in a program 1 Decide which data values you will need and assign them names In the area of a circle example the only input needed is the radius which we can assign to R 2 In the beginning of the program insert an INPUT instruction for each variable whose value you will need Later in the program when you write the part of the calculation that needs a given value insert a variable instruction to bring that value back into the stack Since the INPUT instruction also leaves the value you just entered in the X register you don t have to recall the variable at a later time you could INPUT it and use it when you need it You might be able to save some memory space this way However in a long program it is simpler to just input all your data up front and then recall individual variables as you need them Remember also that the user of the program can do calculations while the program is stopped waiting for input This can alter the contents of the stack which might affect the next calculation to be done by the program 12 12 Simple Programming File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Thus the program should not assume that the X Y and Z registers contents will be the same before and after the INPUT instruction If you collect all the data in the beginning
112. Printed Date 2003 4 24 Size 17 7 x 25 2 cm S u Part 3 Appendixes and Reference File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Support Batteries and Service Calculator Support You can obtain answers to questions about using your calculator from our Calculator Support Department Our experience shows that many customers have similar questions about our products so we have provided the following section Answers to Common Questions If you don t find an answer to your question contact us at the address or phone number listed on the inside back cover Answers to Common Questions Q How can determine if the calculator is operating properly A Refer to page A 5 which describes the diagnostic self test Q My numbers contain commas instead of periods as decimal points How do restore the periods A Use the EX function page 1 14 Q How do change the number of decimal places in the display A Use the EX menu page 1 15 Q How do 1 clear all or portions of memory A EX displays the CLEAR menu which allows you to clear all variables all programs in program entry only the statistics registers or all of user memory not during program entry Q What does an E in a number for example 2 51E 1 mean Support Batteries and Service A 1 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm A Exponent of ten that is 2 51 x 1
113. Programming 12 13 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i Using VIEW for Displaying Data The programmed VIEW instruction Fs variable stops a running program and displays and identifies the contents of the given variable such as H 8 53398 This is a display only and does not copy the number to the X register If Fraction display mode is active the value is displayed as a fraction m Pressing copies this number to the X register W f the number is wider than 10 characters pressing Wea displays the entire number If it is a binary number with more than 12 digits use the and keys to see the rest m Pressing or erases the VIEW display and shows the X register E Pressing EX clears the contents of the displayed variable Press to continue the program If you don t want the program to stop see Displaying Information without Stopping below For example see the program for Normal and Inverse Normal Distributions in chapter 16 Lines T15 and T16 at the end of the T routine display the result for X Note also that this VIEW instruction in this program is preceded by a RCL instruction The RCL instruction is not necessary but it is convenient because it brings the VIEWed variable to the X register making it available for manual calculations Pressing while viewing a VIEW display would have the same effect The other application programs in chapters 15 through 17
114. R S However no information about the integration is available until the calculation finishes normally To resume the calculation press again Pressing while an integration calculation is running cancels the FN operation In this case you should start J FN again from the beginning To write a program for FN The program can use equations and RPN operations in whatever combination is most convenient 1 Begin the program with a label This label identifies the function that you want to integrate FH abel 2 Include an INPUT instruction for each variable including the variable of integration INPUT instructions enable you to integrate with respect to any variable in a multi variable function INPUT for the variable of integration Solving and Integrating Programs 14 7 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm a is ignored by the calculator so you need to write only one program that contains a separate INPUT instruction for every variable including the variable of integration If you include no INPUT instructions the program uses the values stored in the variables or entered at equation prompts 3 Enter the instructions to evaluate the function E A function programmed as a multi line RPN sequence must calculate the function values you want to integrate WI A function programmed as an equation is usually included as an expression specifying the integrand though it can be any
115. RFLOW is displayed briefly when the program eventually stops B Flag 6 is automatically set by the calculator any time an overflow occurs although you can also set flag 6 yourself It has no effect but can be Programming Techniques 13 9 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i tested Flags 5 and 6 allow you to control overflow conditions that occur during a program Setting flag 5 stops a program at the line just after the line that caused the overflow By testing flag 6 in a program you can alter the program s flow or change a result anytime an overflow occurs Flags 7 8 and 9 control the display of fractions Flag 7 can also be controlled from the keyboard When Fraction display mode is toggled on or off by pressing EX FDISP flag 7 is set or cleared as well Flag Fraction Control Flags Status Clear Fraction display Fraction Reduce Default off display real denominators fractions to numbers in the not greater than smallest form current display the c value format Set Fraction display Fraction No reduction of on display real denominators fractions Used numbers as are factors of only if flag 8 is fractions the c Value set Flag 10 controls program execution of equations When flag 10 is clear the default state equations in running programs are evaluated and the result put on the stack When flag 10 is set equations in running programs are display
116. RTN A subroutine is itself a routine and it can call other subroutines B XEQ must branch to a label LBL for the subroutine It cannot branch to a line number m Atthe very next RTN encountered program execution returns to the line after the originating XBQ For example routine Q in the Normal and Inverse Normal Distributions program in chapter 16 is a subroutine to calculate Q x that is called from routine D by line D3 EG amp Routine Q ends with a RTN instruction that sends program execution back to routine D to store and display the result at line DO4 See the flow diagrams below The flow diagrams in this chapter use this notation ABS GTO E gt O Program execution branches from this line to the line marked from 1 Bai LEL B 0 Program execution branches from a line marked gt to 1 to this line 13 2 Programming Techniques File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm DAi LEL D Starts here DAS IHPUT amp Da EG Q Q Calls subroutine Q Dama STO Q Q Return here OHS VIEH O46 GTO D Starts D again Ai LEL Q OD Starts subroutine 116 ETH Returns to routines D Nested Subroutines A subroutine can call another subroutine and that subroutine can call yet another subroutine This nesting of subroutines the calling of a subroutine within another subroutine is limited to a stack of subroutines seven levels
117. Separates two numbers keyed in sequentially completes equation entry evaluates the displayed equation and stores result if appropriate Copies x into the Y register lifts y into the Z register lifts z into the T register and loses t Activates or cancels toggles Equation entry mode Natural exponential Returns e raised to the x power Natural exponential Returns e raised to the specified power Fa Converts C to F Turn on and off Fraction display mode E OA F3 n Selects Fixed display with n decimal places Ox nx 11 Displays the menu to set clear and test flags ra label Selects labeled program as the current function used by SOLVE and J FN F PARTS FF Fractional part of x ra FS n If flag n n 1 through 11 is set executes the next program line if flag n is clear skips the next program line F Converts liters to gallons Operation Index F 7 Size 17 7 x 25 2 cm GRAD EN MODES GR Sets Grads angular mode GTO label EX label Sets the program pointer to the beginning of program label in program memory EX J Sets program pointer to line nn of label nn program label EX CJ CJ Sets program pointer to PRGM TOP HEX E Hx Selects Hexadecimal base 16 mode EX Displays the HYP_ prefix for hyperbolic functions HMS Ez Hours to hours minutes seconds Converts x from a decimal fraction to hours minutes seconds format
118. The Automatic Memory Stack File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 3 4 9 The stack drops its contents The T top register replicates its contents The stack lifts its contents The T register s contents are lost The stack drops JE gt Notice that when the stack lifts it replaces the contents of the T top register with the contents of the Z register and that the former contents of the T register are lost You can see therefore that the stack s memory is limited to four numbers E Because of the automatic movements of the stack you do not need to clear the X register before doing a new calculation Most functions prepare the stack to lift its contents when the next number enters the X register See appendix B for lists of functions that disable stack lift How ENTER Works You know that separates two numbers keyed in one after the other In terms of the stack how does it do this Suppose the stack is again filled with 1 2 3 and 4 Now enter and add two new numbers The Automatic Memory Stack 2 5 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 5 6 Lifts the stack Lifts the stack and replicates the X register Does not lift the stack D aa Drops the stack n replicate the T register replicates the contents of the X register into the Y register The next number you key in or recall writes over the copy of the first num
119. The Ideal Gas Law describes the relationship between pressure volume temperature and the amount moles of an ideal gas PxV NxRxT where P is pressure in atmospheres or N m2 Vis volume in liters N is the number of moles of gas R is the universal gas constant 0 0821 liter atm mole K or 8 314 J mole K and T is temperature Kelvins K C 273 1 Enter the equation Keys Display Description r3 P FH Selects Equation mode and starts the equation V fea N R T PxWuzHaxRETE PxuzHxRxT Terminates and displays the equation Wes CK 13E3 615 8 Checksum and length A 2 liter bottle contains 0 005 moles of carbon dioxide gas at 24 C Assuming that the gas behaves as an ideal gas calculate its pressure Since Equation mode is turned on and the desired equation is already in the display you can start solving for P Keys Display Description ra P value Solves for P prompts for V 2 H value Stores 2 in V prompts for N 005 E value Stores 005 in N prompts for R 082 T value Stores 0821 in R prompts for T 7 4 Solving Equations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 24 T 297 16888 Calculates T Kelvins 273 1 SOLV HG Stores 297 1 in T solves for P in P B B85618 atmospheres A 5 liter flask contains nitrogen gas The pressure is 0 05 atmospheres when the temperature is 18 C Calculate the density of the gas N x 28 V where 28 is the molecular wei
120. VE ACTIVE SOLVE C SOLVE 3 SOLWE FH File name 32sii Manual E 0424 Printed Date 2003 4 24 Attempted to refer to a nonexistent program label or line number with GTO GTO LJ KEQ or FH Note that the error HOHEXISTEWT can mean WB you explicitly from the keyboard called a program label that does not exist or E the program that you called referred to another label which does not exist The catalog of programs EX PGH indicates no program labels stored SOLVE cannot find the root of the equation using the current initial guesses see page C 8 A SOLVE operation executed in a program does not produce this error the same condition causes it instead to skip the next program line the line following the instruction SOLVE variable Warning displayed momentarily the magnitude of a result is too large for the calculator to handle The calculator returns 9 99999999999E499 in the current display format See Range of Numbers and Overflow on page 1 12 This condition sets flag 6 If flag 5 is set overflow has the added effect of halting a running program and leaving the message in the display until you press a key Indicates the top of program memory The memory scheme is circular so PRGM TOF is also the line after the last line in program memory The calculator is running a program other than a SOLVE or FN routine Attempted to execute SOLVE variable or J FH d variable without a
121. You can store a new seed with the SEED function executed by pressing 8D If memory is cleared the seed is reset to zero 4 12 Real Number Functions File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Example Combinations of People A company employing 14 women and 10 men is forming a six person safety committee How many different combinations of people are possible Keys Display Description 24 6 E Twenty four people grouped six at a time Wed PROB Cnr Pons SDR Probability menu E n E 134 596 8888 Total number of combinations possible It employees are chosen at random what is the probability that the committee will contain six women To find the probability of an event divide the number of combinations for that event by the total number of combinations Keys Display Description 14 6 6 Fourteen worriers grouped six at a time E PROB En 3 883 BOGE Number of combinations of six women on the committee 134 596 AAAA Brings total number of combinations back into the X register A A293 Divides combinations of women by total combinations to find probability that any one combination would have all warriors Real Number Functions 4 13 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Parts of Numbers The functions in the PARTS menu P PARTS shown in the following table and the EX function alter the number in the X reg
122. able name and its current value such as amp z 5006 6 14 Entering and Evaluating Equations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm To leave the number unchanged just press R S WB To change the number type the new number and press R S This new number writes over the old value in the X register You can enter a number as a fraction if you want If you need to calculate a number use normal keyboard calculations then press R S For example you can press 2 ENTER 5 R S Tocalculate with the displayed number press before typing another number Tocancel the prompt press LC The current value for the variable remains in the X register If you press during digit entry it clears the number to zero Press again to cancel the prompt M To display digits hidden by the prompt press fea SHOW Each prompt puts the variable value in the X register and disables stack lift If you type a number at the prompt it replaces the value in the X register When you press R S stack lift is enabled so the value is retained on the stack The Syntax of Equations Equations follow certain conventions that determine how they re evaluated E How operators interact What functions are valid in equations M How equations are checked for syntax errors Operator Precedence Operators in an equation are processed in a certain order that makes the evaluation logical and predictable
123. ags so that lines WOZ and W11 take the natural logarithms of both the X and Y inputs for a Power model curve Note that lines S03 S04 L04 and E03 clear flags O and 1 to ensure that they will be set only as required for the four curve models Program Lines Description sas CF Clears tlag O the indicator for In X Sa4 CF i Clears flag 1 the indicator for In Y Las SF 4 Sets flag O the indicator for In X La4 CF 1 Clears flag 1 the indicator for In Y Fa3 CF B Clears tlag O the indicator for In X Ea4 SF 1 Sets flag 1 the indicator for In Y Pas SF Sets flag O the indicator for In X Pad SF i Sets flag 1 the indicator for In Y Wa FS G If flag O is set War LH takes the natural log of the X input HiBFS 1 If flag 1 is set Wii LH takes the natural log of the Y input Programming Techniques 13 13 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Example Controlling the Fraction Display The following program lets you exercise the calculator s fraction display capability The program prompts for and uses your inputs for a fractional number and a denominator the c value The program also contains examples of how the three fraction display flags 7 8 and 9 and the message display flag 10 are used Messages in this program are listed a MESSAGE and are entered as equations 1 Set Equation entry mode by pressing F the EQN annunciator turns on 2 Pr
124. air charge for out of warranty service The Calculator Service Center listed on the inside of the back cover can tell you how much this charge is The full charge is subject to the customer s local sales or value added tax wherever applicable Calculator products damaged by accident or misuse are not covered by the fixed service charges In these cases charges are individually determined based on time and material Shipping Instructions If your calculator requires service ship it to the nearest authorized service center or collection point Be sure to mM Include your return address and description of the problem E Include proof of purchase date if the warranty has not expired B Include a purchase order check or credit card number plus expiration date Visa or MasterCard to cover the standard repair charge In the United States and some other countries the serviced calculator can be returned C O D if you do not pay in advance W Ship the calculator in adequate protective packaging to prevent damage Such damage is not covered by the warranty so we recommend that you insure the shipment B Pay the shipping charges for delivery to the Hewlett Packard service center whether or not the calculator is under warranty Warranty on Service Service is warranted against defects in materials and workmanship for 90 days from the date of service A 8 Support Batteries and Service File name 32sii Manual E 0424 Printed Date 200
125. alance of loan or savings account P The periodic payment F The future value of a savings account or balance of a loan Example Part 1 You are financing the purchase of a car with a 3 year 36 montld loan at 10 5 annual interest compounded monthly The purchase price of the car is 7 250 Your down payment is 1 500 B 7 250 1 500 I 10 5 per year N 36 months F 0 P Keys Display Description EX FX Selects FIX 2 display format 2 Wes EV Px188xci ci Displays the leftmost part of the as needed TVM equation P I value Selects P prompts for l 10 5 12 178 88 Converts your annual interest rate E input to the equivalent monthly rate H value Stores 0 88 in prompts for N 17 4 Miscellaneous Programs and Equations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm E 36 F value O Evalue 7250 B 5 758 08 1500 7 SULVIBC F 1 96 59 Stores 36 in N prompts for F Stores O in F prompts for D Calculates B the beginning loan balance Stores 5750 in B calculates monthly payment P The answer is negative since the loan has been viewed from the borrower s perspective Money received by the borrower the beginning balance is positive while money paid out is negative Part 2 What interest rate would reduce the monthly payment by 10 Keys ra E SOLVE E3 RND 10 4 Display PxlHBxcl cl c Pp 155 283 Pp 155 283 P 1 5
126. ams 15 21 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i Program Lines Description lar GTOCio Starts root finding routine Checksum and length CE86 010 5 Hai LBL H Evaluates polynomials using Horner s method and synthetically reduces the order of the polynomial using the root Haz ECL H H amp 3 STO i Uses pointer to polynomial as index Had 1 Starting value for Horner s method Checksum and length B85F 006 0 T81 LBL J Starts the Horner s method loop T82 ENTER Saves synthetic division coefficient J03 RCLx x Multiplies current sum by next power of x J64RCL i2 Adds new coefficient 345 OSE i Counts down the loop 66 GTO J Repeats until done Tar RTH Checksum and length 139C 010 5 S61 LEL S Starts solver setup routine Sez STOH Stores location of coefficients to use SH 25H sa4 STO First initial guess Sas 7 Second initial guess SA6 FH H Specifies routine to solve sa SOLVE X Solves for a real root S88 GTO H Gets synthetic division coefficients for next lower order polynomial 23H29 HH Sig Generates DIVIDE BY O error if no real root found Checksum and length 27C3 015 0 Gai LBL n Starts quadratic solution routine QAZ xtv Exchanges ag and aj 15 22 Mathematics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Program Lines nas 2 nod QAS 7 QAE ENTER QAF ENTER pag STOF QAG x 18 RA ALl
127. an set the maximum denominator that s used B You can select one of three fraction formats The next few topics show how to change the fraction display Setting the Maximum Denominator For any traction the denominator is selected based on a value stored in the calculator If you think of fractions as a b c then c corresponds to the value that controls the denominator The c value defines only the maximum denominator used in Fraction display mode the specific denominator that s used is determined by the fraction format discussed in the next topic B To set the c value press n Wed Uc where n is the maximum denominator you want n can t exceed 4095 This also turns on Fraction display mode m To recall the c value to the X register press 1 Wea Lc To restore the default value or 4095 press O fea Uc You also restore Fractions 5 5 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i the default if you use 4095 or greater This also turns on Fraction display mode The c function uses the absolute value of the integer part of the number in the X register It doesn t change the value in the LAST X register Choosing Fraction Format The calculator has three fraction formats Regardless of the formot the displayed fractions are always the closest fractions within the rules for that format E Most precise fractions Fractions have any denominator up to the c value and they
128. ances from the Earth to these stars into meters The Automatic Memory Stack 2 11 File name 32sii Manual E O424 Printed Date 2003 4 24 Size 177 x 25 2 cm To Rigel Centaurus 4 3 yr x 9 5 x 10 9 m yr To Sirius 8 7 yr x 9 5 x 10 9 m yr Keys Display Description 4 3 4 3808 Light years to Rigel Centaurus 9 5 E 15 9 5E15 Speed of light c 4 6858E616 Meters to R Centaurus 8 7 EX 9 5868615 Retrieves c 2 2658616 Meters to Sirius Chain Calculations The automatic lifting and dropping of the stack s contents let you retain intermediate results without storing or reentering them and without using parentheses Work from the Parentheses Out For example solve 12 3 x 7 It you were working out this problem on paper you would first calculate the intermediate result of 12 3 1243 2 15 then you would multiply the intermediate result by 7 15 x7 105 Solve the problem in the same way on the HP 32SIl starting inside the parentheses Keys Display Description 12 3 15 886868 Calculates the intermediate result first 2 12 The Automatic Memory Stack File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm E You don t need to press to save this intermediate result before proceeding since it is a calculated result it is saved automatically Keys Display Description 7 1m5 80888 Pressing the function key produces the answer This result can be used in fur
129. annunciators 13 11 solving 72 C1 clearing 13 11 stack usage 6 13 default states 13 8 B 5 storing variable value 6 13 equation evaluation 13 10 Index 5 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm equation prompting 13 10 traction display 5 6 13 9 meanings 13 8 operations 13 11 overflow 13 9 setting 13 1 lesting 13 8 13 11 unassigned 13 9 FLAGS menu 13 11 flow diagrams 132 J FN See integration FN in programs 14 5 14 9 integrating programs 14 solving programs 14 1 fractional part function 4 15 Fraction display mode affects rounding 5 9 affects VIEW 12 15 setting 1 20 5 1 A2 showing hidden digits 3 3 fractions accuracy indicator 5 2 5 3 and equations 5 10 and programs 5 10 12 15 base 10 only 52 calculating with 5 1 denominators 1 19 5 5 5 6 13 9 13 3 displaying 1 20 5 1 5 2 5 5 A 2 flags 5 6 13 9 formats 5 6 not statistics registers 5 2 reducing 5 3 5 6 rounding 5 9 round off 5 4 5 9 setting format 5 6 13 9 13 13 showing integer digits 3 3 5 5 Index 6 File name 32sii Manual E 0424 Printed Date 2003 4 24 typing 1 19 5 1 functions complex number 9 3 in equations 6 6 6 17 F 1 in programs 12 7 list of F 1 memory usage 1222 B2 names in display 4 15 127 nonprogrammable 12 24 one number 1 14 2 9 9 3 real number 4 1 two number 1 15 2 10 9 3 future balance finance 17 1 G gam
130. ant to enter a new equation that starts with a top row function such as LN To select an equation Display the equation in the equation list as described above The displayed equation is the one that s used for all equation operations Example Viewing an Equation View the last equation you entered Keys Display Description F3 R 2xeCxCOos T Displays the current equation in the equation list zxCxC stcT hR2 Shows two more characters to the 6 8 Entering and Evaluating Equations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm right 2xeCxCOS T A Shows one character to the left Leaves Equation mode Editing and Clearing Equations You can edit or clear an equation that you re typing You can also edit or clear equations saved in the equation list To edit an equation you re typing 1 Press repeatedly until you delete the unwanted number or function If you re typing a decimal number and the _ digit entry cursor is on deletes only the rightmost character If you delete all characters in the number the calculator switches back to the B equation entry cursor If the E equation entry cursor is on pressing deletes the entire rightmost number or function 2 Retype the rest of the equation 3 Press or L to save the equation in the equation list To edit a saved equation 1 Display the desired equation See Displaying and Selecting Equations above 2
131. ast setting To increase or decrease the contrast hold down the LC key and press L or E Highlights of the Keyboard an Display Shifted Keys Each key has three functions one printed on its face a left shifted function orange and a right shifted function blue The shifted function Getting Started 1 1 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 2 names are printed in orange and blue above each key Press the appropriate shift key EX or Kz3 before pressing the key for the desired function For example to turn the calculator off press and release the fa shift key then press LC Pressing E or fea turns on the corresponding Kal or Fd annunciator symbol at the top of the display The annunciator remains on until you press the next key To cancel a shift key and turn off its annunciator press the same shift key again Alpha Keys Shifted x Menu name function lt Letter for alphabetic key Most keys have a letter written next to them as shown above Whenever you need to type a letter for example a variable or a program label the A Zannunciator appears in the display indicating that the alpha keys are active Variables are covered in chapter 3 labels are covered in chapter 6 Backspacing and Clearing One of the first things you need to know is how to clear how to correct numbers clear the display or start over 1 2 Getting Started File
132. ation about changing the number base Fractions in the Display In Fraction display mode numbers are evaluated internally as decimal numbers then they re displayed using the most precise fractions allowed In addition accuracy annunciators show the direction of any inaccuracy of the fraction compared to its 12 digit decimal value Most statistics registers are exceptions they re always shown as decimal numbers Display Rules The fraction you see may differ from the one you enter In its default condition the calculator displays a fractional number according to the following rules To change the rules see Changing the Fraction Display later in this chapter W The number has an integer part and if necessary a proper fraction the numerator is less than the denominator 5 2 Fractions File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm u B The denominator is no greater than 4095 mM The fraction is reduced as far as possible Examples These are examples of entered values and the resulting displays For comparison the internal 12 digit values are also shown The A and V annunciators in the last column are explained below Entered Value Internal Value Displayed Fraction 2 3 8 2 3 500000000 14 15 32 14 4687500000 24 12 4 50000000000 4 i172 6 18 5 9 60000000000 a 3 5 34 12 2 83333333333 w2 5 6 15 8192 183105468750 AB 7 3823 12345678 12345 3 Illegal entry A 16 3 16384 Illegal e
133. ations in Equation and Program modes T PROB SD Restarts the random number sequence with the seed x ER SF n Sets flag n n O through 11 Shows the full mantissa all 12 digits of x or the number in the current program line displays hex checksum and decimal byte length for equations and programs Sine Returns sin x Ex Hyperbolic sine Returns sinh x r3 variable Solves the displayed equation or the program selected by FNz using initial estimates in variable and x Inserts a blank space character during equation entry EX Square of argument Square root of x variable Store Copies x into variable variable Stores variable x into variable variable Stores variable x into variable variable Stores variable x x into variable variable F 12 Operation Index File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm 1 15 6 12 6 13 12 6 20 12 22 4 5 14 1 6 6 2 u E TAN TANH VIEW variable File name 32sii Manual E 0424 Printed Date 2003 4 24 Keys and Description Stores variable x into variable Run stop Begins program execution at the current program line stops a running program and displays the X register Displays the summation menu Lo x Returns sample standard deviation of x values Y x xy n 1 Wea s Returns sample standard deviation of y values X yf n1
134. back to polar form a ib r cos 0 isin 0 re r 0 Polar or phasor form imaginary a b real Example Vector Addition 9 6 Operations with Comb Numbers File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm u Add the following three loads You will first need to convert the polar coordinates to rectangular coordinates y L2 185 lb 62 170 Ib 5 143 L 1 X L3 100 lb 261 Keys Display Description a OG Sets Degrees mode 62 185 Enters L1 and converts it to Wea 86 5522 rectangular form 143 170 3 135 7680 Eaters and converts L2 Ex 458 9158 Adds vectors 26 100 B 15 6434 Enters and converts L3 ER 64 5592 Adds L L2 L3 E 178 9372 Converts vector hack to polar form displays r 111 1489 Displays 0 Operations with Comb Numbers 9 7 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 10 Base Conversions and Arithmetic The BASE menu EX lets you change the number base used for entering numbers and other operations including programming Changing bases also converts the displayed number to the new base BASE Menu Decimal mode No annunciator Converts numbers to base 10 Numbers have integer and fractional parts Hexadecimal mode HEX annunciator on Converts numbers to base 16 uses integers only The top row keys become digits LA through LEJ Octal mode OCT annunciator on Converts numbers to base 8 u
135. because the value already in the Y register is accumulated as the y value For this reason the calculator will perform linear regression and show you values based on y even when you have entered only x data or even if you have entered an unequal number of x and y values No error occurs but the results are obviously not meaningful To recall a value to the display immediately after it has been entered press E LASTx Entering Two Variable Data When your data consist of two variables x is the independent variable and y is the dependent variable Remember to enter an x y pair in reverse order y x so that y ends up in the Y register and X in the X register Press EX to clear existing statistical data Key in the y value first and press ENTER Key in the corresponding x value and press Ait The display shows n the number of statistical data pairs you have accumulated 5 Continue entering x y pairs n is updated with each entry To recall an x value to the display immediately after it has been entered press Ez LASTx 11 2 Statistical Operations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Correcting Errors in Data Entry If you make a mistake when entering statistical data delete the incorrect data and add the correct data Even if only one value of an x y pair is incorrect you must delete and reenter both values To correct statistical data
136. ber left in the X register The effect is simply to separate two sequentially entered numbers Y ou can use the replicating effect of clear the stack quickly press O ENTER All stack registers now contain zero Note however that you don t need to clear the tech before doing calculations Using a Number Twice in a Row You can use the replicating feature of to other advantages To add a number to itself press Filling the to with a Constant The replicating effect of together with the replicating effect of stack drop from T into Z allows you t fill the stack with a numeric constant for calculations 2 6 The Automatic Memory Stack File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm u Example Given bacterial culture with a constant growth rate of 50 how large would population of 100 be at the end 3 days Replicates T register Fills the stack with the growth rate Keys in the initial population Calculates the population after 1 day Calculates the population after 2 days mm c Calculates the population after 3 days How CLEAR x Works Clearing the display X register put zero in the X register The next number you key in or recall writes over this zero There are three ways to clear the contents of the X register that is to clear x 1 Press 2 Press 3 Press EN x Mainly used during program entry Note these exceptions B During program entry deletes th
137. ble RCL variable RCLx variable RCL variable RND File name 32sii Manual E 0424 Printed Date 2003 4 24 Keys and Description Selects the period as the radix mark decimal point T PROB F Executes the RANDOM function Returns a random number in the range O through 1 variable Recall Copies variable into the X register variable Returns x variable variable Returns x variable variable Returns x x variable Lx Round Returns x variable Et Round Rounds x to n decimal places in FIX n display mode to n 1 significant digits in SCI n or ENG n display mode or to decimal number closest to displayed fraction in Fraction display mode Wes Return Marks the end of a program the program pointer returns to the top or to the calling routine Roll down Moves t to the Z register z to the Y register y to the X register and x to the T register Wes Roll up Moves t to the X register z to the T register y to the T register and x to the Y register Displays the standard deviation Menu Operation Index F 11 Size 177 x 25 2 cm SCI n Wed SCRI SEED SF n Wea SHOW SIN SINH SOLVE variable SPACE SQ SQRT STO variable STO variable STO variable STO x variable STO variable EN OS C Selects Scientific display with n decimal places n O through 11 Scroll Enables and disables scrolling of equ
138. branching to 13 2 13 4 13 15 checksums 12 23 Index 10 File name 32sii Manual E 0424 Printed Date 2003 4 24 clearing 12 6 duplicate 12 6 entering 12 3 12 6 executing 12 10 indirect addressing 13 19 13 20 132 moving to 12 10 1221 purpose 12 3 typing name 1 2 viewing 1222 program lines See programs program names See program labels program pointer 12 6 12 10 12 11 12 19 1221 B 5 programs See program labels base mode 1225 branching 13 2 13 4 13 6 13 15 calculations in 12 13 calling routines 13 2 13 3 catalog of 1 21 1222 checksums 1222 1223 B 3 clearing 12 6 12 22 12 23 clearing all 12 6 12 23 comparison test 13 conditional tests 13 6 13 7 13 8 13 11 13 16 14 6 data input 12 5 12 12 data output 12 5 12 12 12 14 12 18 deleting 1 22 deleting all 1 4 deleting equations 12 7 12 20 deleting lines 12 20 designing 12 3 13 1 editing 1 3 12 7 1220 editing equations 12 7 12 20 Size 17 7 x 25 2 cm entering 12 5 equation evaluation 13 10 equation prompting 13 10 equations in 12 4 12 6 errors in 12 19 executing 12 10 flags 13 8 13 11 for integration 14 7 for SOLVE 14 1 C 1 fractions with 5 10 12 15 13 9 functions not allowed 12 24 indirect addressing 13 19 13 20 1321 inserting lines 12 6 12 20 interrupting 12 19 lengths 12 22 1223 B 3 line numbers 12 3 1220 12 21 loop counter 13 16 13 17 looping 13 1
139. can reset itself if it is dropped or if power is interrupted Clearing Memory The usual way to clear user memory is to press EX ALL However there is 1so more powerful clearing procedure that resets additional intormation and is useful if e keyboard is not functioning properly It the calculator tails to respond to keystrokes and you are unable to restore operation by resetting it or changing the batteries try the following MEMORY CLEAR procedure These keystrokes clear all of memory reset the calculator and restore all format and modes to their original default settings shown below User Memory and the Stack B 3 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm a N m Press and hold down the key Press and hold down x 3 Press 2 You will be pressing three keys simultaneously When you release all three keys the display shows MEMORY CLEAR if the operation is successful Category CLEAR ALL MEMORY CLEAR Default Angular mode Base mode Contrast setting Decimal point Denominator c value Display format Flags Fraction display mode Random number seed Equation pointer Equation list FN label Program pointer Program memory Stack lift Stack registers Variables Unchanged Unchanged Unchanged Unchanged Unchanged Unchanged Unchanged Unchanged Unchanged EQN LIST TOP Cleared Null PRGM TOP Cleared Enabled Cleared to zero Cleared to zero D
140. ceccceseeceesecseueeeesueeeeeneeeeenees C 3 When SOLVE Cannot Find Root seen C 8 RoURd COIT BITOE asco ete DER OR ud e e REN tu UE ERSS C 14 Under TOW ces cecaccs svat at EE EMI MELLE EM ML LEE C 15 D More about Integration How the Integral Is Evaluated eeeseeessssess D 1 Conditions That Could Cause Incorrect Results D 2 Conditions That Prolong Calculation Time D 8 E Messages F Operation Index Index Contents 11 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Part Basic Operation File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Getting Started Important Preliminaries Turning the Calculator On and Off To turn the calculator on press LC ON is printed below the key To turn the calculator off press fz3 OFF That is press and release the P shift key then press which has OFF printed in blue above it Since the calculator has Continuous Memory turning it off does not affect any information you ve stored You can also press EX to turn the calculator off To conserve energy the calculator turns itself off after 1O minutes of no use If you see the low power indicator in the display replace the batteries as soon as possible See appendix A for instructions Adjusting Display Contrast Display contrast depends on lighting viewing angle and the contr
141. chases were Price per Part x 425 4 40 4 70 4 10 Number of Parts y 250 800 900 1000 Find the average price weighted for the purchase quantity for this part Remember to enter y the weight frequency before x the price Keys Display Description EX Clears the statistics registers 250 4 25 1 6808 Enters data displays n 800 4 6 2 8888 900 4 7 3 888 Statistical Operations 11 5 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 1000 4 4 0686 Four data pairs accumulated T Xn 4 4214 Calculates the mean price weighted for the quantity purchased Sample Standard Deviation Sample standard deviation is a measure of how dispersed the data values are about the mean standard deviation assumes the data is a sampling of a larger complete set of data and is calculated using n 1 as a divisor E Press Wz x for the standard deviation of x values B Press F3 for the standard deviation of y values The ox and ov keys in this menu are described in the next section Population Standard Deviation Example Sample Standard Deviation Using the same process times as in the above mean example May Kitt now wants to determine the standard deviation time sx of the process 15 5 9 22 10 0 12 5 12 0 9 5 Calculate the standard deviation of the times Treat all the data as x values Keys Display Description ER Clears the statistics registers 1
142. clearing 2 5 part of stack 2 1 testing 13 7 unaffected by VIEW 12 15 X ROOT arguments 6 18 Index 15 Size 17 7 x 25 2 cm Batteries are delivered with this product when empty do not throw them away but correct as small chemical waste Bij dit produkt zijn batterijen Wanneer deze leeg zijn moet u ze niet weggooien maar inleveren als KCA File name 32sii Manual E 0424Page 16 376 Printed Date 2003 4 24 Size 17 7 x 25 2 cm
143. clearing statistics registers 11 2 11 13 clearing variables 1 22 3 5 contents 1 21 deallocating B 3 equations B 2 full A 1 integration usage 8 2 maintained while off 1 1 programs 1221 1222 B 3 size 1 21 P 1 stack 2 1 statistics registers 11 13 usage 1222 B 1 B2 variables 3 5 MEMORY CLEAR A 4 B 4 E 3 MEMORY FULL B 1 E 3 menu keys 1 5 menus example of using 1 7 general operation 1 5 leaving 1 3 1 8 list of 1 6 messages clearing 1 3 1 21 displaying 12 15 12 18 in equations 12 15 responding to 1 21 E 1 summary of E 1 Size 17 7 x 25 2 cm minimum of function C 9 modes See angular mode base mode Equation mode Fraction display mode Program entry mode MODES menu angular mode 4 4 setting radix 1 1 6 money finance 17 1 N negative numbers 1 11 9 3 10 5 nested routines 13 3 14 10 normal distribution 16 12 numbers See binary numbers hex numbers octal numbers variables bases 10 1 1225 changing sign of 1 11 1 14 9 3 clearing 1 3 1 4 1 11 1 13 complex 9 1 decimal places 1 16 display format 1 16 10 5 doing arithmetic 1 14 editing 1 3 1 11 1 13 E in 1 11 1 12 A 1 exchanging 2 4 finding parts of 4 15 fractions in 1 19 5 1 in equations 6 Oi in programs 12 6 internal representation 1 16 10 5 large and small 1 11 1 13 limitations 1 11 mantissa 1 12 memory usage 1222 B2 File name 32sii Manual E 0424 P
144. ct to the width of the interval of integration With a given number of sample points a function f x that has three More about Integration D 5 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm fluctuations can be better characterized by its samples when these variations are spread out over most of the interval of integration than if they are confined to only a small fraction of the interval These two situations are shown in the following two illustrations Considering the variations or fluctuation as a type of oscillation in the function the criterion of interest is the ratio of the period of the oscillations to the width of the interval of integration the larger this ratio the more quickly the calculation will finish and the more reliable will be the resulting approximation D 6 More about Integration File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm f x l l Calculated integral of this function l will be accurate l l f x Calculated integral of this function may be accurate a b In many cases you will be familiar enough with the function you want to integrate that you will know whether the function has any quick wiggles relative to the interval of integration If you re not familiar with the function More about Integration D 7 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm and you suspect
145. cts like ER x only when the X register is displayed also acts like Ex x when the X register is displayed and digit entry is terminated no cursor present It cancels other displays menus labeled numbers messages equation entry and program entry 2 2 The Automatic Memory Stack File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm E Reviewing the stack RV Roll Down The roll down key lets you review the entire contents of the stack by rolling the contents downward one register at a time You can see each number when it enters the X register Suppose the stack is filled with 1 2 3 4 press 1 2 3 4 Pressing RH four times rolls the numbers all the way around and back to where they started What was in the X register rotates into the T register the contents of the T register rotate into the Z register etc Notice that only the centents of the registers are rolled the registers themselves maintain their positions and only the X register s contents are displayed R Roll Up The Wea Rt roll up key has a similar function to RH except that it rolls the stack contents upward one register at a time The contents of the X register rotate into the Y register what was in the T register rotates into the X register and so on X XN The Automatic Memory Stack 2 3 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 7 Exchanging the
146. d at equation prompts 3 Enter the instructions to evaluate the function E A function programmed as a multi line RPN sequence must be in the form of an expression that goes to zero at the solution If your equation is f x g x your program should calculate f x g x O is implied B A function programmed as an equation can be any type of equation equality assignment or expression The equation is evaluated by the program and its value goes to zero at the solution If you want the equation to prompt for variable values instead of including INPUT instructions make sure flag 11 is set 4 Endthe program with a RTN Program execution should end with the value of the function in the X register SOLVE works only with real numbers However if you have a complex valued function that can be written to isolate its real and imaginary parts SOIVE can solve for the parts separately Example Program Using RPN Write a program using RPN operations that solves for any unknown in the equation for the Ideal Gas Law The equation is Px V NxRxT where P Pressure atmospheres or N m V Volume liters N Number of moles of gas 14 2 Solving and Integrating Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm R The universal gas constant 0 0821 liter atm mole K or 8 314 J mole K T Temperature kelvins K C 273 1 To begin put the calculator in Program mode if n
147. d function press the appropriate EX or Wed shift key first For example calculate 1 32 and 148 84 Then square the last result and change its sign Keys Display Description 32 32 Operand 8 8313 Reciprocal of 32 148 84 12 2888 Square root of 148 84 EX 148 848 Square of 12 2 145 5406 Negation of 148 8400 The one number functions also include trigonometric logarithmic hyperbolic and parts of numbers functions all of which are discussed in chapter 4 Two Number Functions To use a two number function such as LE LE XJ G or We Key in the first number Press to separate the first number from the second Key in the second number Do not press Press the function key For a shifted function press the appropriate shift o dum key first d before pressing a function key Getting Started 1 13 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 2 For example To calculate Press Display 12343 12 ENTER 3 4 15 8888 12 3 12 ENTER 3 l 3 088 12x 3 12 ENTER 3 X 36 68 123 12 ENTER 3 VA 101 728 8888 Percent change from 88 5 3 4cHG 37 5888 to 5 The order of entry is important only for non commutative functions such as E ES or fed CHG If you type numbers in the wrong order you can still get the correct answer without re typing them by pressing to swap the order of the numbers on the stack Then press the intended function key This
148. d go to step 10 Variables Used gt lt Dummy variable of integration Population mean default value zero Probability corresponding to the upper tail area Population standard deviation default value of 1 Variable used temporarily to pass the value Sx 27 to the inverse program Input value that defines the left side of the upper tail area Statistics Programs 16 15 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Example 1 Your good friend informs you that your blind date has 36 intelligence You interpret this to mean that this person is more intelligent than the local population except for people more than three standard deviations above the mean Suppose that you intuit that the local population contains 10 000 possible blind dates How many people fall into the 36 band Since this problem is stated in terms of standard deviations use the default value of zero for M and 1 for S Keys Display Description S M B Baaan Starts the initialization routine 571 BEHA Accepts the default value of zero for M i 66686 Accepts the default value of 1 for S D 5 value Starts the distribution program and prompts for X 3 Q 6 0 i4 Enters 3 for X and starts computation of Q X Displays the ratio of the population smarter than everyone within three standard deviations of the mean 10000 13 5849 Multiplies by the population Displays the approximate number of blind dates in the
149. d stores T the angle 0 pas GTO D Loops for review of inputs Checksum and length 2ED3 007 5 Hai LEL H This routine converts from the old system to the new system Mathematics Programs 15 33 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i Program Lines Hae INPUT amp Hea INPUT Y Had RCL x Has RCL H Hee RCL M Hia CMPLA Has RCL T Hao 7 Hig i H110 rowv x Hi2 CMPLAx His STO U Hi4 xt His STO U Hi xiv Hi VIEW I HiS VIE V HiS CTO H Description Prompts for and stores X the old x coordinate Prompts for and stores Y the old y coordinate Pushes Y up and recalls X to the X register Pushes X and Y up and recalls N to the X register Pushes N X and Y up and recalls M Calculates X M and Y N Pushes X M and Y N up and recalls T Charges the sign of T because sin T equals sin T Sets radius to 1 for computation of cos T and sin T Calculates cost T and sin T in X and Y registers Calculates X M cos T Y N sin T and Y N cos T X M sin T Stores x coordinate in variable U Swaps positions of the coordinates Stores y coordinate in variable V Swaps positions of coordinates back Halts program to display U Halts program to display V Goes back for another calculation Checksum and length 3A46 028 5 uai LBL Oe IHPUT U OHS IHPUT V da4 ROL U OHS RCL T ide 1 Dar 0 r2v x DaS CMHPLAx O89 RCL H O16 ECL M Dii C
150. deep not counting the topmost program level The operation of nested subroutines is as shown below MAIN program top level End of program Attempting to execute a subroutine nested more than seven levels deep causes an SEH OVERFLOW error Programming Techniques 13 3 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Example A Nested Subroutine The following subroutine labeled S calculates the value of the expression Va b c d as part of a larger calculation in a larger program The subroutine calls upon another subroutine a nested subroutine labeled Q to do the repetitive squaring and addition This saves memory by keeping the program shorter than it would be without the subroutine sHiLBL Starts subroutine here sHe IHPLT A Enters A 2B IHPUT B Enters B SsH4 IHPLT C Enters C SHS INPUT D Enters D S66 RCL D Recalls the data 2B ECL C SHS RCL EB 549 RCL A Sig x2 Sii XEG B A2 S12 WEG Q A B2 S13 NEG Q A2 B2 C 514 SQRT VA B2 C D 215 ETH Returns to main routine Hi LEL Q Nested subroutine HHZ xiu Em xz B4 Adds x taS ETH Returns to subroutine S 13 4 Programming Techniques File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Branching GTO As we have seen with subroutines it is often desirable to transfer execution to a part of the program other than the next line This is called branch
151. e currently displayed program line and cancels program entry During digit entry backspaces over the displayed number If the display shows a labeled number such as R22 BBG pressing The Automatic Memory Stack 2 7 File name 32sii Manual E O424 Printed Date 2003 4 24 Size 177 x 25 2 cm or cancel that display and shows the X register WB When viewing an equation displays the cursor at the end the equation to allow for editing B During equation entry backspaces over the displayed equation one function at a time For example if you intended to enter 1 and 3 but mistakenly entered 1 and 2 this what you should do to correct your error T Z Y CX 1 exe 1 2 Lifts the stack Lift the stack and replicates the X register Overwrites the X register Clears x by overwriting it with zero eS da Overwrites x replaces the zero The LAST X Register The LAST X register is a companion to the stack it holds the number that was in the X register before the last numeric function was executed A numeric function is an operation that produces a result from another number or numbers such as x Pressing EX LASTx returns this value into the X register This ability to retrieve the last x has two main uses 1 Correcting errors 2 Reusing a number in a calculation 2 8 The Automatic Memory Stack File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm See appendix B
152. e in 1 7 of an hour Use FIX 6 display format Keys Display Description EY Fx 6 Sets FIX 6 display format EITE Biz 1 7 as a decimal fraction Wes 8 883429 Equals 8 minutes and 34 29 seconds Ex Fx 4 8 534 Restores FIX 4 display format Angle Conversions When converting to radians the number in the x register is assumed to be degrees when converting to degrees the number in the x register is assumed to be radians To convert an angle between degrees and radians 1 Key in the angle in decimal degrees or radians that you want to convert 2 Press Wea or E DEG The result is displayed 4 10 Real Number Functions File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Unit conversions The HP 328II has eight unit conversion functions on the keybord kg lb 2 C gt F 2cm gt in gt gt gal 1 EX o 8 4536 kilograms 1 ea gt b 2 2646 pounds 32 ev A BABA C 100 3 gt F 212 8888 F 1 Ex 2 5400 centimeters 100 3 39 2781 inches 1 Ex 3 7854 liters 1 ra 8 2642 gallons Probability Functions Factorial To calculate the factorial of a displayed positive integer x o x x 253 press EX the left shifted key Gamma To calculate the gamma function of a noninteger x T x key in x 1 and press fea X The x function calculates T x 1 The value for x cannot be a negative integer Real Number F
153. e mean menu X 9 d XM See Mean below The standard deviation menu x s ox ov See Sample Standard Deviation and Population Standard Deviation later in this chapter Ex The summation menu n x 2 x xw See Summation Statistics later in this chapter Mean Mean is the arithmetic average of a group of numbers B Press F3 X for the mean of the x values m Press Wea for the mean of the y values B Press fsa XM for the weighted mean of the x values using the 11 4 Statistical Operations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm y values as weights or frequencies The weights can be integers or non integers Example Mean One Variable Production supervisor May Kitt wants to determine the average time that a certain process takes She randomly picks six people observes each one as he or she carries out the process and records the time required in minutes 15 5 9 25 10 0 12 5 12 0 8 5 Calculate the mean of the times Treat all data as x values Keys Display Description ER Clears the statistics registers 15 5 1 6606 Enters the first time 9 25 10 12 5 Enters the remaining data 12 8 5 6 8088 six data points accumulated T x 11 2917 Calculates the mean time to complete the process Example Weighted Mean Two Variables A manufacturing company purchases a certain part four times a year Last year s pur
154. e name 32sii Manual E 0424 Printed Date 2003 4 24 This routine multiplies a column matrix and a 3 x 3 matrix Sets index value to point to last clement in first row Mathematics Programs 15 15 Size 17 7 x 25 2 cm i Program Lines Mas AEG H Had S Hao AEG H Hae 9 Description Sets index value to point to last element in second row Sets index value to point to last element in third row Checksum and length C1D3 009 0 Hii LBL H Hee STU i HAS ROL J Had ROL K HBS ROL L He ROLxC 12 Ha AEG P HBS AEG P HBS 24 Hib ST i Hii RV Hie sTUcio His VIEWC i 2 Hi4 RTH This routine calculates product of column vector and row pointed to by index value Saves index value in i Recalls J from column vector Recalls K from column vector Recalls L from column vector Multiplies by last element in row Multiplies by second element in row and adds Multiplies by first element in row and adds Sets index value to display X Y or Z based on input row Gets result back Stores result Displays result Returns to the calling program or to PEGM TOP Checksum and length 4E9D 021 0 F i LBL F PHe xz F s DSE i PH4 DSE i PHS OSE i PHE RCLx 12 Pay PHe RTH This routine multiples and adds values within a row Gets next column value Sets index value to point to next row value Multiples column value by row value Adds product to previous sum Returns to the calling program
155. e or too small to display in the current decimal place setting will automatically be displayed in scientific format Scientific Format SC SCI format displays a number in scientific notation one digit before the or radix mark with up to 11 decimal places if they fit and up to three digits in the exponent After the prompt SCI type in the number of decimal places to be displayed For 10 or 11 places press LJ O or CJ 1 The integer part of the number will always be less than 10 For example in the number 1 2346E5 the 2 3 4 and 6 are the decimal digits you see when the calculator is set to SCI 4 display mode The 5 following the E is the exponent of 10 1 2346 x 10 Getting Started 1 15 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i Engineering Format EH ENG format displays a number in a manner similar to scientific notation except that the exponent is a multiple of three there can be up to three digits before the or radix mark This format is most useful for scientific and engineering calculations that use units specified in multiples of I0 such ass micro milli and kilo units After the prompt EHG type in the number of digits you want after the first significant digit For 10 or 11 places press LJ O or LJ 1 For example in the number 123 46E3 the 2 3 4 and 6 are the significant digits after the first significant digit you
156. e same way that evaluates an equation in the equation list For program evaluation in an equation is essentially treated as There s no programmable equivalent to for an assignment equation other than writing the equation as an expression then using STO to store the value in a variable For both types of calculations you can include RPN instructions to control input output and program flow Data Input and Output For programs that need more than one input or return more than one output you can decide how you want the program to enter and return information For input you can prompt for a variable with the INPUT instruction you can get an equation to prompt for its variables or you can take values entered in advance onto the stack 12 4 Simple Programming File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm For output you can display a variable with the VIEW instruction you can display a message derived from an equation or you can leave unmarked values on the stack These are covered later in this chapter tinder Entering and Displaying Data Entering a Program Pressing EX toggles the calculator into and out of Program entry mode turns the PRGM annunciator on and off Keystrokes in Program entry mode are stored as program lines in memory Each instruction or number occupies one program line and there is no limit other than available memory on the number of lines in a program
157. e stack 2 3 root functions 4 2 roots See SOLVE checking 7 6 C 3 in programs 14 5 multiple 7 8 none found 77 C 9 of equations 7 1 of programs 14 1 polynomial 15 22 quadratic 15 22 rounding fractions 5 9 12 18 numbers 4 15 round off fractions 5 4 5 9 integration 8 6 SOLVE C 16 statistics 11 1 trig functions 4 4 routines calling 13 2 nesting 13 3 14 10 parts of programs 13 1 RPN compared to equations 6 18 Index 12 File name 32sii Manual E 0424 Printed Date 2003 4 24 12 4 in programs 2 4 origins 2 1 ending prompts 6 13 6 15 7 2 12 14 interrupting programs 12 19 resuming programs 12 15 12 16 12 19 running programs 12 22 stopping integration 8 2 14 7 stopping SOLVE 7 7 14 1 running programs 12 10 12 22 S sample standard deviations 11 6 SCI format See display format in programs 12 6 setting 1 17 SCRI 6 8 127 scrolling binary numbers 1 0 7 equations 6 8 127 12 16 seed random number 4 13 self test calculator A 5 service A shift keys 1 2 SHOW equation checksums 6 21 R 2 equation lengths 6 21 B 2 fraction digits 3 3 5 5 number digits 1 18 12 6 program checksums 12 22 12 23 B 3 program lengths 12 23 B 3 prompt digits 6 16 10 8 12 14 Size 17 7 x 25 2 cm variable digits 3 3 3 4 10 8 12 15 sign conventions finance 17 1 sign of numbers 1 11 1 14 9 3 10 5 simultaneous equations 15 13 sine
158. e the equation to find its positive and negative roots Keys Display Description O X 10 iB Your initial guesses for the positive root F3 HO P Selects Equation mode displays the equation r3 X SOLVING Calculates the positive root 4 2 8088 using guesses O an 10 2 888 Final two estimates are they same 6 B 8BBaaaaaaBB ffx 0 O X10 i Your initial guesses for the negative root Wes Ae 2 Redisplays the equation r3 X SOLVING Calculates negative root 3 BAHA using guesses O and 10 3 a aasaaaaaaaad f x 0 Certain cases require special consideration m f the function s graph has a discontinuity that crosses the x axis then the SOLVE operation returns a value adjacent to the discontinuity see figure a below In this case f x may be relatively large E Values of f x may be approaching infinity at the location where the graph changes sign see figure b below This situation is called a pole Since the SOLVE operation determines that there is a sign change More about Solving C 5 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm B u u between two neighboring values of x it returns the possible root However the value for f x will be relatively large If the pole occurs at a value of x that is exactly represented with 12 digits then that value would cause the calculation to halt with an error message f x f x b Special Case A Discontinuity a
159. e the integral by replacing co the upper limit of integration by a number not so large as 10477 say 107 Rerun the previous integration problem with this new limit of integration Keys Display Description O E 3 1E3_ New upper limit r3 4xEXPE E Selects Equation mode displays the equation Wes X IHTEGRRTIHG Integral The calculation takes a 1 686E8 minute or two D 8 More about Integration File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm u 1 824E 4 Uncertainty of approximation This is the correct answer but it took a very long time To understand why compare the graph of the function between x O and x 10 which looks about the same as that shown in the previous example with the graph of the function between x O and x 10 f x 0 10 You can see that this function is interesting only at small values of x At greater values of x the function is not interesting since it decreases smoothly and gradually in a predictable manner The algorithm samples the tunction with higher densities of sample points until the disparity between successive approximations becomes sufficiently small For a narrow interval in an area where the function is interesting it takes less time to reach this critical density To achieve the same density of sample points the total number of sample points required over the larger interval is much greater than the number required over the
160. ecessary position the program pointer to the top of program memory Keys Display Description EX EX Sets Program mode JLI FREM TOP Type in the program Program Lines Description Gai LEL G Identifies the programmed function GHZ INPUT F Stores P Gas IHFUT Stores V 5584 IMPUTH X Stores N GS INPUT E Stores R GH INPUT T Stores T Ga RCL F Pressure Gas RCLx V Pressure x volume Geo RCL H Number of moles of gas Gia RCLx R Moles x gas constant G11RCLx T Moles x gas constant x temp Giz Px V Nx Rx I G13 RTH Ends the program Checksum and length 053B 019 5 Press to cancel Program entry mode Use program G to solve for the pressure of 0 005 moles of carbon dioxide in a 2 liter bottle at 24 C Keys Display Description ra G Selects G the program SOLVE evaluates to find the value of the Solving and Integrating Programs 14 3 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 2 F3 P V value 2 H value 005 E value 0821 T value 24 273 1 T 29r 1600 SULVIBC FzH BHe6lB Example Program Using Equation unknown variable Selects P prompts for V Stores 2 in V prompts for N Stores 005 in N prompts for R Stores 0821 in R prompts for T Calculates T Stores 297 1 in T solves for P Pressure is 0 0610 atm Write a program that uses an equation to solve the Ideal Gas Law Keys Display ET PROM Ex eTo LJ L
161. eceueeeeneeeeueeeens 4 11 Contents 3 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm FIC OMG EE T E 4 11 relie NR EUST 4 11 Probapility den ioo pbad one 4 12 Pars or NUMOS sacer tnus dan tare buta 4 14 Names of uncll liscu estet tabwon te SER Due estes nd 4 14 5 Fractions EMENN I TOGHONS e o E 5 Fractions in the Display cccccceccceecceeeeceeeeeeeeeeaneees 5 2 DIS OIG NT RE E EEN AT E T 5 2 ACCURACY INGICGIONS accessori erna N 5 3 tonger CIOS REN EE E S 5 4 Changing the Fraction Display ccccccseeceeeeeceeneeeeens 5 5 Setting the Maximum Denominator sess 5 5 Choosing Fraction Format cccccseccceeceesneeeeeneeeeens 5 6 Examples of Fraction Displays ccccccseceseeeeeeeeeeees 5 7 Rounding FRACHONS EE TEE TETTE TEE T TT 5 8 FRACTIONS in EQUGNONS eusessmerissimierese ecu ees eee tesst ut ecce 5 9 FROCHONS im PFOGIFGITIS auc soeur oae Eod up PUdenba es du duis qoiaud 5 10 6 Entering and Evaluating Equations How You Can Use Equations sese 6 Summary of Equation Operations eeeeeee 6 3 Entering Equations into the Equation List sssuss 6 4 Variables in Equations ccccccsecceseceeseseeneceeneeeenees 6 5 Number in Equations eesee 6 5 Funcions Ih EQUOHONS neci eani Ue Su eo ier adi e a ote teunds 6 6 4 Contents File name 32sii Manual E 0424 Printed
162. ect the approximation until its third decimal place you can consider all the displayed digits in this approximation to be accurate If the uncertainty of an approximation is larger than what you choose to tolerate you can increase the number of digits in the display format and repeat the integration provided that f x is still calculated accurately to the number of digits shown in the display In general the uncertainty of an Integrating Equations 8 7 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm u integration calculation decreases by a factor of ten for each additional digit specitied in the display format Example Changing the Accuracy For the integral of Si 2 just calculated specify that the result be accurate to four decimal places instead of only two Keys Display E SC A4 1 88B8BE 3 7 BABAE r SIHCHO E r3 X IHTEGRRTIHG 1 6854EB8 1 BB8Bg8a8E 5 EX FK 4 X 1 8888E 5 EX DEG 1 G888B8E 5 Description Specifies accuracy to four decimal places The uncertainty from the last example is still in the display Rolls down the limits of integration from the Z and T registers into the X and Y registers Displays the current equation Calculates the result Note that the uncertainty is about 1 100 as large as the uncertainty of the SCI 2 result calculated previously Restores FIX 4 format Restores Degrees mode This uncertainty indicates
163. ection is significant Goes back to start of loop if correction is significant Continues if correction is not significant Displays the calculated value of X Loops to calculate another X Checksum and length C2AD 033 5 WHI LEL BaZ ROL M WES RCL amp WE FH F 065 FH aD RAG 2 BEY T GAS x RAS SORT i318 ECL 4311 STO T Giz Riz 7 Hid 8 5 Riz File name 32sii Manual E 0424 Printed Date 2003 4 24 This subroutine calculates the upper tail area Q x Recalls the lower limit of integration Recalls the upper limit of integration Selects the function defined by LBL F for integration Integrates the normal function using the dummy variable D Calculates S x4 27 Stores result temporarily for inverse routine Adds half the area under the curve since we integrated using the mean as the lower limit Statistics Programs 16 13 Size 17 7 x 25 2 cm i Program Lines Description O16 RTH Returns to the calling routine Checksum and length F79E 032 0 Fai LBL F This subroutine calculates the integrand for the normal function g UC M3 2 FH2 ECL D FHA ECL M FH4 ECL S Fas x FHE 2 Fay FHS 7 Fag es Fig RTH Returns to the calling routine Checksum and length 3DC2 015 0 Flags Used None Memory Required 155 5 bytes 107 5 for program 48 for variables Remarks The accuracy of this program is dependent on the display setting For inputs in the rare between 3
164. ecursively For example attempting to calculate a multiple integral will result in an J JFH error Also SOLVE and J FN cannot call a routine that contains an FH l abel instruction if attempted a SOLVE ACTIVE or JFH ACTIVE error will be returned SOLVE cannot call a routine that contains an JFN instruction produces a SOLWE FM gt error just as FN cannot call a routine that contains a SOLVE instruction produces an JE SOLVE error The SOLVE variable and JFN d variable instructions in a program use one of the seven pending subroutine returns in the calculator Refer to Nested Subroutines in chapter 13 The SOLVE and JFN operations automatically set Decimal display format 14 10 Solving and Integrating Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 15 Mathematics Programs Vector Operations This program performs the basic vector operations of addition subtraction cross product and dot or scalar product The program uses three dimensional vectors and provides input and output in rectangular or polar form Angles between vectors can also be found Mathematics Programs 15 1 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i This program uses the following equations Coordinate conversion X R sin P cos T Re aK eq Y R sin P sin T T arctan Y X Z Z R cos P P arctan SS VASA Vector addition and subtraction vi v2 X UJ
165. ed as messages causing them to behave like a VIEW statement 1 Program execution halts 2 The program pointer moves to the next program line 3 The equation is displayed without affecting the stack You can clear the display by pressing or Pressing any other key executes that key s function 13 10 Programming Techniques File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 4 IF the next program line is a PSE instruction execution continues after a 1 second pause The status of flag 10 is controlled only by execution of the SF and CF operations from the keyboard or by SF and CF statements in programs Flag 11 controls prompting when executing equations in a program it doesn t affect automatic prompting during keyboard execution When flag 11 is clear the default state evaluation SOLVE and J FN of equations in programs proceed without interruption The current value of each variable in the equation is automatically recalled each time the variable is encountered INPUT prompting is not affected When flag 11 is set each variable is prompted for wheat it is first encountered in the equation A prompt for a variable occurs only once regardless of the number of times the variable appears in the equation When solving no prompt occurs for the unknown when integrating no prompt occurs for the variable of integration Prompts halt execution Pressing resumes the calculation using t
166. ed by the calculator If you ve entered statistical data you can see the contents of the statistics registers Press Ex V RR then use EX and EX lo view the statistics registers Example Viewing the Statistics Registers Use to store data pairs 1 2 and 3 4 in the statistics registers Then view the stored statistical values Keys Display Description Ez z Clears the statistics registers 2 1 8088 Stores the first data pair 1 2 4 3 2 BBG Stores the second data pair 3 4 EX V RR x 14 8888 Displays VAR catalog and views Xxy register Ex Z 2B8 BBBB8B8 Views y register Ez Zx 1 8 8888 Views Xx register ER 6 8888 Views Xy register ER zx 4 HB B8B Views x register ER n 2 0808 Views n register 2 0000 Leaves VAR catalog The Statistics Registers in Calculator Memory The memory space 48 bytes for the statistics registers is automatically allocated if it doesn t already exist when you press or Z The registers are deleted and the memory deallocated when you execute EX z 11 12 Statistical Operations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm If not enough calculator memory is available to hold the statistics registers when you first press or the calculator displays MEMORY FULL You will rived to clear variables equations or programs or a combination to make room for the statistics registers betore you can enter
167. ed to RPN 6 18 12 4 controlling evaluation 13 10 deleting 1 4 6 10 Size 17 7 x 25 2 cm deleting in programs 12 7 12 20 syntax 6 16 6 20 12 15 displaying 6 8 TVM equation 17 1 displaying in programs 12 15 types of 6 11 12 18 13 10 uses 6 editing 1 3 6 9 6 10 variables in 6 5 7 1 editing the programs 12 7 12 20 with i 13 24 entering 6 5 6 7 error messages E entering in programs 12 6 eins evaluating 6 12 6 13 6 14 7 6 124 13 10 clearing 1 3 functions 6 6 6 17 F 1 correcting 27 E I in programs 12 4 12 6 127 estimation statistical 11 8 16 1 1224 13 10 executing programs 12 10 integrating 82 exponential curve fitting 16 1 lengths 6 21 127 H2 lel of Sad nenialton did exponential functions 1 12 4 2 9 3 exponents of ten 1 11 1 12 long 6 8 memory usage 1222 B2 expression equations 6 11 6 12 messages in 12 15 multiple roots 7 8 no root 7 7 F no size limit 6 5 numbers in 6 6 factorial function 4 12 numeric value of 6 12 6 13 6 14 Fl 76 124 not programmable 5 10 13 9 operation summary 6 4 13 13 parentheses 6 6 6 7 6 16 toggles display mode 1 20 5 1 polynomial 15 22 A2 precedence of operators 6 16 toggles flag 13 9 prompt for values 6 13 6 15 ood financial calculations 17 1 prompting in programs 13 10 142 14 8 FIX format 1 16 See also display roots 7 1 format scrolling 6 8 12 7 12 16 flags simultaneous 15 13
168. eeeeceeeeeeeeueeeeeneeeeans A 3 Testing Calculator Operation ccccceeccceeeceeeeeeeeneeeeaes A 4 UR E E E ETTE EE A 5 Limited One Year Warranty ccccccecceeecceseeceeeeeeaeeees A 6 What Is COVEN euecesitesce vtt usa e Ye eh Rata eni edo s A 6 What Is Not Covered arcciasccsnisrnniavnniaiistantantlentearcsiaen A 6 Consumer Transaction in the United Kingdom A 7 If the Calculator Requires Service eeeeeees A 7 Service Charge cccccceccccsecceceecceeeeeeeeeeceeaeeeeeneeeeens A 8 Shipping Instructions ecu eoroehnus nsa e oo OU eb aq dU aes eani nies A 8 Wairaniy ON SEV CE messa ins e A 8 Service AGES MENS errnit A 9 Regulatory Information cccccccsseccceeeesceeeeeeceeueeseeaneees A 9 B User Memory and the Stack Managing Calculator Memory esee B 1 Resetting the Calculator eessesseeeeeeeee B 3 Clearing Memory ssspnessasvotek uita NOU P eERLAT HAM INR EIER B 3 The Status of Stack Lift so Lieu scum oue n idonei adios B 4 Disabling Ope ranlOnSas cs2ics cipio cdi pr tudolt bte tuta e RUE hou qd0 bs B 5 10 Contents File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Neutral Operations ves e Regen ENRPT cn Vae T Esse B 5 The Status of the LAST X Register c cceccceeeeeeceeeeeeeeees B C More about Solving How SOLVE Finds a Root sssessee e C Interpreting Results ccccc
169. efix functions that require two arguments are CHG XROOT Cn r and Pn r Separate the two arguments with a space In an equation the XROOT function takes its arguments in the opposite order from RPN usage For example 8 3 to is equivalent to ASR ODT u3 22 All other two argument functions take their arguments in the Y X order used for RPN For example 28 4 Enr is equivalent to Cnr 28 45 For two argument functions be careful if the second argument is negative The second argument must not start with subtraction For a number use LZ For a variable use parentheses and LE These are valid equations Entering and Evaluating Equations 6 17 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm ACHGO s amp 22 ACHGOA C T22 Six of the equation functions have names that differ from their equivalent RPN operations RPN Operation Equation function x SQ ex EXP 10x ALOG 1 x INV Xy X ROOT y i Example Perimeter of a Trapezoid The following equation calculates the perimeter of a trapezoid This is how the equation might appear in a book Perimeter a b h erimeter a ane sind 0 D b The following equation obeys the syntax rules for HP 32SII equations 6 18 Entering and Evaluating Equations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Parentheses used to group items 4 N P A B Hx 1 SIN T 1 SIN
170. egrees Decimal Medium 4095 FIX 4 Cleared Off Zero EQN LIST TOP Cleared Null PRGM TOP Cleared Enabled Cleared to zero Cleared to zero Memory may inadvertently be cleared if the calculator is dropped or if power is interrupted The Status of Stack Lift The tour stack registers are always present and the stack always has a stack lift status That is to say the stack lift is always enabled or disabled regarding its behavior when the next number is placed in the X register Refer to chapter 2 The Automatic Memory Stack B 4 User Memory and the Stack File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm E All functions except those in the following two lists will enable stack lift Disabling Operations The four operations ENTER X and Clx disable stack lift A number keyed in after one of these disabling operations writes over the number currently in the X register The Y Z and T registers remain unchanged In addition when and act like Clx they also disable stack lift The INPUT function disables stack lift as it halts a program for prompting so any number you then enter writes over the X register but it enables stack lift when the program resumes Neutral Operations The following operations do not affect the status of stack lift DEG RAD FIX SCI DEC HEX OCT CLVARS GRAD ENG ALL BIN PSE SHOW RADIX CLE RADIX and STOP E and and L
171. em distinct Program Line Numbers Line numbers are preceded by the letter for the label such as R81 It one label s routine has more than 99 lines then the line number appears with a decimal point instead of the leftmost number such as A 41 for line 101 in label A For more than 199 lines the line number uses a comma such as R81 for line 201 Program Returns Programs and subroutines should end with a return instruction The keystrokes are Wea RIN When a program finishes running the last RTN instruction returns the program pointer to FRGM TOP the top of program memory Simple Programming 12 3 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i Using RPN and Equations in Programs You can calculate in programs the same ways you calculate on the keyboard m Using RPN operations which work with the stack as explained in chapter 2 B Using equations as explained in chapter 6 The previous example used a series of RPN operations to calculate the area of the circle Instead you could have used an equation in the program An example follows later in this chapter Many programs are a combination of RPN and equations using the strengths of both Strengths of RPN Operations Strengths of Equations Use less memory Easier to write and read Execute a bit faster Can automatically prompt When a program executes a line containing an equation the equation is evaluated in th
172. ence the term Reverse Polish Notation or RPN The stack consists of four storage locations called registers which are stacked on top of each other These registers labeled X Y Z and T store and manipulate four current numbers The oldest number is stored in the T top register The stack is the work area for calculations The Automatic Memory Stack 2 1 File name 32sii Manual E O424 Printed Date 2003 4 24 Size 177 x 25 2 cm i 0 0000 i Oldest number T Z 100000 Y X 0 0000 Displayed The most recent number is in the X register this is the number you see in the display In programming the slack is used to perform calculations to temporarily store intermediate results to pass stored data variables among programs and subroutines to accept input and to deliver output The X Register Is in the Display The X register is what you see except when a menu a message or a program line is being displayed You might have noticed that several function names include an x or y This is no coincidence these letters refer to the X and Y registers For example EX raises ten to the power of the number in the X register the displayed number Clearing the X Register Pressing Ex x always clears the X register to zero it is also used to program this instruction The key in contrast is context sensitive It either clears or cancels the current display depending on the situation it a
173. equipment that is not authorized by Hewlett Packard that system configuration has to comply with the requirements of Paragraph 2 of the German Federal Gazette Order VFG 1046 84 dated December 14 1984 Noise Declaration In the operator position under normal operation per ISO 7779 LoA lt 7OaB Support Batteries and Service A 9 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm User Memory and the Stack This appendix covers B The allocation and requirements of user memory W How to reset the calculator without affecting memory W How to clear purge all of user memory and reset the system defaults and W Which operations affect stack lift Managing Calculator Memory The HP 32SIl has 384 bytes of user memory available to you for any combination of stored data variables equations or program lines SOLVE FN and statistical calculations also require user memory The J FN operation is particularly expensive to run All of your stored data is preserved until you explicitly clear it The message MEMORY FULL means that there is currently not enough memory available for the operation you just attempted You need to clear some or all of user memory For instance you can W Clear the contents of any or all variables see Clearing Variables its chapter 3 W Clear any or all equations see Editing and Clearing Equations in chapter 6 WB Clear any or all programs see
174. er in the X register to the closest decimal representation of the fraction The rounding is done according to the current c value and the states of flags 8 5 8 _ Fractions File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm and 9 The accuracy indicator turns off if the fraction matches the decimal representation exactly Otherwise the accuracy indicator stays on See Accuracy Indicators earlier in this chapter In an equation or program the RND function does fractional rounding if Fraction display mode is active Example Suppose you have a 56 4 inch space that you want to divide into six equal sections How wide is each section assuming you can conveniently measure 1 16 inch increments What s the cumulative roundoff error Keys Display Description 16 f Sets up fraction format for 1 16 inch increments Flags 8 and 9 should be the same as for the previous example 56C 3 LC 4 D Stores the distance in D 26 34d 6 Lx AS 7 16 The sections are a bit wider than 9 7 16 inches EX 97 16 Rounds the width to this value 6 56 548 Width of six sections D B 1x48 The cumulative round off error Wea CF 8 6178 Clears flag 8 EX B 1258 Turns off Fraction display mode Fractions in Equations When you re typing an equation you can t type a number as a fraction When an equation is displayed all numeric values are shown as decimal values Fraction display mode is ignored
175. er operations press fea L_ to complete the function arguments otherwise you don t have to add the trailing y If the first key in an equation is a function from the top row of keys on the calculator and if the displayed equation has the annunciator turned on you have to press EM SCRI first to turn off the annunciator See Displaying and Selecting Equations later in this chapter for more information 6 6 X Entering and Evaluating Equations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Parentheses in Equations You can include parentheses in equations to control the order in which operations are performed Press P LU and P L to insert parentheses For more information see Operator Precedence later in this chapter Example Entering an Equation Enter the equation r 2 x c x cos f a Keys Display Description Wes W 8 25xqxD 2 Shows the last equation used in the equation list R fea k Starts a new equation with variable R 2 R 2 Enters a number changing the cursor to C R 2xCxB Enters infix operators R 2xCxCOScN Enters a prefix function with a left parenthesis T A xCxCOSCT R2M Enters the argument and right Wes parenthesis This final parenthesis is optional R 2xCxC scT Terminates the equation and displays it 3 CE 56C1 6198 8 Shows its checksum and length Leaves Equation mode Displaying and Selecting Equations The equa
176. ered Batteries and damage caused by the batteries are not covered by the Hewlett Packard warranty Check with the battery manufacturer about battery and battery leakage warranties This warranty does not apply if the product has been damaged by accident or misuse or as the result of service or modification by other than an authorized Hewlett Packard service center No other express warranty is given The repair or replacement of a product is your exclusive remedy ANY OTHER IMPLIED WARRANTY OF MERCHANTABILITY OR FITNESS IS LIMITED TO THE ONE YEAR DURATION OF THIS WRITTEN WARRANTY Some states provinces or countries do not allow limitations on how long an implied warranty lasts so the above limitation may not apply to you IN NO EVENT SHALL HEWLETT PACKARD COMPANY BE LIABLE FOR CONSEQUENTIAL DAMAGES Some states provinces or countries do not allow the exclusion or limitation of incidental or consequential damages so the above limitation or exclusion may not apply to you A 6 Support Batteries and Service File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Products are sold on the basis of specitications applicable at the time of manutacture Hewlett Packard shall have no obligation to modify or update products once sold Consumer Transaction in the United Kingdom This warranty shall not apply to consumer transactions and shall not affect the statutory rights of a consumer In relation to such tran
177. ers you enter four separate numbers To do a complex operation press Ex before the operator For example to do 2 i4 315 press 4 ENTER 2 ENTER 5 ENTER 3 EN CMPLX The result is 5 i 9 Press to see the imaginary part The Complex Stack The complex stack is really the regular memory stack split into two double registers tor holding two complex numbers z 1x i z iy and z2x i z2y Operations with Comb Numbers 9 1 File name 32sii Manual E O424 Printed Date 2003 4 24 Size 177 x 25 2 cm ly Z1 X ly2 2 Real Stack Complex Stack Since the imaginary and real parts of a complex number are entered and stored separately you can easily work with or alter either part by itself imaginary part real part Complex input z or z and z2 Complex result z Always enter the imaginary part the y part of a number first The real portion of the result zx is displayed press to view the imaginary portion zy For two number operations the first complex number z1 is replicated in the stack s Z and T registers 9 2 Operations with Comb Numbers File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Complex Operations Use the complex operations as you do real operations but precede the operator with E CMPLX To do an operation with one complex number 1 Enter the complex number z composed of x i y by keying in y X 2 Select the complex function
178. ers other than itself and 1 then the program returns the input value If the input is not a prime number then the program returns the first prime number larger than the input The program identifies non prime numbers by exhaustively trying all possible factors If a number is riot prime the program adds 2 assuring that the value is still odd and tests to see if it has found a prime This process continues until a prime number is found 17 6 Miscellaneous Programs and Equations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm VIEW Prime Note x is the value in the X register ae Miscellaneous Programs and Equations 17 7 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm E Program Listing Program Lines Description Yi LEL Y This routine displays prime number P THe VIEW F Checksum and length 5DOB 003 0 281 LBL Z This routine adds 2 to P caz 2 HA RCL F Checksum and length OC68 004 5 Pai LBL F This routine stores the input value for P Poe STOP FH 2 Pid Pio FP F B Pa x v7 Tests for even input FHa31 PHS STO F P183 Increments P if input an even number Fii STO D Stores 3 in test divisor D Checksum and length 40BA 016 5 61 LBL x This routine tests P to see if it is prime abe ROL FP aba ROL D G4 FP Finds the fractional part of P D 405 x m Tests for a remainder of zero nof prime 66 GTO Z If the nu
179. es Description Si LEL S This routine initializes the standard deviation program sas Stores default value for mean S s STU M sB4 INPUT M Prompts for and stores mean M Sas i Stores detault value tor standard deviation SHE STO S SB INPUT S Prompts for and stores standard deviation S Sas RTH Stops displaying value of standard deviation Checksum and length E5FA 012 0 061 LEL D This routine calculates Q X given X Daz INPUT X Prompts for and stores X Da3 xEG Q Calculates upper tail area De4 STO Q Stores value in Q so VIEW function can display it Das VIEW Q Displays Q X pae GTO D Loops to calculate another Q X Checksum and length 2D6A 009 0 Ii LBL I This routine calculates X given Q X IB2 INPUT Prompts for and stores Q X I3 RCL M Recalls the mean I84 STO X Stores the mean as the guess for X called Xguess Checksum and length 35BF 006 0 Tai LETT This label defines the start of the iterative loop TH2 KEQ Calculates GI guess G X 16 12 Statistics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Program Lines T s RCL n TH4 RCL amp THS STOO THE RV THY AEG F THES RCL T THs Tif STO s T11 ABS Tiz Hpi TiS xiv Ti4 GTD T TIS RCL amp Ti amp VIEW 5 Tir GTO I Description Calculates the derivative at Xguess Calculates the correction for Xguess Adds the correction to yield a new Xguess Tests to see if the corr
180. es X t mb Displays linear regression menu rr A 9838 Correction coefficient data closely approximate a straight line Ex m A AZET Slope of the line E b 4 5566 y intercept Statistical Operations 11 9 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm y 8 50 Fa X 7 50 c 70 9 r 0 9880 7 S S 6 50 S Q2 m 0 0387 HN 5 50 Pa S AH b 4 8560 4 50 X O 20 40 60 80 What if 70 kg of nitrogen fertilizer were applied to the rice field Predict the grain yield based on the above statistics Keys Display Description 70 DN Enters hypothetical x value F3 2 7 5615 The predicted yield in tons per hectare Limitations on Precision of Data Since the calculator uses finite precision 12 to 15 digits it follows that there are limitations to calculations due to rounding Here are two examples 11 10 Statistical Operations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Normalizing Close Large Numbers The calculator might be unable to correctly calculate the standard deviation and linear regression for a variable whose data values differ by a relatively small amount To avoid this normalize the data by entering each value as the difference from one central value such as the mean For normalized x values this difference must then be added back to the calculation of x and x and y and b roust also be adjusted For example if
181. ess letter tor each alpha character in the message press the key for each space character 3 Press to insert the message in the current program line and end Equation entry mode Fui Fae FAS FAS FHS FE Fay FHS FHS Fil Fil Fle Fis Fi Fis Program Lines Description LEL F Begins the fraction program CF Clears three fraction flags LFS CF 3 SF ig Displays messages DEC Selects decimal base IHPUT V Prompts for a number IHPFUT D Prompts for denominator 2 4095 RCL V Displays message then shows the decimal number DECIMAL PSE TOP REL O c Sets c value and sets flag 7 MOST PRECISE Displays message then shows the fraction 13 14 Programming Techniques File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Program Lines Description Fig PSE Fir STOF Fis SF 8 Sets flag 8 Fis FACTOR DENOM Displays message then shows the fraction F2h PSE Fei STOF Fee SF oS Sets flag 9 F23 FISED DENOM Displays message then shows the fraction F 4 PSE Fea STOF Fee GTOF Goes to beginning of program Checksum and length 10C3 102 0 Use the above program to see the different forms of fraction display Keys Display F V value 2 53 UO value 16 DECIMAL 2 D300 MOST PRECISE woulla2 FRCTUE DEHBHLUFP File name 32sii Manual E O424 Description Executes label F prompts for a fractional number V Stores 2 53 in V prompts for denominator D Stores
182. essive iterations yield approximations that take into account the presence of the most rapid but characteristic fluctuations For example consider the approximation of More about Integration D 3 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i n xe dx 0 Since you re evaluating this integral numerically you might think that you should represent the upper limit of integration as 10477 which is virtually the largest cumber you ears key into the calculator Try it and what happens Enter the function f x xe Keys Display Description r3 Select equation mode X AxERPCM Enter the equation X ra AxEMPC ED End of the equation r3 CE 297F amp 18 5 Checksum and length Cancels Equation mode Set the display format to SCI 3 specity the lower and upper limits of integration as zero and 1004 than start the integration Keys Display Description al SC 1 3 Specifies accuracy level and O E 499 1E4999 limits of integration a3 4xExPE E2 Selects Equation mode displays the equation F3 X HTEGRATING Approximation of the integral I 6 BAGEA The answer returned by the calculator is clearly incorrect since the actual integral of f x 2 xe from zero to co is exactly 1 But the problem is not that co was represented by 10497 since the actual integral of this function from zero to 1047 is very close to 1 The reasons or the incorrect answer becomes apparent fro
183. esult 8 2 8 6 8 7 D 2 using 8 2 variable of 8 2 intercept curve tit 11 8 16 1 interest finance 17 3 intermediate results 2 13 inverse function 1 14 9 3 inverse hyperbolic functions 4 6 inverse normal distribution 16 12 inverse trigonometric functions 4 4 ISG 13 16 K keys alpha 1 2 letters 1 2 shifted 1 2 top row actions 6 8 12 7 L LASTx function 2 9 LAST X register 2 9 B 8 Index 7 Size 17 7 x 25 2 cm lender finance 17 1 length conversions 4 12 letter keys 1 2 limits of integration 8 2 14 7 linear regression estimation 11 8 16 1 linear regression menu 11 8 logarithmic curve fitting 16 1 logarithmic functions 4 2 9 3 loop counter 13 16 13 17 13 21 looping 13 15 13 16 tukasiewicz 2 1 M mantissa 1 12 1 18 mass conversions 4 12 math complex number 9 1 9 4 general procedure 1 14 intermediate results 2 13 long calculations 2 13 order of calculation 2 16 real number 4 1 stack operation 2 5 9 2 matrix inversion 15 13 maximum of function C 9 mean menu 1 4 means statistics calculating 11 4 normal distribution 16 12 MEM program catalog 1 21 12 22 reviews memory 1 21 Index 8 File name 32sii Manual E 0424 Printed Date 2003 4 24 variable catalog 1 21 3 4 memory amount available 1 21 B 2 clearing 1 4 1 22 A 1 A 4 B 1 11 4 clearing equations 6 10 clearing programs 1 22 12 6 12 23
184. et If it is then the next line in the program is executed It it is not then the next line is skipped This is the Do if True rule illustrated under Conditional Instructions earlier in this chapter If you test a flag from the keyboard the calculator will display YES or HU It is good practice in a program to make sure that any conditions you will be testing start out in a known state Current flag settings depend on how they have been left by earlier programs that have been run You should not assume that any given flag is clear for instance and that it will be set only if something in the program sets it You should make sure of this by clearing the flag before the condition arises that might set it See the example below Example Using Flags The Curve Fitting program in chapter 16 uses flags O and 1 to determine whether to take the natural logarithm of the X and Y inputs WI lines SO3 and S04 clear both of these flags so that lines WO7 and W11 in the input loop routine do not take the natural logarithms of the X and Y inputs for a Straight line model curve 13 12 Programming Techniques File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm m line LO3 sets flag O so that line WO7 takes the natural log of the X input for a Logarithmic model curve mM line E04 sets flag 1 so that line W11 takes the natural log of the Y input for an Exponential model curve E lines PO3 and P04 set both fl
185. ey re displayed using ALL or SCI format If a long number is shortened in the display press a to view all digits To enter an equation in a program line 1 Press We to activate Equation entry mode The EQN annunciator turns on 2 Enter the equation as you would in the equation list See chapter 6 for details Use to correct errors as you type 3 Press to terminate the equation and display its left end The equation does not become part of the equation list After you ve entered an equation you can press Wea lo see its checksum and length Hold the key to keep the values in the display For a long equation the gt and annunciators show that scrolling is active for this program line You can use and to scroll the display Press F SCRI to turn off and to use the top row keys to enter program instructions Keys That Clear Note these special conditions during program entry always cancels program entry It never clears a number to zero m f the program line doesn t contain an equation deletes the current program line It backspaces if a digit is being entered cursor present m f the program line contains an equation begins editing the equation It deletes the rightmost function or variable if an equation is being entered W cursor present m EX EG H deletes a program lime if it contains an equation WI To program a function to clear the K register use EX x 12 6 Simple Programming
186. ff press EM FDISP When you turn off Fraction display mode the display goes back to the previous display format FIX SCI ENG and ALL also turn off Fraction display mode WI Functions work the same with fractions as with decimal numbers except for RND which is discussed later in this chapter This chapter gives more information about using and displaying fractions Entering Fractions You can type almost any number as a fraction on the keyboard including an improper fraction where the numerator is larger than the denominator However the calculator displays A if you disregard these two restrictions WI The integer and numerator must not contain more than 12 digits total B The denominator must not contain more than 4 digits Fractions 5 1 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Example Keys Display Description EX Turns on Fraction display mode 1 5 i 1x42 Enters 1 5 shown as a fraction 1L 3L A ENTER 1 3 4 Enters 1 3 4 Ex 1 7588 Displays x as a decimal number Ex i 344 Displays x as a fraction If you didn t get the same results as the example you may have accidentally changed how fractions are displayed See Changing the Fraction Display later in this chapter The next topic includes more examples of valid and invalid input fractions You can type fractions only if the number base is 10 the normal number base See chapter 10 for inform
187. ffen preterred because m it takes fewer keystrokes m t requires fewer registers in the stack Note When using the left to right method be sure that no more yl than four intermediate numbers or results will be needed at D one time the stack can hold no more than four numbers The above example when solved left to right needed all registers in the stack at one point Keys Display Description 4 14 Saves 4 and 14 as intermediate i4 6086 numbers in the stack The Automatic Memory Stack 2 15 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 7 3 3 At this point the stack is full with numbers for this calculation 21 8888 Intermediate result 25 0888 Intermediate result 2 33 8688 Intermediate result ga izis Final result More Exercises Practice using RPN by working through the following problems Calculate 14 12 x 18 12 9 7 78 0000 A Solution 14 ENTER 12 4 18 ENTER 12 x 9 ENTER 7 3 Calculate 232 13x 9 1 7 412 1429 A Solution 23 EX x 13 ENTER 9 x 2 7 Ux C Calculate 5 4x 0 8 12 5 0 73 0 5961 Solution 5 4 ENTER 8 x 7 ENTER 3 LA 12 5 ey O 3 Or 5 4 ENTER 8 x 12 5 ENTER 7 ENTER 3 L9 O E LE Calculate 8 33x 4 5 2 8 33 7 46 x 0 32 4 3x 8 15 2 75 1 71x 2 01 A Solution 4 5 28 2 16 The Automatic Memory Stack File name 32sii Manual E
188. g To clear all variables at once Press EX WARS Arithmetic with Stored Variables Storage arithmetic and recall arithmetic allow you to do calculations with a number stored in a variable without recalling the variable into the stack A calculation uses one number from the X register and one number from the specified variable Storage Arithmetic Storage arithmetic uses Lt J x or Lx to do arithmetic in the variable itself and to store the result there It uses the value in the X register and does riot affect the stack New value of variable Previous value of variable x x For example suppose you want to reduce the value in A 15 by the number in the X register 3 displayed Press A Now A 12 while 3 is still in the display 3 4 Storing Data into Variables File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm A 12 Results 15 3 12 thatis A x STO 7 w Recall Arithmetic Recall arithmetic uses a Lt J Lx or to do arithmetic in the X register using a recalled number and to leave the result in the display Only the X register is affected New x Previous x x Variable For example suppose you want to divide the number in the X register 3 displayed by the value in A 12 Press A Now x 0 25 while 12 is still in A Recall arithmetic saves memory in programs using A one instruction uses half as much memory as A two instr
189. g File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Editing Program You can modify a program in program memory by inserting deleting and editing program lines If a program line contains an equation you can edit the equation if any other program line requires even a minor change you must delete the old line and insert a new one To delete a program line 1 Select the relevant program or routine EX label activate program entry EX J and press EX or EX to locate the program line that must be changed Hold the arrow key down to continue scrolling If you know the line number you want pressing E CJ label nn moves the program pointer there 2 Delete the line you want to change if it contains an equation press EX EH otherwise press LJ The pointer then moves to the preceding line If you are deleting more than one consecutive program line start with the last line in the group 3 Key in the new instruction if any This replaces the one you deleted 4 Exit program entry or To insert a program line 1 Locate and display the program line that is before the spot where you would like to insert a line 2 Key in the new instruction it is inserted after the currently displayed line For example if you wanted to insert a new line between lines A04 and AO5 of a program you would first display line A04 then key in the instruction or instructions Subsequent prog
190. g fourth order polynomial If not complex roots determine largest real root yo Stores largest real root of cubic Checksum and length C333 060 0 Fal LBL F Fuzz FHS sSru 0 File name 32sii Manual E 0424 Printed Date 2003 4 24 Starts fourth order solution routine J a3 2 Mathematics Programs 15 25 Size 17 7 x 25 2 cm Program Lines Description Fa4 STO E K yo 2 Fino Fae 1 Far irx Creates 107 as a lower bound for M FHS ECL E K FAS x2 K Fig RCL A M K2 ag Fiil xiv Fiz CLx If M2 lt 10 7 use O for M2 Fis SHET M K a Fi4 STOA Stores M Fis RCL O J Fie ECL E JK Fir ECL a Fis 2 FiS a 2 Fel JK a1 2 Fel x F22 i Use 1 if JK a7 2 0 F23 STO B Stores 1 or JK a 1 2 Fed ABS F25 5T0 6 Calculates sign of C Fee ECL OU J F2 x J2 F28 RCL C J2 a2 Feo REEF E F38 RCL E J a2 yo F31 SORT C Jf a y F32 5TOx B Stores C with proper sign Fas RCL O J Fad ECL EB J 4 IL F35 ECL E K F36 ECL A K M Far XEG T Calculate and display two roots of the fourth order 15 26 Mathematics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Program Lines Description polynomial Fas RCL O J F39 ECL E J L F4H ECL E K F4i ECL A K M Checksum and length 9133 061 5 T81 LEL T Starts routine to calculate and display two roots Taz REB B Uses quadratic routine to calculate two roots
191. ght of nitrogen Keys Display Description uz PxV HxRET Displays the equation Fa N P 0 0618 Solves for N prompts for P 05 Wee BHA Stores 05 in P prompts for V 5 k70 0821 Stores 5 in V prompts for H T7297 1668 Retains previous R prompts for T 18 Calculates T Kelvins 273 1 T7291 100 SOLVIHG Stores 291 1 in T solves for N H H 8185 28 6 2929 Calculates mass in grams N x 28 Vl A A586 Calculates density in grams per liter Understanding and Controlling SOLVE SOLVE uses an iterative repetitive procedure to solve for the unknown variable The procedure starts by evaluating the equation using two initial guesses for the unknown variable Based on the results with those two guesses SOLVE generates another better guess Through successive iterations SOLVE finds a value for the unknown that makes the value of the equation equal to Zero Solving Equations 7 5 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i When SOLVE evaluates an equation it does it the same way does any in the equation is treated as a For example the Ideal Gas Law equation is evaluated as P x V N x R x T This ensures that an equality or assignment equation balances at the root and that an expression equation equals zero at the root Some equations are more difficult to solve than others In some cases you need to enter initial guesses in order to find a solution See Choosing Ini
192. ging sign of numbers 1 11 1 14 9 3 checksums equations 6 21 12 7 12 24 programs 12 22 1223 7eCHG arguments 4 clearing equations 6 10 general information 1 3 memory 1 22 A 1 messages 1 21 numbers 1 11 1 13 programs 1 22 1223 statistics registers 11 2 11 13 variables 1 22 3 4 3 5 K register 2 2 2 7 clearing memory A 4 B 4 CLEAR menu 1 4 CMPLX 9 1 9 3 combinations 4 13 commas in numbers 1 16 A 1 comparison tests 13 7 complex numbers coordinate systems 9 6 entering 9 1 on stack 92 operations 9 1 9 3 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size polynomial roots 15 22 viewing 9 2 conditional tests 13 6 13 7 13 8 13 11 13 16 14 6 constant filling stack 2 7 Continuous Memory 1 1 contrast adjustment 1 1 conversion functions 4 8 conversions angle format 4 1 1 angle units 4 1 1 coordinates 4 8 9 6 15 1 length units 4 12 mass units 4 12 number bases 10 1 temperature units 4 12 time format 4 11 volume units 4 12 coordinates converting 4 5 4 8 15 1 transtorming 15 34 correlation coefficient 11 8 16 1 cosine trig 4 4 9 3 cross product 15 1 cubic equations 15 22 curve fitting 11 8 16 1 c value 5 6 B 5 B 8 D Decimal mode See base mode decimal point 1 16 A 1 degrees angle units 4 3 A 2 converting to radians 4 11 Index 3 177 x 25 2 cm denominators controlling 5 6 13 9 13 13 range of 1 1
193. hat might actually be messages This is especially useful in programs as described in chapter 12 Verifying Equations When you re viewing an equation not while you re typing an equation you can press P to show you two things about the equation the equation s checksum and its length Hold the key to keep the values in the display The checksum is a four digit hexadecimal value that uniquely identifies this equation No other equation will have this value If you enter the equation incorrectly it will not have this checksum The length is the number of bytes of calculator memory used by the equation 6 20 Entering and Evaluating Equations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm The checksum and length allow you to verity that equations you type are correct The checksum and length of the equation you type in an example should match the values shown in this manual Example Checksum and Length of an Equation Find the checksum and length for the pipe volume equation at the beginning of this chapter Keys Display Description Wes EN V e 25xqxD 2x Displays the desired equation as required Wed SHOW hold CK 5826 826 8 Display equation s checksum and length release V B 2z5xgxD zx Redisplays the equation Leaves Equation mode Entering and Evaluating Equations 6 21 File name 32sii Manual E O424 Printed Date 2003 4 24 Size 177 x 25 2 cm Solving Equati
194. he statistics registers Statistics Programs 16 3 Size 17 7 x 25 2 cm i Program Lines 43 STU i zaq Description Stores the index value in i for indirect addressing Sets the loop counter to zero for the first input Checksum and length 8C2F 006 0 Hai LEL H Wee 1 Ha Had STO amp WHOS IHPLUT amp Hae FS B Ma LH Has STU EB WAS IHPLUT Wik Fo i Wii LH Wie STO R Wis RCL B Wid z Wis GTO H Defines the beginning of the input loop Adjusts the loop counter by one to prompt for input Stores loop counter in X so that it will appear with the prompt for X Displays counter with prompt and stores X input If flag O is set takes the natural log of the X input Stores that value for the correction routine Prompts for and stores Y If flag 1 isset takes the natural log of the Y input Accumulates B and R as x y data pair in statistics registers Loops for another X Y pair Checksum and length AAD5 022 5 Ui LBL U Ube RCL UBS RCL B lad z Liam GTO H Defines the beginning of the undo routine Recalls the most recent data pair Deletes this pair from the statistical accumulation Loops for another X Y pair Checksum and length AFAA 007 5 RHI LBL F RAS F RAS STO R rad VIEH F RAS b Defines the start f the output routine Calculates the correlation coefficient Stores it in R Displays the correlation coefficient Calculates the coefficient b
195. he value for the variable you keyed in or the displayed current value of the variable if is your sole response to the prompt Flag 11 is automatically cleared after evaluation SOLVE or J FN of an equation in a program The status of flag 11 is also controlled by execution of the SF and CF operations from the keyboard or by SF and CF statements in programs Annunciators for Set Flags Flags O 1 2 and 3 have annunciators in the display that turn on when the corresponding flag is set The presence or absence of O 1 2 or 3 lets you know at any time whether any of these four flags is set or not However there is no such indication for the status of flags 4 through 11 These status of these flags can be determined by executing the FS Instruction from the keyboard See Using Flags below Programming Techniques 13 11 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Using Flags Pressing 0 displays the FLAGS menu SF CF F87 Atter selecting the function you want you will be prompted for the flag number 0 1 1 For example press a SF O to set flag O press a SF LJ to set flag 10 press fs SF LY 1 to set flag 11 FLAGS Menu Set flag Set flag n Clear flag Clears flag n Is flag set Tests the status of flag n A flag test is a conditional test that affects program execution just as the comparison tests do The FS n instruction tests whether the given flag is s
196. i Stores index for register 29 Updates xf in register 29 2 XT Stores index for register 31 Updates S xt in register 31 Gets or 1 Increments or decrements N Displays current number of data pairs Goes to label I for next data input Checksum and length 214E 030 0 581 LBL G GHZ zx G ss STO S GH4 VIEH S GAS x GHEE STO M G r VIEW PN LHS CTO I Calculates statistics for grouped data Grouped standard deviation Display grouped standard deviation Weighted mean Displays weighted mean Goes back tor more points Checksum and length 4A4A 012 0 Ui LBL U Ube i UBS ROL F Lad 7 UBS GTO F Undo data entry error Enters decrement for N Recalls last data frequency input Changes sign of fi Adjusts court and summations Checksum and length 615A 015 5 File name 32sii Manual E 0424 Printed Date 2003 4 24 Statistics Programs 16 19 Size 17 7 x 25 2 cm i Flags Used None Memory Required 143 bytes 71 for programs 72 for data Program Instructions Key in the program routines press when done Press S to start entering new data Key in x value data point and press R S Key in f value frequency and press R S Press after VIEWing the number of points entered Repeat steps 3 through 5 for each data point SY ee ados It you discover that you have made a data entry error xj or f after you have pressed in step 4 press U and then press again Then g
197. i Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i 10 11 6 For More Information cceee eee 8 9 Operations with Comb Numbers The Complex Stack cccccccsecccsecceeesceeesceeescseneceeneeeens 9 Complex Operations eeseeseee e 9 3 Using Complex Number in Polar Notation 9 6 Base Conversions and Arithmetic Arithmetic in Bases 2 8 and 16 eene 10 2 The Representation of Numbers ccccccseeceeseeeeeeneeees 10 4 Negative Numbers essssssee 10 4 Range of Numbers sssse 10 5 Windows for Long Binary Numbers 10 6 SHOWing Partially Hidden Numbers 10 6 Statistical Operations Entering Statistical Data seesssesssseeeeeenee 11 1 Entering One Variable Data sssssesse 11 2 Entering Two Variable Data ssseesesess 11 2 Correcting Errors in Data Entry sseussuss 11 3 Syroursiree Mollet oniTol RR NN 11 4 ITO TEE UU I T 11 4 Sample Standard Deviation ccccccecceeeceeeeeeenees 11 6 Population Standard Deviation sssssse 11 7 Liriedr regression eoque uiu ctvotre t peo r tib PI Dde 11 7 Limitations on Precision of Datd ccccseeceeeeeeeeeeeeees 11 10 Summation Values and the Statistics Registers 11 11 Contents File name 3
198. i3 means the variable specified by the number in variable i an indirect reference but that i or i 3 means variable i The following program uses an equation to find the sum of the squares of variables A through Z Program Lines EMI LEL E EH2z CF ib Description Begins the program Sets equations for execution 13 24 Programming Techniques File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm EB3 CF ii Disables equation prompting Fad 1 826 Sets counter for to 26 ES STD i Stores counter EHE a8 Initializes sum Checksum and length EA5F 017 0 Program Lines Description Fai LEL F Starts summation loop Fa2 j3 2 Equation to evaluate the ith square Press F to start the equation Ckecksum and length of equation 48AD 006 0 Fas Adds ith square to sum Fa4 ISG i Tests for end of loop Fas GTOF Branches for next variable Fa RTH Ends program Checksum and length of program 19A8 013 5 Programming Techniques 13 25 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 14 Solving and Integrating Programs Solving a Program In chapter 7 you saw how you can enter an equation it s added to the equation list and then solve it for any variable You can also enter a program that calculates a function and then solve it for any variable This is especially useful if the equation you re solving changes for certain conditions or if it
199. in the display and above means you can press to see characters in that direction Shows the checksum and length for the equation so you can check your keystrokes By comparing the checksum and length of your equation with those in the example you can verify that you ve entered the equation properly See Verifying Equations at the end of this chapter for more information Evaluate the equation to calculate V Keys Display LI value Description Prompts for variables on the right hand side of the equation 6 2 Entering and Evaluating Equations File name 32sii Manual E O424 Printed Date 2003 4 24 Size 177 x 25 2cm Keys Display 20 1L 2 OF 2 1 2 L value 16 75 5398 Description Prompts for D first value is the current value of D Enters 2 2 inches as a fraction Stores D prompts for L value is current value of L Stores L calculates V in cubic inches and stores the result in V Summary of Equation Operations All equations you create are saved in the equation list This list is visible whenever you activate Equation mode You use certain keys to perform operations involving equations They re described in more detail later Entering and Evaluating Equations 6 3 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm XEQ Wea SOLVE Wes L Ex CLEAR EX Lt or EX L Wea SHOW Enters and leaves Equation mode
200. ing Unconditional branching uses the GTO go fo instruction to branch to a program label It is not possible to branch to a specific line number during a program A Programmed GTO Instruction The GTO label instruction press Ex label transfers the execution of a running program to the program line containing that label wherever it may be The program continues running from the new location and never automatically returns to its point of origination so GTO is not used for subroutines For example consider the Curve Fitting program in chapter 16 The GTO 2 instruction branches execution from any one of three independent initializing routines to LBL Z the routine that is the common entry point into the heart of the program Programming Techniques 13 5 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm S41 LBL Can start here SaScTaz 7 Branches to Z Can start here LHi LBL L LAS CTO F gt Branches to Z E81 LELE Can start here EAS CTO F EO Branches to Z 781 LEL F PE Branch to here Using GTO from the Keyboard You can use EX to move the program pointer to a specified label or line number without starting program execution B ToPRGHM TOP EN E TES J B Toaline number EX CJ label nn nn lt 100 For example EX CJ A05 W Toalabel EN label but only if program entry is not active no program lines displayed PRGM off For example ER A 13
201. ing the integral of an equation or program This might take a while A running SOLVE or FN operation was interrupted by pressing or R S Data error E Attempted to calculate combinations or permutations with r n with non integer r or n or with n 21017 E Attempted to use a trigonometric or hyperbolic function with an illegal argument with x an odd multiple of 90 or ASIN with x lt 1 or x 1 with xx 1 or x2 1 B with x 1 A syntax error in the equation was detected during equation evaluation SOLVE or J FN Attempted a factorial or gamma operation with x as a negative integer Exponentiation error m Attempted to raise O to the Oh power or to a negative power E Attempted to raise a negative number to a non integer power E Attempted to raise complex number O i O to a number with a negative real part Attempted an operation with an indirect address but the number in the index register is invalid i 34or amp i 1 Attempted to take a logarithm of zero or O iO Attempted to take a logarithm of a negative number All of user memory has been erased see page B 3 The calculator has insufficient memory available to do the operation See appendix B The condition checked by a test instruction is not true Occurs only when executed from the keyboard Size 177 x 25 2 cm E HUHERISTEHT HU LABELS HO ROOT FHO OVERFLO M PROM TOP RUA IAG SELECT FH SOL
202. iques 13 7 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Tests of Comparison x y x 0 There are 12 comparisons available for programming Pressing EX or F displays a menu for one of the two categories of tests m x y for tests comparing x and y W x 0 for tests comparing x and O Remember that x refers to the number in the X register and y refers to the number in the Y register These do not compare the variables X and Y Select the category of comparison then press the menu key for the conditional instruction you want The Test Menus x y x 0 for x z y for x40 lt for x lt y lt for x lt 0 lt for x lt y for x lt 0 gt for x gt y gt for x gt 0 gt for x zy 2 for x20 for x y for x 0 It you execute a conditional test from the keyboard the calculator will display TES or H Example The Normal and Inverse Normal Distributions program in chapter 16 uses the x lt y conditional in routine T Program Lines Description Tad Calculates the correction for X guess Tig STO Adds the correction to yield a new X guess Til ABS T 13 8 Programming Techniques File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Tis s lt Tests to see if the correction is significant Tid GTOT Goes back to start of loop if correction is signiticant Continues if correction is not significant
203. ish to estimate Y based on x key in x at the X value prompt TI 12 then press to see y 17 If you wish to estimate x based on y press until you see the 1 value prompt key in y then press to see X 87 For more estimations go to step lO or 11 13 For a new case go to step 2 Variables Used B Regression coefficient y intercept of a straight line 16 8 Statistics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm also used for scratch M Regression coefficient slope of a straight line Correlation coefficient also used for scratch 7 X The x value of a data pair when entering data the hypothetical x when projecting Y or X x estimate when given a hypothetical y Y The y value of a data pair when entering data the hypothetical y when projecting x or y y estimate when given a hypothetical x i Index variable used to indirectly address the correct X Y projection equation Statistics registers Statistical accumulation and computation Example 1 Fit a straight line to the data below Make an intentional error when keying in the third data pair and correct it with the undo routine Also estimate y for an x value of 37 Estimate x for a y value of 101 X 40 5 38 6 37 9 36 2 35 1 34 6 Y 104 5 102 1 00 97 5 95 9 94 Keys Display Description S 471 6688 Starts straight line routine 40 5 1 value Enters x value of data pair 104 5 472 686
204. ister in simple ways These functions are primarily used in programming PARTS Menu Integer part Removes the fractional part of x and replaces it with zeros For example the integer part of 14 2300 is 14 000 Fractional part Removes the integer part of x and replaces it with zeros For example the fractional part of 14 2300 is 0 2300 Absolute value Replaces x with its absolute value The RND function EX rounds x internally to the number of digits specified by the display format The internal number is represented by 12 digits Refer to chapter 5 for the behavior of RND in Fraction display mode Names of Function You might have noticed that the name of a function appears in the display when you press and hold the key to execute it The name remains displayed for as long as you hold the key down For instance while pressing x the display shows SRT SQRT is the name of the function as it will appear in program lines and usually in equations also 4 14 Real Number Functions File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 2 Fractions Fractions in chapter 1 introduces the basics about entering displaying and calculating with fractions E To enter a fraction press L twice after the integer part and between the numerator and denominator To enter 2 2 8 press 2 LJ 3 LJ 8 To enter 8 press LJ 5 LJ 8 or 5 LJ C 8 m To turn Fraction display mode on and o
205. l 3 GZ ENTER 4 EX part 2 HRA Ez A 2586 z2 z3 13 23 Z z2 z3 E 2 5000 3 BAHA Result is 2 5 i 9 Evaluate 4 i 2 5 3 i 2 3 Do not use complex operations when calculating just one part of a complex number Keys Display Description CJ 2 5 GA ENTER 4 4088 Enters imaginary part of first complex number as a traction 4 4 90868 Enters real part of first complex number 2 CO 3 GZ ENTER 6 6667 Enters imaginary part of second complex number as a traction 3 Ex 11 7333 Completes entry of second number and then multiplies the two complex numbers 3 8667 Result is 11 7333 i 3 8667 Evaluate ez where z 1 i Use EN CMPLX to evaluate z 2 enter 2 as 2 i Q Keys Display Description Operations with Comb Numbers 9 5 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Intermediate result of 0 2 E i EEEE EX A STT Real part of final results 8 4794 Final result is 0 8776 i 0 4794 Using Complex Number in Polar Notation Many applications use real numbers in polar form or polar notation These forms use pairs of numbers as do complex numbers so you can do arithmetic with these numbers by using the complex operations Since the HP 32Sll s complex operations work on numbers in rectangular form convert polar form to rectangular form using We before executing the complex operation then convert the result
206. l root finder Key in F the order of the polynomial and press At each prompt key in the coefficient and press R S You re not prompted for the highest order coefficient it s assumed to be 1 You must enter O for coefficients that are O Coefficient A must not be O ai adi c Terms mid Coefficients x3 x2 6 Alter you enter the coefficients the first root is calculated A real root is displayed as X real value A complex root is displayed as 7 real part Complex roots always occur in pairs of the for u i v and are labeled in the output as real part and i imaginary part which you ll see in the next step 7 Press repeatedly to see the other roots or to see i imaginary part the imaginary part of a complex root The order of the polynomial is same as the number of roots you get 8 For a new polynomial go to step 3 A through E Coefficients of tints of polynomial scratch Order of polynomial scratch Scratch Pointer to polynomial coefficients The value f a real root or the real part of complex root The imaginary part of a complex root also used as are index variable Mathematics Programs 15 29 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Example 1 Find the roots of x x4 101x3 101x2 100x 100 Q Keys Display P F value 9 E value I LU value 101 C7 value 101 E value 100 H value 100 J R5 21 8888 s i HHHH R S s BBA S 16
207. lates R cos P and R sin P Stores Z R cos P Calculates R sin P cos T and R sin P sin T Saves X R sin P cos T Mathematics Programs 15 3 Size 17 7 x 25 2 cm Program Listing Program Lines Description Pla xian Pi4 STO Y Saves Y R sin P sin T P15 GTO F Loops back for another display of polar form Checksum and length D518 022 5 E i LEL E Defines the beginning of the vector enter routine Ea 2 RCL X Copies values in X Y and Z to U Vand W respectively E i STO U EH4 ECL Y EHS STU V EHE ECL Z EH STU H Eas GTO B Loops back for polar conversion and display input Checksum and length 1032 012 0 Ai LBL X Detines beginning of vector exchange routine B2 RCL x Exchanges X Y and Z with U V and W respectively ABS Ae U AHS STU x abo ROL Y ABE xi aby STO Y Abs ROL Z ABD Ae H Ale STO Z 11 GTO Q Loops back for polar conversion and display input Checksum and length DACE 016 5 A i LEL A Defines beginning of vector addition routine Hee RCL amp HS ROL U 15 4 Mathematics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Program Listing Program Lines Description Aa4 STOR Saves X U in X HS ECL V Hoe RCL Y Hey STU Y Saves V Yin Y HHS ECL Z ARABS ECL H Hib STO Z Saves Z Win Z Aii CTO Q Loops back for polar conversion and display input Checksum and length 641B 016 5 S iLBL Detines the beginning of
208. lator Operation Use the following guidelines to determine if the calculator is working properly Test the calculator atter every step to see if its operation has been restored If your calculator requires service refer to page A 7 The calculator won t turn on steps 1 4 or doesn t respond when you press the keys steps 1 3 Reset the calculator Hold down the key and press LN It may be necessary to repeat these reset keystrokes several times 2 Erase memory Press and hold down LC then press and hold down both and Memory is cleared and the MEMORY CLEAR message is displayed when you release all three keys Remove the batteries see Changing the Batteries and lightly press a coin against both battery contacts in the calculator Replace the batteries and turn on the calculator It should display MEMORY LL ERE Install new batteries see Changing the Batteries a 4 If these steps fail to restore calculator operation it requires service E Ifthe calculator responds to keystrokes but you suspect that it is malfunctioning 1 Do the self test described in the next section If the calculator fails the self test it requires service 2 If the calculator passes the self test you may have made a mistake operating the calculator Reread portions of the manual and check Answers to Common Questions page A 1 3 Contact the Calculator Support Department The address and phone number are li
209. layed B Display a labeled program Press EX while the label is displayed mM Delete specific programs Press EX while the label is displayed mM See the checksum associated with a given program segment Press Wz SHOW The catalog shows you how many bytes of memory each labeled program segment uses The programs are identified by program label LEL C H l 5 where 61 5 is the number of bytes used by the program Simple Programming 12 21 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i Clearing One or More Programs To clear a specific program from memory 1 Press EX FGM and display using EX and EX the label of the program 2 Press EH CLEAR 3 Press to cancel the catalog or to back out To clear all programs from memory 1 Press EX to display program lines PRGM annunciator on 2 Press EX FGM to clear program memory 3 The message CL FGMS Y H prompts you for confirmation Press 4 Press EX to cancel program entry Clearing all of memory EX ALL also clears all programs The Checksum The checksum is a unique hexadecimal value given to each program label and its associated lines until the next label This number is useful for comparison with a known checksum for an existing program that you have keyed into program memory If the known checksum and the one shown by your calculator are the same then you have correctly entered all
210. limits of integration lower limit first Wes COSCXxSINHCT2 Displays the current equation F3 FH 4 Prompts for the variable of integration T 472 6688 Prompts for value of X 3 INTEGRATING x 3 Starts integrating and 0 870 calculates the result for MU O Wes s 0 260 The final result for J o 3 8 4 Integrating Equations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Example Sine Integral Certain problems in communications theory for example pulse transmission through idealized networks require calculating an integral sometimes called the sine integral of the form Find Si 2 Enter the expression that defines the integrand s function sinx X If the calculator attempted to evaluate this function at x O the lower limit of integration an error DIVIDE BY amp would result However the integration algorithm normally does not evaluate functions at either limit of integration unless the endpoints of the interval of integration are extremely close together or the number of sample points is extremely large Keys Display Description Wea The current equation Selects Equation mode or EH LIST TOP X SIHCXEB Starts the equation Wea SIHCEON The closing right parenthesis is required in this case RCL X SIHCES EB SIN HI H Terminates the equation Wes CE 4919 669 4 Checksum and length Leaves Equation mode Now integrate this function with respect
211. ll then see the confirmation prompt CLR 1 20 Getting Started File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm E ALL Y H which safeguards against the unintentional clearing of memory 2 Press i yes Getting Started 1 21 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 2 The Automatic Memory Stack This chapter explains how calculations take place in the automatic memory stack You do not need to read and understand this material to use the calculator but understanding the material will greatly enhance your use of the calculator especially when programming In part 2 Programming you will learn how the stack can help you to manipulate and organize data for programs What the Stack Is Automatic storage of intermediate results is the reason that the HP 32SIl easily processes complex calculations and does so without parentheses The key to automatic storage is the automatic RPN memory stack HP s operating logic is based on an unambiguous parentheses free mathematical logic known as Polish Notation developed by the Polish logician Jan Lukasiewicz 1878 1956 While conventional algebraic notation places the operators between the relevant numbers or variables Ehukasiewicz s notation places them before the numbers or variables For optimal efficiency of the stack we have modified that notation to specify the operators after the numbers H
212. low The ending value of f x is the value of the potential asymptote mM The search is concentrated in a local flat region of the function see figure c below The ending value of f x is the value of the function in this region f x f x f x Case Where No Root Is Found The SOLVE operation returns a math error if an estimate produces an operation that is not allowed for example division by zero a square root of a negative number or a logarithm of zero Keep in mind that SOLVE can generate estimates over a wide range You can sometimes avoid math errors by using good guesses If a math error occurs press unknown variable or Wz variable to see the value that produced the error More about Solving C 9 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Example A Relative Minimum Calculate the root of this parabolic equation x 6x 13 0 It has a minimum at x 3 Enter the equation as an expression Keys Display Description r3 Selects Equation mode X 2 Enters the equation 6 X 13 4 Z xX 13 r3 Checksum and length CE SFCC 15 Cancels Equation mode Now solve to find the root Keys Display Description O X 10 iB Your initial guesses for the root 3 W 2 xMTlZ Selects Equation mode displays the equation r3 X HO FOOT FHD Search fails with guesses O and 10 F3 3 888988188881 Displays the final estimate of x T 3 48666469443 Previous estimate
213. m J i LEL J T z JH3 EHTER JH4 2 JBS RCL THG xiy Tar RTH THe 4 Ta Jif 7 Jii x27 I12RV 113 RTH Checksum and length 23C2 019 5 You can subsequently delete line JO3 to save memory More about Solving C 13 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm a Solve for X using initial guesses of 10 9 and 10 8 Keys Display Description E 8 X 1E 8_ Enters guesses E 8 Wes J 1 BHB8BmBE 8 Selects program J as the function Wes X HO ROOT FHD No root found using very small guesses near zero thereby restricting the search to the flat region of the function i BAAGE S The last two estimates are far 8 6625 apart and the final value of f x is 1 8888 large If you use larger guesses then SOLVE can find the roots which are outside the flat region at x 2 and x 2 Round Off Error The limited 12 digit precision of the calculator can cause errors due to rounding off which adversely affect the iterative solutions of SOLVE and integration For example x 1 109 10 20 has no roots because f x is always greater than zero However given initial guesses of 1 and 2 SOLVE returns the answer 1 0000 due to round off error Round off error can also cause SOLVE to fail to find a root The equation x 7 0 has a root at 4 7 However no 12 digit number exactly equals 7 so the calculator can never make the function equal to zero Further
214. m the graph of f x over the interval of integration D 4 More about Integration File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm f x The graph is a spike very close to the origin Because no sample point happened to discover the spike the algorithm assumed that f x was identically equal to zero throughout the interval of integration Even if you increased the number of sample points by calculating the integral in SCI 11 or ALL format none of the additional sample points would discover the spike when this particular function is integrated over this particular interval For better approaches to problems such as this see the next topic Conditions That Prolong Calculation Time Fortunately functions exhibiting such aberrations a fluctuation that is uncharacteristic of the behavior of the function elsewhere are unusual enough that you are unlikely to have to integrate one unknowingly A function that could lead to incorrect results can be identified in simple terms by how rapidly it and its low order derivatives vary across the interval of integration Basically the more rapid the variation in the function or its derivatives and the lower the order of such rapidly varying derivatives the less quickly will the calculation finish and the less reliable will be the resulting approximation Note that the rapidity of variation in the function or its low order derivatives must be determined with respe
215. ma function 4 12 go to See GIO grads angle units 4 3 A 2 Grandma Hinkle 1 1 7 grouped standard deviation 16 19 GTO finds PRGM TOP 12 6 12 21 13 5 finds program labels 12 10 12 21 13 5 finds program lines 12 20 12 21 13 5 GTO 13 4 13 16 guesses for SOLVE 7 2 7 6 7 7 7 10 14 5 H help about calculator A 1 hexadecimal numbers See hex Size 17 7 x 25 2 cm numbers HEX annunciator 10 1 hex numbers See numbers arithmetic 10 3 converting to 10 1 range of 10 6 typing 10 1 Horner s method 12 26 humidity limits for calculator A 2 hyperbolic functions 4 6 i 3 8 13 19 i 3 8 13 19 13 20 13 24 imaginary part complex numbers 9 1 9 2 indirect addressing 13 19 13 20 132 INPUT always prompts 13 10 entering program data 12 12 in integration programs 14 8 in SOLVE programs 142 responding to 12 14 showing hidden digits 12 14 integer part function 4 15 integration accuracy 8 2 8 6 8 7 D2 base mode 12 25 14 10 difficult functions D 2 D 7 display format 8 2 8 6 8 8 evaluating programs 14 7 how it works D 1 in programs 14 9 interrupting B 3 File name 32sii Manual E 0424 Printed Date 2003 4 24 limits of 8 2 14 7 D 7 memory usage 8 2 1222 B2 B 3 purpose 8 1 restrictions 14 10 results on stack 82 8 7 resuming 14 7 stopping 82 14 7 subintervals D 7 D 9 time required 8 6 D 7 transforming variables D 9 uncertainty of r
216. mber is not prime tries next possibility aber ROL FP sls SORT AHS RCL D HIE xv bur to see whether all possible factors have been tried 17 8 Miscellaneous Programs and Equations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Program Lines Description 411 GTO Y If all factors have been tried branches to the display routine 122 Calculates the next possible factor D 2 alfa 570 O 414 GTO X Branches to test potential prime with new factor Checksum and length O61F 021 0 Flags Used None Memory Required 61 bytes 45 for program 16 for variables Program Instructions 1 Key in the program routines press when done 2 Key in a positive integer greater than 3 3 Press P to run program Prime number P will b e displayed 4 To see the next prime number press R S Variables Used P Prime value and potential prime values D Divisor used to test the current value of P Remarks No test is made to ensure that the input is greater than 3 Example What is the first prime number after 789 What is the next prime number Keys Display Description Miscellaneous Programs and Equations 17 9 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm E 789 P P 797 4888 Calculates next prime number atter 789 P 889 4088 Calculates next prime number atter 797 17 10 Miscellaneous Programs and Equations File name 32sii Manual E 0424
217. more the C 14 More about Solving File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm function never changes sign SOLVE returns the message HO ROOT FHOD However the final estimate of x press to see it is the best possible 12 digit approximation of the root when the routine quits Underflow Underflow occurs when the magnitude of a number is smaller than the calculator can represent so it substitutes zero This can affect SOLVE results For example consider the equation x whose root is infinite in value Because of underflow SOLVE returns a very large value as a root The calculator cannot represent infinity anyway More about Solving C 15 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm D More about Integration This appendix provides information about integration beyond that given in chapter 8 How the Integral Is Evaluated The algorithm used by the integration operation JFH dx calculates the integral of a function f x by computing a weighted average of the function s values at many values of x known as sample points within the interval of integration The accuracy of the result of any such sampling process depends on the number of sample points considered generally the more sample points the greater the accuracy if f x could be evaluated at an infinite number of sample points the algorithm could neglecting the limitation imposed b
218. name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Keys for Clearing Description Backspace B Keyboard entry mode Erases the character immediately to the left of the digit entry cursor or backs out of the current menu Menus are described in Using Menus on page 1 4 If the number is completed no cursor clears the entire number Equation entry mode Erases the character immediately to the left of I the equation entry cursor If a number entry in your equation is complete erases the entire number If the number is not complete erases the character immediately to the left of the number entry cursor changes back to E when number entry is complete also clears error messages and deletes the current program line during program entry Clear or Cancel Clears the displayed number to zero or cancels the current situation such as a menu a message a prompt a catalog or Equation entry or Program entry mode Getting Started 1 3 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i Keys for Clearing continued Key ES Description The CLEAR menu x VARS ALL Contains options for clearing x the number in the X register all Data all variables all of memory or all statistical data It you select ALL a new menu CLR ALL Y H is displayed so you can verity your decision before erasing everything in memory
219. nd XEQ Their actions differ only in how they evaluate assignment equations E returns the value of the equation regardless of the type equation m returns the value of the equation unless it s an assignment type equation For an assignment equation returns the value f the right side only and also enters that value into the variable on the left side it stores the value in the variable Entering and Evaluating Equations 6 11 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm The following table shoves the two ways to evaluate equations Type of Equation Result for Result for Equality g x f x g x f x Example x y2 r Dayar Assignment y f x f x y f x Example A 2 O 5x bxh O5xbxh A e seb Expression f x Example x 1 x Also stores the result in the left hand variable A for example To evaluate an equation 1 Display the desired equation See Displaying and Selecting Equations above 2 Press or XEQ The equation prompts for a value for each variable needed If you ve changed the number base it s automatically changed back to base 10 3 For each prompt enter the desired value m If the displayed value is good press R S E If you want a different value type the value and press R S Also see Responding to Equation Prompts later in this chapter The evaluation of an equation takes no values from the stack it uses only
220. nd a Pole Example Discontinuous Function Find the root of the equation IP x 2 1 5 Enter the equation Keys Display Description ER Selects Equation mode E PARTS IF Enter the equation RCL X Wea U Ea 1 5 ENTER IPCe 3 1 5 Fa SHOW CK 8H55 Hi 8 Checksum and length C 6 More about Solving File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm Cancels Equation mode Now solve to find the root Keys Display Description O X5 5 Your initial guesses for the root Wes IFC 3 1 5 Selects Equation mode displays the equation Wes X SOLVING Finds a root with guesses O A HHEH and 5 r3 i 29999999999 Shows root to 11 decimal places ce 2 Baamgaaagaas The previous estimate is slightly bigger 5 B88 f x is relatively large Note the difference between the last two estimates as well as the relatively large value for f x The problem is that there is no value of x for which f x equals zero However at x 1 99999999999 there is a neighboring value of x that yields ant opposite sign for f x Example A Pole Find the root of the equation 120 x 6 As x approaches 4 6 f x becomes a very large positive or negative number Enter the equation as an expression Keys Display Description F3 Selects Equation mode More about Solving C 7 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm u X LE
221. nd the other two is less than the uncertainty tolerable in the final approximation the calculations ends leaving the current approximation in the X register and its uncertainty in the Y register It is extremely unlikely that the errors in each of three successive approximations that is the differences between the actual integral and the approximations would all be larger than the disparity among the approximations themselves Consequently the error in the final approximation will be less than its uncertainty provided that f x does not vary rapidly Although we can t know the error in the final approximation the error is extremely unlikely to exceed the displayed uncertainty of the approximation In other words the uncertainty estimate in the Y register is an almost certain upper bound on the difference between the approximation and the actual integral Conditions That Could Cause Incorrect Results Although the integration algorithm in the HP 32SIl is one of the best available in certain situations it like all other algorithms for numerical integration might give you an incorrect answer The possibility of this occurring is extremely remote The algorithm has been designed to give accurate results with almost any smooth function Only for functions that exhibit extremely erratic behavior is there any substantial risk of obtaining an inaccurate answer Such functions rarely occur in problems related to actual physical si
222. ndex value to its original value Jas RCL Y JH4 RCL B JH3 RCL M IH6 irs Ja v Calculates x Y B 1 M JOS RTH Returns to the calling routine Checksums and length 7139 012 0 Flags Used Flag O is set if a natural log is required of the X input Flag 1 is set if a natural log is required of the Y input Statistics Programs 16 7 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i Memory Required 270 bytes 174 for program 96 for data statistic registers 48 Program instructions l 2 6 7 8 9 Key in the program routines press when done Press and select the type of curve you wish to fit by pressing E Sfor a straight line mL for a logarithmic curvy mE for an exponential curve or W P for a power curve Key in x value and press R S Key in y value and press R S Repeat steps 3 and 4 for each data pair If you discover that you have made an error atter you have pressed in step 3 with the value prompt still visible press again displaying the value prompt and press U to undo remove the last data pair If you discover that you made an error after step 4 press U In either case continue at step 3 After all data are keyed in press R to see the correlation coefficient R Press to see the regression coefficient B Press to see the regression coefficient M Press to see the X value prompt for the X Y estimation routine 10 ff you w
223. nted Date 2003 4 24 Size 17 7 x 25 2 cm Contents Part 1 Basic Operation 1 Getting Started Important Preliminaries cccecccceccceeecceeceeeeeeeeeeaneees 1 1 Turning the Calculator On and Off 1 1 Adjusting Display Contrast ccccceeccceeeeceeeeeeeenees 1 1 Highlights of the Keyboard an Display 1 1 Shifted Keys 1 1 Alpha Keys ssssesssessee m nnn 1 2 Backspacing and Clearing ssesseeesss 1 2 IS NAG EIU PNE Eo 1 4 EU EHE Lost scenes erencar anes EE E ual RUP Susa 1 7 ANNUNCIO eessensetdntextia teen evie sum equ UN 2E SEEN 1 7 Keying in Numbers sess 1 9 Making Numbers Negotive cccccceseceeseeeeeseeeees 1 10 Exponent of Jen cate cnosacaasenecsucenmacapsscnonmecsacereatsanmeess 1 10 Understanding Digit Entry ccccseccessecceeeeeeeenees 1 11 Range Number and OVERFLOW 000ccce neces 1 12 Doing Arithmetic eesssesssssesseeene eene 1 12 One Number Functions 0cccceccceeeceeesceeeeeeeneees 1 12 Two Number Functions 00ccccseecceeeeeseseeceeneeeees 1 13 Controlling the Display Format cccsccceceeceeseeeennees 1 14 Periods and Commas in Numbers 1 14 Contents 1 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Number of Decimal Places sssssss
224. ntry Printed Date 2003 4 24 Size 177 x 25 2cm Now find the volume and surface area of a cylinder with a radius of 2 2 cm and a height of 8 cm Keys Display Description C F7 value Starts executing C prompts for R It displays whatever value happens to be in R 2L 10 2 H value Enters 2 2as a fraction Prompts for H 8 VOL AREA Message displayed u 157 796 Volume in cm 5 164 9336 Surface area in cm2 Displaying Information without Stopping Normally a program stops when it displays a variable with VIEW or displays an equation message You normally have to press to resume execution If you want you can make the program continue while the information is displayed If the next program line after a VIEW instruction or a viewed equation contains a PSE pause instruction the information is displayed and execution continues after a 1 second pause In this case no scrolling or keyboard input is allowed The display is cleared by other display operations and by the RND operation if flag 7 is set rounding to a fraction Press Wea to enter PSE in a program The VIEW and PSE lines or the equation and PSE lines are treated as one operation when you execute a program one line at a time Simple Programming 12 17 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Stopping or Interrupting a Program Programming a Stop or Pause STOP PSE m Pressing run
225. ntry A Accuracy Indicators The accuracy of a displayed fraction is indicated by the A and WV annunciators at the top of the display The calculator compares the value of the fractional part of the internal 12 digit number with the value of the displayed fraction E f no indicator is lit the fractional part of the internal 12 digit value exactly matches the value of the displayed fraction W It V is fit the fractional part of the internal 12 digit value is slightly less than the displayed fraction the exact numerator is no more than 0 5 below the displayed numerator Fractions 5 3 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm u This diagram shows how the displayed fraction relates to nearby values A means the exact numerator is a little above the displayed numerator and V means the exact numerator is a little below Y 0 7 16 07 16 407 16 Mw lx i eM F p 6 6 5 7 7 5 8 Js 16 T 16 iy 0 40625 0 43750 0 46875 This is especially important if you change the rules about how fractions are displayed See Changing the Fraction Display later For example if you force all fractions to have 5 as the denominator then 2 3 is displayed as A 4 3 5 because the exact fraction is approximately 2 2333 5 a little above 3 5 Similarly 2 3 is displayed as A 8 35 because the true numerator is a little above 3 If you press Ex VAR to view the VAR catalog the A Y
226. ntry mode is riot active if no program lines are displayed you can also move the program pointer by pressing E label Canceling Program entry mode does not change the position of the program pointer Memory Usage Each program line uses a certain amount of memory W Numbers use 9 5 bytes except for integer numbers from O through 254 12 20 Simple Programming File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm which use only 1 5 bytes All other instructions use 1 5 bytes E Equations use 1 5 bytes plus 1 5 bytes for each function plus 9 5 or 1 5 bytes for each number Each and each uses 1 5 bytes except for prefix functions If during program entry you encounter the message MEMORY FULL then there is not enough room in program memory for the line you just tried to enter You can make more room available by clearing programs or other data See Clearing One or More Programs below or Managing calculator Memory in appendix B The Catalog of Programs MEM The catalog of programs is a list of all program labels with the number of bytes of memory used by each label and the lines associated with it Press EX FGM to display the catalog and press Ex or EX to move within the list You can use this catalog to mM Review the labels in program memory and the memory cost of each labeled program or routine B Execute a labeled program Press or while the label is disp
227. numbers in any of the four bases do arithmetic in any base and display results in any base When writing programs that use numbers in a base other than 10 set the base mode both as the current setting for the calculator and in the program as an instruction Simple Programming 12 23 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i Selecting a Base Mode in a Program Insert a BIN OCT or HEX instruction into the beginning of the program You should usually include a DEC instruction at the end of the program so that the calculator s setting will revert to Decimal mode when the program is done An instruction in a program to change the base mode will determine bow input is interpreted and how output looks during and affer program execution but it does not affect the program lines as you enter them Equation evaluation SOLVE and J FN automatically set Decimal mode Numbers Entered in Program Lines Before starting program entry set the base mode The current setting for the base mode determines the base of the numbers that are entered into program lines The display of these numbers changes when you change the base mode Program line numbers always appear in base 10 An annunciator tells you which base is the current setting Compare the program lines below in the left and right columns All non decimal numbers are right justified in the calculator s display Notice how the number 13 appears a
228. numbers in the equation and variable values The value of the equation is returned to the X register The LAST X register isn t affected Using ENTER for Evaluation If an equation is displayed in the equation list you can press to evaluate the equation If you re in the process of typing the equation pressing only ends the equation it doesn t evaluate it 6 12 Entering and Evaluating Equations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm m f the equation is an assignment only the right hand side is evaluated The result is returned to the X register and stored in the left hand variable then the variable is VIEWed in the display Essentially finds the value of the left hand variable W f the equation is an equality or expression the entire equation is evaluated just as it is for XEQ The result is returned to the X register Example Evaluating an Equation with ENTER Use the equation from the beginning of this chapter to find the volume of a 35 mm diameter pipe that s 20 meters long Keys Display Description We EN W a 25xqxD 2x Displays the desired equation as required 072 5006 Starts evaluating the assignment equation so the value will be stored in V Prompts for variables on the right hand side of the equation Tile current value for D is 2 5000 35 L716 000E Stores D prompts for L whose current value 16 0000 20 1000 Stores L in millimeters calculates V
229. o back to step 3 to enter the correct data 7 When the last data pair has been input press G to calculate and display the grouped standard deviation 8 Press to display the weighted mean of the grouped data 9 To add additional data points press and continue at step 3 To start a new problem start at step 2 Variables Used Data point Data point frequency Data pair counter Grouped standard deviation z nNZ77 x Weighted mean 16 20 Statistics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i Index variable used to indirectly address the correct statistics register Register 28 Summation Lf Register 29 Summation Xxif Register 31 Summation Xxj f Example Enter the following data and calculate the grouped standard deviation Group 2 3 4 5 6 xi 5 8 13 15 22 3 fi 1 7 26 3 A3 73 115 Keys Display Description S value Prompts for the first xi 5 F value Stores 5 in X prompts for first fj 17 H 1 8886 Stores 17 in F displays the counter 475 BAGA Prompts for the second xi 8 F717 BBG Prompts for second fj 26 H 2 BHA Displays the counter 478 PARA Prompts for the third xi 14 F 26 8888 Prompts for the third fi 37 H 3 8888 Displays the counter You erred by entering 14 instead of 13 for x3 Undo your error by executing routine U U H 2 8088 Removes the erroneous data displays the revised counter 714 6886 Prompts tor new third xi 13 F737
230. o compute estimated values for x and y Different subroutines compute x and y for the different models Notice that i is stored and then indirectly addressed in widely separated parts of the program The first four routines S L E P of the program specify the curve fitting model that will be used and assign a number 1 2 3 4 to each of these models This number is then stored during routine Z the common entry point for all models Z STU i Routine Y uses i to call the appropriate subroutine by model to calculate the x and y estimates Line YO3 calls the subroutine to compute y THS SEC 12 13 22 Programming Techniques File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm and line YO8 calls a different subroutine to compute x after i has been increased by 6 THE 6 THY STU THES AERC 12 If i hold Then XEQ i calls To BL A Compute Y for straight line model 2 LBL B Compute Y for logarithmic model 3 LBL C Compute Y for exponential model 4 LBL D Compute Y for power model 7 LBL G Compute x for straight line model 8 LBL H Compute x for logarithmic model 9 LBL Compute x for exponential model 10 LBL J Compute x for power model Example Loop Control With i An index value in i is used by the program Solutions of Simultaneous Equations Matrix Inversion Method in chapter 15 This program uses the looping instructions ISG i and DSE i in conjunction with
231. of the fraction 12 3758 Terminates digit entry displays the number in the current display format If the number you enter has no integer part for example 3 8 just start the number without an integer Keys Display Description s 3155 8 B i8 Enters no integer part 3 LL LJ 8 also works 4 3758 Terminates digit entry displays the number in the current display format FIX 4 1 18 Getting Started File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Displaying Fractions Press EX to switch between Fraction display mode and the current decimal display mode Keys Display Description 12L 3L 8 12348 Displays characters as you key them in 12 3758 Terminates digit entry displays the number in the current display format Ex 12 3 78 Displays the number as a fraction Now add 3 4 to the number in the X register 12 3 8 Keys Display Description L 3L 4 344 Displays characters as you key them in 131 48 Adds the numbers in the X and Y registers displays the result as a fraction EX 13 1258 Switches to current decimal display format Refer to chapter 5 Fractions for more information about using fractions Messages The calculator responds to certain conditions or keystrokes by displaying a message The symbol comes on to call your attention to the message W To clear a message press or Le E To clear a message and perform another function press any other key
232. olar coordinates r and rectangular coordinates x y are measured as shown in the illustration The angle uses units set by the current angular mode A calculated result for 0 will be between 180 and 180 between r and x radians or between 200 and 200 grads To convert between rectangular and polar coordinates 1 Enter the coordinates in rectangular or polar form that you want to convert The order is y x or 0 r 2 Execute the conversion you want press Ex rectangular to polar or F3 polar to rectangular The converted coordinates occupy the X and Y registers 3 The resulting display the X register shows either r polar result or x rectangular result Press to see 0 or y Real Number Functions 4 7 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm fo N Y y X x Example Polar to Rectangular Conversion ale Oo r y x In the following right triangles find sides x and y in the triangle on the left and hypotenuse r and angle 8 in the triangle on the right 10 r y 4 X 3 Keys Display Description ER OG Sets Degrees mode 30 10 F 5 6683 Calculates x 5 686 Displays y 4 3 Ex 5 BHAG Calculates hypotenuse r 53 1381 Displays 0 4 8 Real Number Functions File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Example Conversion with Vectors Engineer P C Bard has determined that in the RC circuit shown
233. ons In chapter 6 you saw how you can use to find the value of the left hand variable in an assignment type equation Well you can use SOLVE to find the value of any variable in any type of equation For example consider the equation x 3y 10 If you know the value of y in this equation then SOLVE can solve for the unknown x If you know the value of x then SOLVE can solve for the unknown y This works for word problems just as well Markup x Cost Price It you know any two of these variables then SOLVE can calculate the value of the third When the equation has only one variable or when known values are supplied for all variables except one then to solve for x is to find a root of the equation A root of an equation occurs where an equality or assignment equation balances exactly or where an expression equation equals zero This is equivalent to the value of the equation being zero Solving an Equation To solve an equation for an unknown variable 1 Press Wz and display the desired equation If necessary type the equation as explained in chapter under Entering Equations into the Equation List 2 Press fj then press the key for the unknown variable For example press fz X to solve for x The equation then prompts Solving Equations 7 1 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm for a value for every other variable in the equation 3 For each prompt ente
234. or example take Planck s constant 6 6262 x 10 94 1 Key in the mantissa the non exponent part of the number If the mantissa is negative press after keying in its digits 1 10 Getting Started File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm E Keys Display 6 6262 6 6262 2 Press LE Notice that the cursor moves behind the E G 6 E262E 3 Key in the exponent The largest possible exponent is 499 If the exponent is negative press after you key in the E or after you key in the value of the exponent 34 6 6262E 34_ For a power of ten without a multiplier such as 1094 just press LE 34 The calculator displays 1E34 Other Exponent Functions To calculate an exponent of ten the base 10 antilogarithm use EW 10 To calculate the result of any number raised to a power exponentiation use see chapter 4 Understanding Digit Entry As you key in a number the cursor _ appears in the display The cursor shows you where the next digit will go it theretore indicates that the number is not complete Keys Display Description 123 123 Digit entry not terminated the number is not complete It you execute a function to calculate a result the cursor disappears because the number is complete digit entry has been terminated Getting Started 1 11 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 2 11 8985 Digit entry is termina
235. ormal distribution 1 6 12 statistical data See statistics registers clearing 1 4 11 2 correcting 1 2 Index 13 Size 17 7 x 25 2 cm entering 1 1 initializing 11 2 memory usage 1222 B2 one variable 11 2 precision 11 1 sums of variables 11 12 two variable 11 2 statistics calculating 11 4 curve fitting 11 8 16 1 distributions 16 12 grouped data 16 19 one variable data 11 2 operations 1 1 1 two variable data 11 2 statistics menus 1 1 1 1 4 statistics registers See statistical data accessing 11 14 clearing 1 4 11 2 11 13 contain summations 11 1 11 12 11 14 correcting data 11 2 initializing 11 2 memory 11 13 memory usage 1222 B2 no fractions 5 2 viewing 11 12 STO 32 12 12 STO arithmetic 3 5 STOP 12 19 storage arithmetic 3 5 subroutines See routines sums of statistical variables 11 12 syntax equations 6 16 6 20 12 15 Index 14 File name 32sii Manual E 0424 T tangent trig 4 4 9 3 A 2 temperatures converting units 4 12 limits for calculator A 2 testing the calculator A 4 A 5 test menus 13 7 time formats 4 11 time value of money 17 1 transtorming coordinates 15 34 T register 2 5 2 7 trigonometric functions 4 4 9 3 troubleshooting A 4 A 5 turning on and off 1 1 TVM 171 twos complement 10 3 10 5 two variable statistics 11 2 U uncertainty integration 8 2 8 6 8 underflow C 16 units conve
236. ositive binary number Keys Display Description 10 4 Base Conversions and Arithmetic File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 546 EX Hx 222 FFFFFFDDE E BASE BH 118111811118 111111111111 EX DEC 546 BAGA Range of Numbers Enters a positive decimal number then converts it to hexadecimal 2 s complement sign changed Binary version indicates more digits Displays the leftmost window the number is negative since the highest bit is l Negative decimal number The 36 bit word size determines the range of numbers that can be represented in hexadecimal 9 digits octal 12 digits and binary bases 36 digits and the range of decimal numbers 11 digits that can be converted to these other bases Range of Numbers for Base Conversions Base Positive Integer of Largest Magnitude Negative Integer of Largest Magnitude Hexadecimal 7FFFFFFFF Octal 377777777777 Binary 011111111111111111111 TIIITITTITTIIT Decimal 34 359 738 367 800000000 400000000000 100000000000000000000 000000000000000 34 359 738 368 When you key in numbers the calculator will not accept more than the maximum number of digits for each base For example if you attempt to key in a 1O digit hexadecimal number digit entry halts and the A annunciator appears Base Conversions and Arithmetic 10 5 File name 32sii Manual E 0424 Printed Date 2003 4 2
237. pe the flag number Press or to clear the ES or HO response Examples of Fraction Displays The following table shows how the number 2 77 is displayed in the three fraction formats for two c values Fraction How 2 77 Is Displayed Format Most precise 277 100 2 7700 A 10 13 2 7692 s of A2 1051 1365 276 A2 3 4 2 7500 enominator 2 A2 3153 4095 2759 amp 212 16 07500 enominator Fractions 5 7 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm The following table shows how different numbers are displayed in the three fraction formats for a c value of 16 Fraction Number Entered and Fraction Displayed Format x 2 2 3 2 9999 216 55 25 242 422 3 A2 7 11 Most precise 2 Factors of 212 v211 16 A2 5 8 denominator Fixed 2016 2816 Y21116 216 16 A2 10 16 denominator x For a value of 16 Example Suppose a stock has a current value of 48 4 If it goes down 2 8 what would be its value What would then be 85 percent of that value Keys Display Description r3 SF 8 Sets flag 8 clears flag 9 for r3 CF 9 factors of denominator format 8 Pa Sets up fraction format for g increments 48 J1L 4 48 1 4 Enters the starting value 2L 5L J 80 2 45 578 Subtracts the change 85 Fea A38 3x44 Finds the 85 percent value to the nearest g Rounding Fractions If Fraction display mode is active the RND function converts the numb
238. ple Calculating with an Equation Suppose you frequently need to determine the volume of a straight section of pipe The equation is V 25nd l There d is the inside diameter of the pipe and is its length You could key in the calculation over and over for example 25 Fa 2 5 E3 16 LX calculates the volume of 16 inches of 2 2 inch diameter pipe 78 5398 cubic inches However by storing the equation you get the HP 32SIl to remember the relationship between diameter length and volume so you can use it many times Put the calculator in Equation mode and type in the equation using the tollowing keystrokes Keys Display Description r3 EQN LIST TOF Selects Equation mode or the current shown by the EQN annunciator or the current equation Entering and Evaluating Equations 6 1 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i E V 3 U N 25 v 0 25 Wea 2 h vse 2SxnxM D 2 B 25xgpxD 2 L A 25x7x0 2xLi UzB z5xpxD zx F SHOW LE 5836 6 26 6 Begins a new equation turning on the E equation entry cursor turns on the A Z annunciator so you can enter a variable name V types V and moves the cursor to the right Digit entry uses the digit entry cursor ends the number and restores the E cursor lypes scrolls o f the left side of the display Terminates and displays the equation gt shows that part of the equation doesn t fit
239. program line EN 377 It x y executes next program line it xzy skips next program line Displays the x 0 comparison tests F 14 Operation Index File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm menu EX s It xzO executes next program line it x 0 skips the next program line E lt If x lt O executes next program line if x gt 0 skips next program line EN 370 4 It x O executes next program line if x20 skips the next program line EN 370 5 It x gt O executes next program line if x lt O skips the next program line Ex X70 t It x20 executes next program line if x O skips the next program line x x70 It x O executes next program line it x40 skips next program lire Ex 37 7 Returns the mean of y values Xyji n EX L amp 9 Given an x value in the X register returns the y estimate based on the regression line Y m x b EX Rectangular to polar coordinates Converts x y to r 6 Power Returns y raised to the x power Notes 1 Function can be used in equations 2 Function appears only in equations Operation Index F 15 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Index Special characters A 1 21 See backspace key C 1 annunciator 1 1 A2 gt annunciators binary numbers 10 7 equations 6 8 127 12 16 _ See equation entry cur
240. program selected by FN using lower limit of the variable of integration in the Y register and upper limit of the variable if integration in the X register Fa Open parenthesis Starts a quantity associated with a function in an equation F Close parenthesis Ends a quantity associated with a function in an equation variable or variable Value of named variable Wed PARTS ABS Absolute value Returns x EX ACOS Arc cosine Returns cos 1x Et EV ACOS Hyperbolic arc cosine Returns cosh x EX Common exponential Returns 10 raised to the specified power antilogarithm E ALL Selects display of all significant digits EX Arc sine Operation Index F 3 Size 177 x 25 2 cm u ASINH ATAN ATANH E BIN C C CF n Ex CLEAR Em ALL Em PM Returns sin x Ex HYP i ASIN Hyperbolic arc sine Returns sinh x EX Arc tangent Returns tan 7 x E E Hyperbolic arc tangent Returns tanh x a LE i Returns the y intercept of the regression line Y mx Displays the base conversion menu EN BASE EH Selects Binary base 2 mode Turns on calculator clears x clears messages and prompts cancels menus cancels catalogs cancels equation entry cancels program entry halts execution of an equation halts a running program EX Denominator Sets denominator limit for displayed
241. quadratic polynomial x x 6 0 Keys Display Description P F value Starts the polynomial root finder prompts for order 2 F value Stores 2 its F prompts for B F value Stores 4 its B prompts for A 6 x4 3 8888 A did Coordinate Transformations Stores 6 its A calculates the first root Calculates the second root This program provides two dimensional coordinate translation and rotation File name 32sii Manual E O424 Mathematics Programs 15 31 Printed Date 2003 4 24 Size 177 x 25 2 cm The following formulas are used to convert a point P from the Cartesian coordinate pair x y in the old system to the pair u v in the new translated rotated system u x m cos y n sin v y n cos 0 y n sin8 The inverse transformation is accomplished with the formulas below x ucos0 vsin0 m y usin c vcosOc n The HP 32SIl complex and polar to rectangular functions make these computations straightforward 15 32 Mathematics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm y y Old coordinate NU AN A system YX TaN 0 0 4 a X New coordinate system Program Listing Program Lines Description Dai LEL D This routine defines the new coordinate system Oa IHPLIT H Prompts for and stores M the new origin s x coordinate D amp s INPUT H Prompts for and stores N the new origin s y coordinate D amp 84 IHPUT T Prompts for an
242. r the desired value m tf the displayed clue is the one you want press R S E If you want a different clue type or calculate the value and press R S For details see Responding to Equation Prompts in chapter 6 You can half a running calculation b pressing or R S When the root is found it s stored in the unknown variable and the variable value is VIEWed in the display In addition the X register contains the root the Y register contains the previous estimate and the Z register contains the value of the equation at the root which should be zero For some complicated mathematical conditions a definitive solution cannot he found and the calculator displays HO ROOT FOUND See Verifying the Result later in this chapter and Interpreting results and When SOLVE Cannot Find Root in appendix C For certain equations it helps t provide one or two initial guesses for the unknown variable before solving the equation This can speed up the calculation direct the answer toward realistic solution and find more than one solution if appropriate See Choosing Initial Guesses later in this chapter Example Solving the Equation of Linear Motion The equation of motion for a free falling object is d vot l 2g where d is the distance vo is the initial velocity t is the time and g is the acceleration due to gravity Type in the equation Keys Display Description EX Clears memory RLL Y r3 EGQH LIST TOP
243. ram lines starting with the original line AO5 are moved down and renumbered accordingly To edit an equation in a program line 1 Locate and display the program line containing the equation 2 Press J This turns on the B editing cursor but does riot delete anything in the equation 3 Press as required to delete the function or number you want to change Simple Programming 12 19 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm then enter the desired corrections 4 Press to end the equation Program Memory Viewing Program Memory Pressing toggles the calculator into and out of program entry PRGM annunciator on program lines displayed When Program entry mode is active the contents of program memory are displayed Program memory starts at PEGM TOP The list of program lines is circular so you can wrap the program pointer froze the bottom to the top and reverse While program entry is active there are three ways to change the program pointer the displayed line mM Use the arrow keys E and ES t J Pressing EX at the last line wraps the pointer around to FRGM TOP while pressing EN at PRGM TOP wraps the pointer around to the last program line To move more than one line at a time scrolling continue to hold the or key Press CJ LJ to move the program pointer to PEGM TOF Press label nn to move to a labeled line number less than 100 It Program e
244. re equal to four significant digits Keys EN MODES RD 5 CJ 7 ENTER r3 7 X COS EA MODES Di 128 57 Display WH rlds H 6235 H 6235 H 6235 4 4 Real Number Functions File name 32sii Manual E 0424 Printed Date 2003 4 24 Description Sets Radians mode RAD annunciator on 5 7 in decimal format Cos 5 7 n Switches to Degrees mode no annunciator Calculates cos 128 57 which is the same as cos 5 7 n Size 17 7 x 25 2 cm Programming Note Equations using inverse trigonometric functions to determine an angle 0 often look something like this 0 arctan y x If x O then y x is undefined resulting in the error DIVIDE BY amp For a program then it would be more reliable to determine 0 by a rectangular to polar conversion which converts x y to r See Coordinate Conversions later in this chapter Hyperbolic Functions With x in the display Hyperbolic sine of x SINH EX Hyperbolic cosine of x COSH EX Hyperbolic tangent of x TANH EX Hyperbolic arc sine of x ASINH E EN Hyperbolic arc cosine of x ACOSH EX EN Hyperbolic arc tangent of x ATANH a EN Percentage Functions The percentage functions are special compared with X and X because they preserve the value of the base number in the Y register when they return the result of the percentage calculation in the X register You can then car
245. re reduced as much as possible For example if you re studying math concepts with fractions you might want any denominator to be possible c value is 4095 This is the default fraction format Factors of denominator Fractions have only denominators that are factors of the c value and they re reduced as much as possible For example if you re calculating stock prices you might want to see 33 1 14 and 37 78 c value is 8 Or if the c value is 12 possible denominators are 2 3 4 6 and 12 WB Fixed denominator Fractions always use the c value as the denominator they re not reduced For example if you re working with time measurements you might want to see 1 25768 c value is 60 To select a fraction format you must change the states of two flags Each flag can be set or clear and in one case the state of flag 9 doesn t matter To Get This Fraction Format Change These Flags 8 Most precise Factors of denominator Fixed denominator 5 6 Fractions File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm E You can change flags 8 and 9 to set the fraction format using the steps listed here Because flags are especially useful in program their use us covered in detail in chapter 13 1 Press Wea to get the flag menu 2 To set a flag press SF and type the flag number such as 8 To clear a flag press CF and type the flag number To see if a flag is set press F 57 and ty
246. requires repeated calculations To solve a programmed function 1 Enter a program that defines the function See To write a program for SOLVE below 2 Select the program to solve press Wz label You can skip this step if you re re solving the same program 3 Solve for the unknown variable press F variable Notice that FN is required if you re solving a programmed function but not if you re solving an equation from the equation list To halt a calculation press or R S The current best estimate of the root is in the unknown variable use Wz to view it without disturbing the stack To resume the calculation press R S To write a program for SOLVE The program can use equations and RPN operations in whatever combination is most convenient 1 Begin the program with a label This label identifies the function shat you want SOLVE to evaluate FH abel Solving and Integrating Programs 14 1 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm u u 2 Include an INPUT instruction for each variable including the unknown INPUT instructions enable you to solve for any variable in a multi variable function INPUT for the unknown is ignored by the calculator so you need to write only one program that contains a separate INPUT instruction for every variable including the unknown If you include no INPUT instructions the program uses the values stored in the variables or entere
247. rinted Date 2003 4 24 negative 1 11 9 3 10 5 order in calculations 1 15 periods and commas in 1 16 A 1 precision 1 16 C 16 prime 17 7 range of 1 13 10 6 real 4 1 8 1 recalling 3 2 reusing 2 6 2 11 rounding 4 15 showing all digits 1 18 10 8 storing 3 2 truncating 10 5 typing 1 11 1 12 10 1 O octal numbers See numbers arithmetic 10 3 converting to 10 1 range of 10 6 typing 10 1 OCT annunciator 10 1 OFF 1 1 one variable statistics 11 2 overflow flags 13 9 E 4 result of calculation 1 13 10 3 10 6 setting response 13 9 E 4 testing occurrence 13 9 P n 4 3 A 2 parentheses in arithmetic 2 13 Index 9 Size 17 7 x 25 2 cm in equations 6 6 6 7 6 16 memory usage 2 22 PARTS menu 4 15 pause See PSE payment finance 17 1 percentage functions 4 6 periods in numbers 1 16 A 1 permutations 4 13 polar to rectangular coordinate conversion 4 8 9 6 15 1 poles of functions C 6 polynomials 12 26 15 22 population standard deviations 1 1 7 power annunciator 1 1 A2 power curve fitting 16 1 power functions 1 12 4 2 9 4 precedence equation operators 6 16 precision numbers 1 16 1 18 C 16 present value See financial calculations PRGM TOP 12 4 126 1221 E 4 prime number generator 17 7 probability functions 4 12 normal distribution 16 12 PROB menu 4 13 program catalog 1 21 12 22 Program entry mode 1 3 12 6 program labels
248. rithm for SOLVE works how to interpret results what happens when no solution is found and conditions that can cause incorrect results Solving Equations 7 11 File name 32sii Manual E O424 Printed Date 2003 4 24 Size 177 x 25 2 cm 8 Integrating Equations Many problems in mathematics science and engineering require calculating the definite integral of a function If the function is denoted by f x and the interval of integration is a to b then the integral can be expressed mathematically as f fogax f x The quantity can be interpreted geometrically as the area of a region bounded by the graph of the function f x the x axis and the limits x a and x b provided that f x is nonnegative throughout the interval of integration The operation operation J FN integrates the current equation with respect to a specified variable J FH d The function may have more than one variable Integrating Equations 8 1 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm u works only with real numbers Integrating Equations FN To Integrating Equations To integrate an equation 1 If the equation that defines the integrand s function isn t stored in the equation list key it in see Entering Equations Into the Equation List in chapter 6 and leave Equation mode The equation usually contains just an expression 2 Enter the limits of integration key in the
249. rogram as FH label FH a variable The programmed J FN instruction does not produce a labeled display f value since this might riot be the significant output for your program that is you might want to do further calculations with this number before displaying it If you do want this result displayed add a PSE fsa or STOP R S instruction to display the result in the X register after the J FN instruction Example FN in a Program The Normal and Inverse Normal Distributions program in chapter 16 includes an integration of the equation of the normal density function D M 2 n 2dD e SJ 2r M Solving and Integrating Programs 14 9 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 2 The amp e D M 5 2 function is calculated by the routine labeled F Other routines prompt for the known values and do the other calculations to find Q D the upper tail area of a normal curve The integration itself is set up and executed from routine Q WHI LEL t6 Gas RCL M Recalls lower limit of integration QAZ REL x Recalls upper limit of integration X D O64 FH F Specifies the function gas FH aD Integrates the normal function using the dummy variable D Restrictions o Solving and Integrating The SOLVE variable and J FN d variable instructions cannot call a routine that contains another SOLVE or J FN instruction That is neither of these instructions can be used r
250. rsions 4 12 V variable catalog 1 21 3 4 variables arithmetic inside 3 5 catalog of 1 21 3 4 clearing 1 22 3 4 3 5 clearing all 1 4 3 5 Printed Date 2003 4 24 Size 17 7 x 25 2 cm clearing while viewing 12 15 default B 5 exchanging with X 3 8 indirect addressing 13 19 13 20 in equations 6 5 7 1 in programs 12 12 14 1 14 7 memory usage 1222 B2 names 3 1 number storage 3 1 of integration 8 2 14 7 polynomials 12 26 program input 12 13 program output 12 14 12 18 recalling 3 2 3 4 separate trom stack 3 2 showing all digits 3 3 3 4 10 8 12 15 solving for 72 14 1 14 5 C 1 storing 3 2 storing trom equation 6 13 typing name 1 2 viewing 3 3 12 14 12 18 vectors application program 15 1 coordinate conversions 4 10 9 7 15 1 operations 5 1 VIEW displaying program data 12 14 12 18 14 5 displaying variables 3 3 10 8 File name 32sii Manual E 0424 Printed Date 2003 4 24 no stack effect 12 15 stopping programs 12 14 volume conversions 4 12 W warranty A 6 weight conversions 4 12 weighted means 11 4 windows binary numbers 10 7 X XEQ evaluating equations 6 12 6 14 running programs 12 10 12 22 X register affected by prompts 6 16 arithmetic with variables 3 5 clearing 1 4 2 2 2 7 clearing in programs 12 7 displayed 2 2 during programs pause 12 19 exchanging with variables 3 8 exchanging with Y 2 4 not
251. ry out subsequent calculations using both the base number and the result without reentering the base number Real Number Functions 4 5 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm To Calculate x of y y x B amp Percentage change from y to x y 0 y x Ta Example Find the sales tax at 6 and the total cost of a 15 76 item Use FIX 2 display format so the costs are rounded appropriately Keys Display Description E F3 2 Rounds display to two decimal places 15 76 15 76 6 f 4 95 Calculates 6 tax 16 71 Total cost base price 6 tax Suppose that the 15 76 item cost 16 12 last year What is the percentage change from last year s price to this year s Keys Display Description 16 12 16 12 15 76 fj 2 23 This year s price dropped about 2 2 from last year s price ER Fx 4 2 2333 Restores FIX 4 format Note The order of the two numbers is important for the CHG uU function The order affects whether the percentage change is considered positive or negative 4 6 Real Number Functions File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Conversion Functions There are four types of conversions coordinate polar rectangular angular degrees radians time decimal minutes seconds and unit cm in C F I gal Kg lb Coordinate Conversions The function names for these conversions are y x gt 6 rand 6 r gt y Xx P
252. s D in Hexadecimal mode Decimal mode set Hexadecimal mode set PRGM PRGM HEX Abs HEX AS HEX PRGM PRGM HEX Hib is Hi Li 12 24 Simple Programming File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Polynomial Expressions and Horner s Method Some expressions such as polynomials use the same variable several times for their solution For example the expression Ax4 Bx Cx Dx E uses the variable x four different times A program to calculate such an expression using RPN operations could repeatedly recall a stored copy of x from a variable A shorter RPN programming method however would be to use a stack which has been filled with the constant see Filling the Stack with a Constant in chapter 2 Rorer s Method is a useful means of rearranging polynomial expressions to cut calculation steps and calculation time It is especially expedient with SOLVE and FN two relatively complex operations that use subroutines This method involves rewriting a polynomial expression in a nested fashion to eliminate exponents greater than 1 Ax4 13x Cx24 Dx E Ax Bx Cx D x E Ax2 Bx C x D x E Ax B x C x D x 4 E Example Write a program using RPN operations for 5x4 2x as 5x 2 x x x then evaluate it for x 7 Keys Display Description m em EN CJC PRGM TOP P Pai LBL F Ex X Pe INPUT X Fills the stack with x Pas ENTER Simple Programming
253. s 10 f x approaches 10 as x becomes a negative number of large magnitude Example A Math Error Find the root of the equation x x 0 3 0 520 Enter the equation as an expression Keys Display Description Wes Selects Equation mode X Enters the equation ra X J 3 mJ Wea 1 CJ 5 ENER saRTCH CH8 3 r3 CK CEBC 34 8 Checksum and length Cancels Equation mode First attempt to find a positive root Keys Display Description O X10 i Your positive guesses for the root F3 SEURTCE CE B 3 Selects Equation mode displays the left end of the equation a X 8 1868 Calculates the root using guesses O and 10 Now attempt to find a negative root by entering guesses O and 10 Notice that the function is undefined for values of x between O and O0 3 since those values produce a positive denominator but a negative numerator causing a negative square root C 12 More about Solving File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Keys Display Description O X 10 GA 18_ Wes SQRTCH CK H 3 Selects Equation mode displays the lett end of the equation Wea X SGRTCNEG Math error Clears error message cancels Equation mode r3 X z H 1288 Displays the final estimate of x Example A Local Flat Region Find the root of the function fx 2x 2 if x 1 f x 1 for 1 xxx 1 a local flat region fx 2 x 2 i x51 Enter the function as the progra
254. s S surface area V volume R radius and H height Use these formulas V nR H S 2x R2 2n RH 20 R R H Keys Display Description EX EX Program entry sets pointer to top CJC PRGM TOF of memory EX e CH1 LBL C Labels program EX R Ch2 INFUTR Labels program EX H COZ INPUT H Instructions to prompt for radius and height T Wes Calculates the volume R 2 H Simple Programming 12 15 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i Keys Display LA4 qx R 2xH a SHOW LkE 9194 812 8 STO V CAS STO V r3 EQN 2 x Wea 2 x RCL R x Wed C RCL R RCL H r3 CAS ZxgxRXxRC 3 SHOW CK A911 G1s 6 S CAF STO 5 Wes SF J0 Cas SF 16 Wea EQN RCL V RCL O RCL L SPACE RCL A RCL R RCL E RCL A ENTER cmo unL AR r CF J0 Cig CF i8 Wes VIEW V Cii WIEW V 1 S CI2 VIEWS 6 C13 RTH PGM LBL C ra CK 6B47 12 16 Simple Programming File name 32sii Manual E O424 Oel s lei Description Checksum and length of equation Store the volume in V Calculates the surface area Checksum and length of equation Stores the surface area in S Sets flag 10 to display equations Displays message in equations Clears flag 10 Displays volume Displays surface area Ends program Displays label C and the length of the program in bytes Checksum and length of program Cancels program e
255. s the integrated Example Bessel Function The Bessel function of the first kind of order O can be expressed as IN Jo zh cos x sint dt Find the Bessel function for x values of 2 and 3 Enter the expression that defines the integrand s function cos x sin Keys Display Description ER ALL Clears memory M Wea Current equation or Selects Equation mode EWM LIST TOP X COSCHE Types the equation LOStaxSlIHcil RCL T COSCHXSIHCTE r3 r3 SOERXSIHCTO 2B Right closing parentheses are optional COSCEXSIHECT Terminates the expression and displays its left end r3 CK F9SB 012 8 Checksum and length Integrating Equations 8 3 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm i Leaves Equation mode Now integrate this function with respect to t from zero to x x 2 Keys Display Description al RD Selects Radians mode O ra 3 1416 Enters the limits of integration lower limit first r3 COSCRXxSIHECT Displays the function F3 jFHa Prompts for the variable of integration T 5 value Prompts for value of X 2 IHTEGERTIHIG x 2 Starts integrating 28 7834 calculates result for MU 0 F3 A 2239 The final result for Jo 2 Now calculate Jo 3 with the same limits of integration You must respecity the limits of integration O x since they were pushed off the stack by the subsequent division by m Keys Display Description O r3 3 1416 Enters the
256. sactions the rights and obligations of Seller and Buyer shall be determined by statute If the Calculator Requires Service Hewlett Packard maintains service centers in many countries These centers will repair a calculator or replace it with an equivalent or newer model whether it is under warranty or not There is a charge for service after the warranty period Calculators normally are serviced and reshipped within 5 working days B In the United States Send the calculator to the Calculator Service Center listed on the inside of the back cover WB In Europe Contact your HP sales office or dealer or HP s European headquarters for the location of the nearest service center Do not ship the calculator for service without first contacting a Hewlett Packard office Hewlett Packard S A 150 Route du Nant d Avril P O Box CH 1217 Meyrin 2 Geneva Switzerland Telephone 022 780 81 11 B In other countries Contact your HP sales office or dealer or write to the U S Calculator Service Center listed on the inside of the back cover for the location of other service centers If local service is unavailable you can ship the calculator to the U S Calculator Service Center for repair Support Batteries and Service A 7 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i All shipping reimportation arrangements and customs costs are your responsibility Service Charge There is a standard rep
257. see when the calculator is set to ENG 4 display mode The 3 following the E is the multiple of 3 exponent of 10 123 46x 103 ALL Format ALL ALL format displays a number as precisely as possible 12 digits maximum If all the digits don t fit in the display the number is automatically displayed in scientific format 123 456 SHOWing Full 12 Digit Precision Changing the number of displayed decimal places affects what you see but it does not affect the internal representation of numbers Any number stored internally always has 12 digits For example in the number 14 8745632019 you see only 14 8746 when the display mode is set to FIX 4 but the last six digits 632019 are present internally in the calculator To temporarily display a number in full precision press Wz This shows you the mantissa but no exponent of the number for as long as you hold down SHOW 1 16 Getting Started File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Keys Display EN ISP Fx 4 45 ENTER 1 3 x 58 5800 EW DISP SC 2 5 8561 m DISP EN 2 S8 Ea ET ISP ALL 58 5 EX FM 4 58 5006 A BiT Wes hold 1789481785948 Fractions Description Displays four decimal places Four decimal places displayed Scientific format two decimal places and an exponent Engineering format All significant digits trailing zeros dropped Four decimal places no exponen
258. selected program label This can happen only the first time that you use SOLVE or J FN after the message MEMORY CLEAR or it can happen if the current label no longer exists A running program attempted to select a program label FH abel while a SOLVE operation was running A running program attempted to solve a program while a SOLVE operation was running A running program attempted to integrate a program Messages E 3 Size 17 7 x 25 2 cm i SULVING SURET CHEGS STAT ERROR TOO BIG AER OVERFLOM TES while a SOLVE operation was running The calculator is solving an equation or program for its root This might take a while Attempted to calculate the square root of a negative number Statistics error E Attempted to do a statistics calculation with n O m Attempted to calculate sx sy X y m r or b with n 1 E Attempted to calculate r x or Xw with x data only all y values equal to zero E Attempted to calculate X V r m or b with all x values equal The magnitude of the number is too large to be converted to HEX OCT or BIN base the number must be in the range 34 359 738 368 lt n x34 359 738 367 A running program attempted an eighth nested EG label Up to seven subroutines can be nested Since SOLVE and FN each uses a level they can also generate this error The condition checked by a test instruction is true Occurs only when executed frown the keyboard Self Test Me
259. ses integers only The L8 J 9 J and unshifted top row keys are inactive Binary mode BIN annunciator on Converts numbers to base 2 uses integers only Digit keys other than LO and L1 and the unshifted top row functions are inactive If a number is longer than 12 digits then the outer top row keys and are active for viewing windows See Windows for Long Binary Numbers later in this chapter Examples Converting the Base of a Number The following keystrokes do various base conversions Convert 125 99 10 to hexadecimal octal and binary numbers Keys Display Description 125 99 EX TD Converts just the integer part 125 Base Conversions and Arithmetic 10 1 File name 32sii Manual E O424 Printed Date 2003 4 24 Size 177 x 25 2 cm HX of the decimal number to base 16 and displays this value ES oc 175 Base 8 EN BASE EH 1111181 Base 2 Eat DEC 125 9988 Restores base 10 the original decimal value has been preserved including its fractional part Convert 24FF 16 to binary base The binary number will be more than 12 digits the maximum display long Keys Display Description Ex HX 24FF Use the key to type F 24FF EN BH 818811111111 The entire binary number does riot fit The annunciator indicates that the number continues to the left the annunciator Points to 18 Displays the rest of the number The full number is 100100111111112 8igB11111111 Displays
260. sing conditional instructions comparisons and flags to determine which instructions or subroutines should be used E Using loops with counters to execute a set of instructions a certain number of times WI Using indirect addressing to access different variables using the same program instruction Routines in Programs A program is composed of one or more routines A routine is a functional unit that accomplishes something specific Complicated programs need routines to group and separate tasks This makes a program easier to write read understand and alter For example look at the program for Normal and lInverse Normal Distributions in chapter 16 Routine S initializes the program by collecting the input for the mean and standard deviation Routine D sets a limit of integration executes routine Q and displays the result Routine Q integrates the function defined in routine F and finishes the probability calculation of Q x Programming Techniques 13 1 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i A routine typically starts with a label LBL and ends with an instruction that alters or stops program execution such as RTN GTO or STOP or perhaps another label Calling Subroutines XEQ RTN A subroutine is a routine that is called from executed by another routine and returns to that same routine when the subroutine is finished The subroutine must start with a LBL and end with a
261. sor W See digit entry cursor Kal fad annunciators 1 2 V annunciator menus 1 5 scrolling 6 8 12 7 12 16 A V annunciator in catalogs 3 4 5 4 in fractions 3 4 5 2 5 3 CJ in fractions 1 19 5 1 A See integration iz 1 11 functions 4 6 J FN See integration n 4 3 A2 A absolute value real number 4 15 addressing indirect 13 19 13 20 13 21 File name 32sii Manual E 0424 Printed Date 2003 4 24 ALL format See display format in equations 6 6 in programs 12 6 Setting 1 17 alpha characters 1 2 angles between vectors 15 1 converting format 4 11 converting units 4 1 implied units 4 3 A 2 angular mode 4 3 A 2 B 5 annunciators alpha 1 2 battery 1 1 A 2 descriptions 1 8 flags 13 11 list of 1 9 low power 1 1 A2 shift keys 1 2 answers to questions A arithmetic binary 10 3 complex number 9 4 general procedure 1 14 hexadecimal 10 3 intermediate results 2 13 long calculations 2 13 octal 10 3 order of calculation 2 16 stack operation 2 5 9 2 assignment equations 6 11 6 12 6 13 7 1 asymptotes of functions C 9 Index 1 Size 177 x 25 2 cm A Z annunciator 1 2 3 2 6 5 backspace key canceling VIEW 3 4 clearing messages 1 3 E 1 clearing X register 2 2 2 8 deleting program lines 12 20 equation entry 1 3 6 9 leaving menus 1 3 1 8 operation 1 3 program entry 12 starts editing 6 10 12 7 12 20 balance finance 17 1
262. ssages S2SlII Uk 5S2eSII FHILn LUPR HP 7 90 E 4 Messages File name 32sii Manual E 0424 Printed Date 2003 4 24 The self test and the keyboard test passed The self test or the keyboard test failed and the calculator requires service Copyright message displayed after successfully completing the self test Size 177 x 25 2 cm Operation Index This section is a quick reference for all functions and operations and their formulas where appropriate The listing is in alphabetical order by the function s name This name is the one used in program lines For example the function named FIX n is executed as EX F X n Nonprogrammable functions have their names in key boxes For example c Non letter and Greek characters are alphabetized before all the letters function names preceded by arrows for example 2 DEG are alphabetized as if the arrow were not there The last column marked refers to notes at the end of the table LU Changes the sign of a number Addition Returns y x Subtraction Returns y x Multiplication Returns y x x Division Returns y x Power Indicates an exponent Deletes the last digit keyed in clears x clears a menu erases last function keyed in an equation starts equation editing deletes a program step Displays previous entry in catalog moves to previous equation in equation list moves program pointer to previous step Displays next entry
263. sss 1 15 SHOW ing Full 12 Digit Precision 1 16 PROCTIONS E 1 17 EMICHING PACHONS em TE Do E 1 17 Displaying Fractions Saone drea MUI UEM 1 19 MES SIGE Soa E DO TO 1 19 Calculator Memory ccccccccceeeceeeeceeeeesaueceaueeeeneeeenees 1 20 Checking Available Memory sseeessss 1 20 Clearing All of Memory eene 1 20 2 The Automatic Memory Stack Whabine SICK 1S arasina toI RMP AUR quim diqSnd 2 The X Register Is in the Display sessssesse 2 2 Clearing the X Register ccccceseccceseeceeeeeeeeneeeeens 2 2 Reviewing the stack sssssessssee 2 3 Exchanging the X and Y Registers in the Stack 2 4 Arithmetic How the Stack Does It seseeesssssess 2 4 How ENTER WOFKS x cis wogeseascsennsutcuseentiaononcenalesuaces 2 5 How CLEAR x VVOIKSs suscite dee tuae bestes uei dope 2 7 The LAST X Register acs setae entation Monate td asa Moe hEu naDI 2 8 Correcting Mistakes with LAST X csccceeseeeeeeeeeeens 2 9 Reusing Numbers with LAST X cccccseccceeeeceeeneees 2 10 Chain Calculations cccccccseccececceeeeseeaseceeueeeeeneeees 2 12 Work from the Parentheses Out ssssssss 2 12 mer M 2 14 Order of Calculation ee 2 15 MONE EXEICISOS Leer s oum it hs Medea Nube pan MUR DIM E Db ud 2 16 2 Contents File name
264. standard deviations a display of four or more signiticant figures is adequate tor most application At full precision the input limit becomes 5 standard deviations Computation time is significantly less with a lower number of displayed digits In routine N the constant 0 5 may be replaced by 2 and UZ This will save 6 5 byte at the expense of clarity 16 14 Statistics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Yom do riot need to key in the inverse routine in routines and T if you are not interested in the inverse capability Program Instructions i 2 3 Key in the program routines press when done Press S After the prompt for M key in the population mean and press R S If the mean is zero just press R S After the prompt for S key in the population standard deviation and press R S If the standard deviation is 1 just press To calculate X given Q X skip to step 9 of these instructions To calculate Q X given X D 8 9 After the prompt key in the value of X and press R S The result Q X is displayed To calculate Q X for a new X with the same mean and standard deviation press R S and go to step 7 To calculate X given Q X press XEQ I 10 After the prompt key in the value of Q X and press R S The result X is displayed 11 To calculate X for a new Q X with the same mean and standard deviation press an
265. statistical data Refer to Managing Calculator Memory in appendix B Access to the Statistics Registers The statistics register assignments in the HP 32SIl are shown in the following table Statistics Registers Register Number Description n 28 Number of accumulated data pairs Ex 29 Sum of accumulated x values Xy 30 Sum of accumulated y values Xx 31 Sum of squares of accumulated x values Ly 32 Sum of squares of accumulated y values Exy 33 Sum of products of accumulated x and y values You can load a statistics register with a summation by storing the numb r 28 through 33 of the register you want in i number and then storing the summation value 2 Similarly you can press Fs to view a register value the display is labeled with the register name The SUMS menu contains functions for recalling the register values See Indirectly Addressing Variables and Labels in chapter 13 for more information Statistical Operations 11 13 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Part 2 Programming Statistics Programs File name 32sii Manual E 0424Page 14 162 Printed Date 2003 4 24 Size 177 x 25 2 cm 12 Simple Programming Part 1 of this manual introduced you to functions and operations that you can use manually that is by pressing a key for each individual operation And you saw how you can use equations to repeat calculations without doing all of
266. sted on the inside back cover A 4 Support Batteries and Service File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm The Self Test It the display can be turned on but the calculator does not seem to be operating properly do the following diagnostic self test 1 Hold down the key then press 7 at the same time 2 Press any key eight times and watch the various patterns displayed After you ve pressed the key eight times the calculator displays the copyright message CUPR HP8 98 and then the message KBD 81 3 Starting at the upper left corner and moving from left to right press each key in the top row Then moving left to right press each key in the second row the third row and so on until you ve pressed every key m you press the keys in the proper order and they are functioning properly the calculator displays KED followed by two digit numbers The calculator is counting the keys using hexadecimal base E you press a key out of order or if a key isn t functioning properly the next keystroke displays a fail message see step 4 4 The self test produces one of these two results E The calculator displays 32 I 1 0K if it passed the self test Go to step 5 The calculator displays 32811 FRIL followed by a one digit number if it failed the self test If you received the message because you pressed a key out of order reset the calculator hold down LC press and do the
267. stop during program entry inserts a STOP instruction This will halt a running program until you resume it by pressing trom the keyboard You can use STOP rather than RTN in order to end a program without returning the program pointer to the top of memory E Pressing fsa during program entry inserts a PSE pause instruction This will suspend a running program and display the contents of the X register for about 1 second with the following exception If PSE immediately follows a VIEW instruction or an equation that s displayed flag 10 set the variable or equation is displayed instead and the display remains after the 1 second pause Interrupting a Running Program You can interrupt a running program at any time by pressing or R S The program completes its current instruction betore stopping Press run stop to resume the program If you interrupt a program and then press LXEQ EN GTO or Fea RIN you cannot resume the program with R S Reexecute the program instead label Error Stops If an error occurs in the course of a running program program execution halts and an error message appears in the display There is a list of messages and conditions in appendix E To see the line in the program containing the error causing instruction Press E PRGM The program will have stopped at that point For instance it might be a instruction which caused an illegal division by zero 12 18 Simple Programmin
268. t Reciprocal of 58 5 Shows full precision until you release SHOW The HP 328II allows you to type in and display fractions and to perform math operations on them Fractions are real numbers of the form a b c where a b and c are integers O b c and the denominator c must be in the range 2 through 4095 Entering Fractions Fractions can be entered onto the stack at any time 1 Key in the integer part of the number and press CJ The first LJ separates the integer part of the number from its fractional part 2 Key in the fraction numerator and press L again The second LJ separates the numerator from the denominator 3 Key in the denominator then press or a function key to File name 32sii Manual E 0424 Getting Started 1 17 Printed Date 2003 4 24 Size 17 7 x 25 2 cm terminate digit entry The number or result is formatted according to the current display format The a b c symbol under the LJ key is a reminder that the L key is used twice for fraction entry For example to enter the fractional number 12 3 8 press these keys Keys Display Description 12 12 Enters the integer part of the number J 2 The L key is interpreted in the normal manner 3 12 3 Enters the numerator of the fraction the number is still displayed in decimal form J 12 37 The calculator interprets the second LJ as a fraction and separates the numerator from denominator 8 12 348 Appends the denominator
269. t equals the cross product of the radius vector and the force vector r x F key in the vector representing the lever and take the cross product Keys Display Description 1 07 T 898 7T 832 Sets R equal to 1 07 125 P739 9445 Sets T equal to 125 63 R 1 8786 Sets P equal to 63 C R 18 B82805 Calculates cross product and displays R of result T 55 3719 Displays T of cross product P 124 3412 Displays P of cross product R 478 4554 Displays rectangular form of cross product Y 12 2439 Z l H l656H The dot product can be used to resolve the force still in v2 along the axis of the lever Keys Display Description P R718 8285 Starts polar input routine T 55 3719 Detines the radius as one unit vecior 125 P 124 23412 Sets T equal to 125 63 k71 BEGA Sets P equal to 63 Mathematics Programs 15 11 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm D 224 1882 Calculates dot product G 34 8496 Calculates angle between resultant force vector and lever k71 6998 Gets back to input routine Solutions of Simultaneous Equations This program solves simultaneous linear equations in two or three unknowns It does this through matrix inversion and matrix multiplication A system of three linear equations AX DY GZ J BX EY HZ K CX FY IZ L can be represented by the matrix equation below A D Gj X J B E AVY K C F IZ L The matrix equation may be solved for X Y and
270. tal number Drops leftmost three digit s Shows all digits ER DEC 11 219 473 637 B8B Restores Decimal mode Base Conversions and Arithmetic 10 7 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 1 Statistical Operations The statistics menus in the HP 32SIl provide functions to statistically analyze a set of one or two variable data B Mean sample and population standard deviations m linear regression and linear estimation X and y B Weighted mean x weighted by y WB A Summation statistics n Xx Xy Yx2 xy and Xy L R Xy S O SUMS x y r m b SX SY OX Oy x y xW n x y x y xy Entering Statistical Data One and two variable statistical data are entered or deleted in similar fashion using the or EN key Data values are accumulated as summation statistics in six statistic s registers 28 through 33 whose names are displayed ire the SUMS menu Press F and see nx x wv2xwv Note Always clear the statistics registers before entering a new set of TF statistical data press ER Statistical Operations 11 1 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i Entering One Variable Data 1 Press EX to clear existing statistical data 2 Key in each x value and press 3 The display shows n the number of statistical data values now accumulated Pressing actually enters two variables into the statistics registers
271. ted Pressing terminates digit entry To separate two numbers key in the first number press to terminate digit entry and then key in the second number 123 122 6686 A completed number 4 127 6686 Another completed number If digit entry is not terminated if the cursor is present backspaces to erase the last digit If digit entry is terminated no cursor acts like and clears the entire number Try it Range Number and OVERFLOW The smallest number available on the calculator is 1 x 10 47 The largest number is 9 99999999999 x 10479 displayed as 1 88E548 because of rounding W f a calculation produces a result that exceeds the largest possible number 9 99999999999 x 1047 is returned and the warning message UMERFLUM appears W f a calculation produces a result smaller that the smallest possible number zero is returned No warning message appears Doing Arithmetic All operands numbers must be present before you press a function key When you press a function key the calculator immediately executes the function shown on that key All calculations can be simplified into one number functions and or two number functions One Number Functions To use a one number function such as Ux Lx EV e or EA 1 12 Getting Started File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm u 1 Key in the number You don t need to press ENTER 2 Press the function key For a shifte
272. ter than its true value If neither part of A V is on the exact value of the fraction is being displayed Left shift is active Right shift is active Program entry is active Blinks while program is running Equation entry mode is active or the calculator is evaluating an expression or executing an equation 0123 Indicates which flags are set flags 4 through 11 have no annunciator RAD or GRAD Radians or Grad angular mode is set DEC mode default has no annunciator HEX OCT BIN Indicates the active number base DEC base 10 default has no annunciator 1 8 Getting Started File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm HP 32SII Annunciator continued Annunciator Meaning Lower Row The top row keys on the calculator are redetined according to the menu labels displayed above menu pointers There are more digits to the left or right Use P to see the rest of a decimal number use the left and right scrolling keys Vx to see the rest of an equation or binary number Both these annunciators may appear simultaneously in the display indicating that there are more characters to the lett and to the right Press either of the indicated menu keys or to see the leading or trailing characters The alphabetic keys are active Attention Indicates a special condition or an error Battery power is low Keying in Numbers Chapter Yo
273. that it may cause problems you can quickly plot a few points by evaluating the function using the equation or program you wrote for that purpose If for any reason after obtaining an approximation to an integral you suspect its validity there s a simple procedure to verify it subdivide the interval of integration into two or more adjacent subintervals integrate the function over each subinterval then add the resulting approximations This causes the function to be sampled at a brand new set of sample points thereby more likely revealing any previously hidden spikes If the initial approximation was valid it will equal the sum of the approximations over the subintervals Conditions That Prolong Calculation Time In the preceding example the algorithm gave an incorrect answer because it never detected the spike in the function This happened because the variation in the function was too quick relative to the width of the interval of integration If the width of the interval were smaller you would get the correct answer but it would take a very long time if the interval were still too wide Consider an integral where the interval of integration is wide enough to require excessive calculation time but not so wide that it would be calculated incorrectly Note that because f x xe approaches zero very quickly as x approaches oo the contribution to the integral of the function at large values of x is negligible Therefore you can evaluat
274. that the result might be correct to only four decimal places In reality this result is accurate to seven decimal places when compared with the actual value of this integral Since the uncertainty of a result is calculated conservatively the calculator s approximation in most cases is more accurate than its uncertainty indicates 8 8 Integrating Equations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm For More Information This chapter gives you instructions for using integration in the HP 32SII over a wide range of applications Appendix D contains more detailed information about how the algorithm for integration works conditions that could cause incorrect results conditions that prolong calculation time and obtaining the current approximation to an integral Integrating Equations 8 9 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm 9 Operations with Comb Numbers The HP 32SIl can use complex numbers in the form X iy It has operations for complex arithmetic x complex trigonometry sin cos tan and the mathematics functions z 1 z z472 In z and eZ where z1 and Z are complex numbers To enter a complex number 1 Type the imaginary part 2 Press ENTER 3 Type the real part Complex numbers in the HP 32Sll are handled by entering each part imaginary and real of a complex number as a separate entry To enter two complex numb
275. the indirect instructions RCL X i and STO i 5 to fill and manipulate a matrix The first part of this program is routine A which stores the initial loop control number in i Program lines Description A i LBL A The starting point tor data input Haz 1 812 Loop control number loop from 1 to 12 in intervals of Programming Techniques 13 23 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i AAS STU I Stores loop control number in i The next routine is L a loop to collect all 12 known values for a 3x3 coefficient matrix variables A I and the three constants J L for the equations Program Lines Lai LEL L LH2 IHPUTC i3 LHS ISG i LH4 GTO L LH3GTOR Description This routine collects all known values in three equations Prompts for and stores a number into the variable addressed by i Adds 1 to i and repeats the loop until i reaches 13 012 When i exceeds the final counter value execution branches back to A Label J is a loop that completes the inversion of the 3 x 3 matrix Program Lines T81LBL J TaZ 57T0 Ci2 Tas DSE JTa4 GTO J TES RTH Equations with i Description This routine completes inverse by dividing by determinant Divides element Decrements index value so it points closer to A Loops for next value Returns to the calling program or to PRGM TOP You can use i in an equation to specify a variable indirectly Notice that
276. the keystrokes each time In part 2 you ll learn how you can use programs for repetitive calculations calculations that may involve more input or output control or more intricate logic A program lets you repeat operations and calculations in the precise manner you want In this chapter you will learn how to program a series of operations In the next chapter Programming Techniques you will learn about subroutines and conditional instructions Example A Simple Program To find the area of a circle with a radius of 5 you would use the formula A z r4 and press 5 Ex x ra to get the result for this circle 78 5398 But what if you wanted to find the area of many different circles Rather than repeat the given keystrokes each time varying only the 5 for the different radii you can put the repeatable keystrokes into a program agi Baz m HAA x Simple Programming 12 1 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm This very simple program assumes that the value for the radius is in the X register the display when the program starts to run It computes the area and leaves it in the X register To enter this program into program memory do the following Keys Display Description ER ALL Y Clears memory ER Activates Program entry mode PRGM annunciator on ER CJL PRGM TOF Resets program pointer to PRGM TOP ER AAI xe Radius Wea BB 7 HES x Area
277. the radius before executing A or E Keys Display Description 5 A RUMH ING Enters the radius then starts 78 5398 program A The resulting area is displayed 2 5 E 19 6358 Calculates area of the second circle using program E 2 r A 124 6251 Calculates area of the third circle Testing a Program If you know there is an error in a program but are not sure where the error is then a good way to test the program is by stepwise execution It is also a good idea to test a long or complicated program before relying on it By stepping through its execution one line at a time you can see the result after each program line is executed so you can verity the progress of known data whose correct results are also known 1 As for regular execution make sure program entry is not active PRGM annunciator off 2 Press EN label to set the program pointer to the start of the program that is at its LBL instruction The GTO instruction moves the program pointer without starting execution If the program is the first or Simple Programming 12 9 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm only program you can press EX CJ Li to move to its beginning 3 Press and hold EX 4 This displays the current program line When you release L X J the line is executed The result of that execution is then displayed it is in the X register To move to the preceding line you can press
278. the stack You can use STO to store the value in a variable for later use B From variables that already have values stored From automatic equation prompting if enabled by flag 11 set This is also handy if you re using equations In a program you can display information in these ways B With a VIEW instruction which shows the name and value of a variable This is the most handy technique B On the stack only the value in the X register is visible You can use PSE for a 1 second look at the X register E n a displayed equation if enabled by flag 10 set The equation is usually a message not a true equation W Some of these input and output techniques are described in the following topics Using INPUT for Entering Data The INPUT instruction Variable stops a running program and displays a prompt for the given variable This display includes the existing value for the variable such as RE BEE where Simple Programming 12 11 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm R is the variable s name 2 is the prompt for information and 0 0000 is the current value stored in the variable Press run stop to resume the program The value you keyed in then writes over the contents of the X register and is stored in the given variable If you have not changed the displayed value then that value is retained in the X register The area of a circle program with an IN
279. the vector subtraction routine SZ i Multiplies X Y and Z by 1 to change the sign SHA S70x A SH4 STU S03 S7O0x 2 SE GTOA Goes to the vector addition routine Checksum and length D051 017 0 Ci LEL C Defines the beginning of the cross product routine Caz ECL Y Ces ECL H Ca4 ECL Z CES ROL V CHE Calculates YW ZV which is the X component Car ROL Z CaS ROL V CES RCL x L18RCLxHM C11 Calculates ZU WX which is the Y component Cie RCL amp Cig RCL U Cid ECL Y Mathematics Programs 15 5 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Program Listing Program Lines Description Cis RCL V Lie Cir STO Z Stores XV YU which is the Z component Cis RV C19 STO Y Stores Y component C28 RY C21 STO Xx Stores X component C22 GTOQ Loops back for polar conversion and display input Checksum and length FEB2 033 0 Da8iLBLD Defines beginning of dot product and vector angle routine DEZ RCL 5 Ds RCL U Da4 ECL Y DES RCL V OBE Dar ECL Z DES ECL H DES Di STOD Stores the dot product of XU YV ZW Dii VIEH D Displays the dot product Diz RCL L D13 RCL R Divides the dot product by the magnitude of the X Y Z vector lid RCL H i15 ECL V Die RCL Ll Dir 5 x0 r DLS wie DiS RENY D28 4x 30 r Calculates the magnitude of the U V W vector Dzi x 5w 15 6 Mathematics Programs File name 32sii Manual E 0424 Printed Date 2003
280. the x and y estimates for each type of curve You will need to reenter the data values each time you run the program for a different curve fit 16 10 Statistics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm 0 9965 0 9945 0 9959 M 139 0088 51 1312 8 9730 B 65 8446 0 0177 0 6640 Y Y when X 37 98 7508 98 5870 98 6845 X X when Y2101 38 2857 38 3628 38 3151 Normal and Inverse Normal Distributions Normal distribution is frequently used to model the behavior of random variation about a mean This model assumes that the sample distribution is symmetric about the mean M with a standard deviation S and approximates the shape of the bell shaped curve shown below Given a value x this program calculates the probability that a random selection from the sample data will have a higher value This is known as the upper tail area Q x This program also provides the inverse given a value Q x the program calculates the corresponding value x Upper tail area X X Statistics Programs 16 11 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm OX 2x This program uses the built in integration feature of the HP 32SIl to integrate G x 0 5 e Xo dy the equation of the normal frequency curve The inverse is obtained using Newton s method to iteratively search for a value of x which yields the given probability Q x Program Lin
281. ther calculations Now study the following examples Remember that you need to press only to separate sequentially entered numbers such as at the beginning of a problem The operations themselves L etc separate subsequent numbers and save intermediate results The last result saved is the first one retrieved as needed to carry out the calculation Calculate 2 3 10 Keys Display Description 3 10 i3 6806 Calculates 3 10 first 2 Lx 0 i1538 Puts 2 before 13 so the division is correct 2 13 Calculate 4 14 7 x 3 2 Keys Display Description 7 3 21 6806 Calculates 7 x 3 14 2 LJ 33 0808 Calculates denominator 4 33 6086 Puts 4 before 33 in preparation for division B iziz Calculates 4 33 the answer Problems that have multiple parentheses can be solved in the same manner using the automatic storage of intermediate results For example to solve 3 4 x 5 6 on paper you would first calculate the quantity 3 4 Then you would calculate 5 6 Finally you would multiply the two intermediate results to get the answer The Automatic Memory Stack 2 13 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm i Work through the problem the same way with the HP 32SIl except that you don t have to write down intermediate answers the calculator remembers them for you Keys Display Description 3 4 7 BABA First adds 3 4 5 6 11 6666 Then adds
282. tial Guesses for SOLVE below If SOLVE is unable to find a solution the calculator displays HO ROOT FHD See appendix C for more information about how SOLVE works Verifying the Result Atter the SOLVE calculation ends you can verify that the result is indeed a solution of the equation by reviewing the values left in the stack B The X register press to clear the VIEWed variable contains the solution root for the unknown that is the value that makes the evaluation of the equation equal to zero mM The Y register press R contains the previous estimate for the root This number should be the same as the value in the X register If it is not then the root returned was only an approximation and the values in the X and Y registers bracket the root These bracketing numbers should be close together B The Z register press again contains this value of the equation at the root For an exact root this should be zero If it is not zero the root given was only an approximation this number should be close to zero If a calculation ends with the HO FOOT FHD the calculator could not converge on a root You can see the value in the X register the final estimate of the root by pressing or to clear the message The values in the X and Y registers bracket the interval that was last searched to find the root The Z register contains the value of the equation at the final estimate of the root W f the X and Y register
283. tion list contains the equations you ve entered You can display the equations and select one to work with Entering and Evaluating Equations 6 7 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm To display equations 1 Press a EQN This activates Equation mode and turns on the EQN annunciator The display shows an entry from the equation list E EGQH LIST TOP if there are no equations in the equation list or if the equation pointer is at the top of the list WI The current equation the last equation you viewed 2 Press EX or EX to step through the equation list and view each equation The list wraps around at the top and bottom EGH LIST TOF marks the top of the list To view a long equation 1 Display the equation in the equation list as described above If it s more than 12 characters long only 12 characters are shown The gt annunciator indicates more characters to the right The annunciator over means scrolling is turned on 2 Press to scroll the equation one character at a time showing characters to the right Press to show characters to the lett and gt turn off if there are no more characters to the left or right Press F SCRL to turn scrolling off and on When scrolling is turned off the left end of the equation is displayed the annunciators are off and the unshifted top row keys perform their labeled functions You must turn off scrolling if you w
284. tistics Programs Curve Fitting This program can be used to fit one of four models of equations to your data These models are the straight line the logarithmic curve the exponential curve and the power curve The program accepts two or more x y data pairs and then calculates the correlation coefficient r and the two regression coetticients m and b The program includes a routine to calculate the estimates x and Y For definitions of these values see Linear Regression in chapter 11 Samples of the curves and the relevant equations are shown below The internal regression functions of the HP 32SIl are used to compute the regression coefficients Statistics Programs 16 1 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm a Straight Line Fit Exponential Curve Fit S E y y y B Mx y BeMx Logarithmic Curve Fit Power Curve Fit L y y y B MlIn x y BxM X X To fit logarithmic curves values of x must be positive To fit exponential curves values of y must be positive To fit power curves both x and y must be positive A LOG HEG error will occur if a negative number is entered for these cases Data values of large magnitude but relatively small differences can incur problems of precision as can data values of greatly different magnitudes Refer to Limitations in Precision of Data in chapter 11 16 2 Statistics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size
285. to x that is X from zero to 2 t 2 Keys Display Description RD Selects Radians mode Integrating Equations 8 5 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 177 x 25 2 cm a O 2 2 Enters limits of integration lower first Was SING Ka 8 Displays the current equation r X INTEGRATING Calculates the result for Si 2 21 6854 Accuracy of Integration Since the calculator cannot compute the value of an integral exactly it approximates it The accuracy of this approximation depends on the accuracy of the integrand s function itself as calculated by your equation This is affected by round off error in the calculator and the accuracy of the empirical constants Integrals of functions with certain characteristics such as spikes or very rapid oscillations might be calculated inaccurately but the likelihood is very small The general characteristics of functions that can cause problems as well as techniques for dealing with them are discussed in appendix D Specifying Accuracy The display format s setting FIX SCI ENG or ALL determines the precision of the integration calculation the greater the number of digits displayed the greater the precision of the calculated integral and the greater the time required to calculate it The fewer the number of digits displayed the faster the calculation but the calculator will presume that the function is accurate to only the number of digits specified in
286. truction For example the following routine uses a loop to diminish a value A by a constant amount B until the resulting A is less than or equal to B 13 16 Programming Techniques File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Program lines Description Hei LEL A Hee IHFUT A HS IHPUT EB Checksum and length 6157 004 5 sH1LBL sua ECLA It is easier to recall A than to remember where it is in the stack S83 RCL B Calculates A B S84 STO A Replaces old A with new result sas RCL E Recalls constant for comparison SHG xiw Is B new A say GTO Yes loops to repeat subtraction 588 VIEHA No displays new A SHS RTH Checksum and length 5FE1 013 5 Loops With Counters DSE ISG When you want to execute a loop a specific number of times use the EX increment skip if greater than or Wz decrement skip if less than or equal to conditional function keys Each time a loop function is executed in a program it automatically decrements or increments a counter value stored in a variable It compares the current counter value to a final counter value then continues or exits the loop depending on the result For a count down loop use Pa variable For a count up loop use EX variable These functions accomplish the same thing as a FOR NEXT loop in BASIC FOR variable initial value T final value STEF increment Programming Techniques 13 17 File name 32sii Manual E 04
287. tuations when they do they usually can be recognized and dealt with ire a straightforward manner Unfortunately since all that the algorithm knows about f x are its values at the sample points it cannot distinguish between f x and any other function that agrees with f x at all the sample points This situation is depicted below D 2 More about Integration File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm showing over a portion of the interval of integration three functions whose graphs include the many sample points in common f x With this number of sample pints the algorithm will calculate the same approximation for the integral of any of the functions shown The actual integrals of the functions shown with solid blue and black lines are about the same so the approximation will be fairly accurate if f x is one of these functions However the actual integral of the function shown with a dashed line is quite different from those of the others so the current approximation will be rather inaccurate if f x is this function The algorithm cores to know the general behavior of the function by sampling the function at more and more points If a fluctuation of the function in one region is not unlike the behavior over the rest of the interval of integration at some iteration the algorithm will likely detect the fluctuation When this happens the number of sample points is increased until succ
288. turns to the calling routine Checksum and length OD3F 009 0 EB1 LEL B This subroutine calculates Y for the logarithmic model BAZ ECL amp x BES LH BH4 ROL M BAS RCL B Calculates Y MInX B Ba RCL Returns to the calling routine Checksum and length 7AB7 009 0 Hai LEL H This subroutine calculates X for the logarithmic model Hae STO i Restores index value to its original value Hes RCL Y H RCL E Hes ROL M HEE e Calculates x el 8 M Ha RTH Returns to the calling routine Checksum and length BOOD 010 5 C81 LEL C This subroutine calculates Y for the exponential model Caz RCL M Cea ECL A Cq e CAS RCLx B Calculates Y BeMX CHE RTH Returns to the calling routine Checksum and length AA19 009 0 16 6 Statistics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Program Lines Description I81 LBL I This subroutine calculates x for the exponential model IBZ STO i Restores index value to its original value In RCL Y Ind RECL B THs LH IB amp RCL M Calculates x In Y B M lar RTH Returns to the calling routine Checksum and length 7D3B 010 5 Dai LEL D This subroutine calculates Y for the power model DEZ RCL 5 Des RCL Fi Daq ys DaS RCLx B Calculates Y B X DAE RTH Returns to the calling routine Checksum and length 30CD 009 0 341 LBL J This subroutine calculates x for the power model Ie2 STO i Restores i
289. u can key in a number that has up to 12 digits plus a 3 digit exponent up to 499 If you try to key in a number larger than this digit entry halts and the A annunciator briefly appears If you make a mistake while keying in a number press to backspace and delete the last digit or press to clear the whole number File name 32sii Manual E O424 Printed Date 2003 4 24 Getting Started 1 9 Size 177 x 25 2 cm i Making Numbers Negative The key changes the sign of a number To key in a negative number type the number then press CZ WB To change the sign of a number that was entered previously just press If the number has an exponent affects only the mantissa the non exponent part of the number Exponent of Ten Exponents in the Display Numbers with exponents of ten such as 4 2 x 10 2 are displayed with an E preceding the exponent such as 4 Z866E 5 A number whose magnitude is too large or too small for the display format will automatically be displayed in exponential form For example in FIX 4 format for four decimal places observe the effect of the following keystrokes Keys Display Description 000062 BABEZ Shows number being entered A 6881 Rounds number to fit the display format 000042 4 26 6E 5 Automatically uses scientific notation because otherwise no significant digits would appear Keying in Exponents of Ten Use E exponent to key in numbers multiplied by powers of ten F
290. uation The value returned by the equation is a function f x of the unknown variable x f x is mathematical shorthand for a function defined in terms of the unknown variable x SOLVE starts with an estimate for the unknown variable x and refines that estimate with each successive execution of the tunction f x If any two successive estimates of the function f x have opposite signs then SOLVE presumes that the function f x crosses the x axis in at least one place between the two estimates This interval is systematically narrowed until a root is found For SOLVE to find a root the root has to exist within the range of numbers of the calculator and the function must be mathematically defined where the iterative search occurs SOLVE always finds a root provided one exists within the overflow bounds if one or more of these conditions are met E wo estimates yield f x values with opposite signs and the function s graph crosses the x axis in at least one place between those estimates figure a below m x always increases or always decreases as x increases figure b below W The graph ot f x is either concave everywhere or convex everywhere figure c below More about Solving C 1 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm u BI f x has one or more local minima or minima each occurs singly between adjacent roots off f x figure d below f x f x UN f x f x
291. uctions Results 312 thatis x A Storing Data into Variables 3 5 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Example Suppose the variables D E and F contain the values 1 2 and 3 Use storage arithmetic to add 1 to each of those variables Keys Display Description 1 D 1 BAGG Stores the assumed values into the 2 E 2 FARE variable 3 F 3 8886 1 STO LE D Add 1 to D E And F E F 1 BAGG ra D O 2 6888 Displays the current value of D Wea E E 3 8886 We F Fe4 6808 1 8888 Clears the VIEW display displays X register again Suppose the variables D E and F contain the values 2 3 and 4 from the last example Divide 3 by D multiply it by E and add F to the result Keys Display Description 3 D 1 5886 Calculates 3 D RCL X E 4 5088 3 Dx E RCL LJ F 5 56606 3 DxE F Exchanging x with Any Variable The Fa key allows yon to exchange the contents of the Displayed X register with 1 contents of any variable Executing this function does not effect the Y Z or T registers 3 6 Storing Data into Variables File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Example Keys Display Description 12 A iz 608 Stores 12 in variable A 3 3 Display x F3 A 12 888 Exchange contents of the X register and variable A Fa A 3 6608 Exchange contents of the X register and variable A The Variable i There is
292. unctions 4 11 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Probability Menu Press fea PROB to see the PROB probability menu shown in the following table It has functions to calculate combinations and permutations to generate seeds tor random numbers and to obtain random numbers trom those seeds PROB Menu Combinations Enter n first then r nonnegative integers only Calculates the number of possible sets of n items taken r at a time No item occurs more than once in a set and different orders of the same r items are not counted separately Permutations Enter n first then r nonnegative integers only Calculates the number of possible arrangements of n items taken r at a time No item occurs more than once in an arrangement and different orders of the same r items are counted separately Seed Stores the number in x as a new seed for the random number generator Random number generator Generates a random number in the range O x x 1 The number is part of a uniformly distributed pseudo random number sequence lt passes the spectral test of D Knuth Seminumerical Algotithims vol 2 London Addison Wesley 1981 The RANDOM function executed by pressing R uses a seed to generate a random number Each random number generated becomes the seed for the next random number Therefore a sequence of random numbers can be repeated by starting with the same seed
293. ute the function again Press first it you want to clear the incorrect result from the stack Example The Automatic Memory Stack 2 9 File name 32sii Manual E O424 Printed Date 2003 4 24 Size 177 x 25 2 cm Suppose you made a mistake while calculating 16 x 19 304 There are three kinds of mistakes you could have made Wring Mistake Correction Calculation 16 19 Wrong function EX E LAST x 15 19 Wrong first number 16 EX 16 ENTER 18 X Wrong second E LASTx LE 19 x number Reusing Numbers with LAST X You can use EX to reuse a number such as a constant in a calculation Remember to enter the constant second just before executing the arithmetic operation so that the constant is the last number in the X register and therefore can be saved and retrieved with EX Example 96 04 52 3947 52 3947 Calculates 2 10 The Automatic Memory Stack File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm PEED 96 04 Y 96 704 96 704 Z LAST X 52 3947 ES LAST X 52 3947 52 3947 Keys Display Description 96 704 96 rAd Enters first number 52 3947 149 987 Intermediate result EN 22 3947 Brings back display from before i 2 8457 Final result Example Two close stellar neighbors of Earth are Rigel Centaurus 4 3 light years away and Sirius 8 7 light years away Use c the speed of light 9 5 x 101 meters per year to convert the dist
294. values aren t close together or the Z register value isn t close to zero the estimate from the X register probably isn t a 7 6 Solving Equations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm E root W It the X and Y register values are close together and the Z register value is close to zero the estimate from the X register may be an approximation to a root Interrupting a SOLVE Calculation To halt a calculation press LC or R S The current best estimate of the root is in the unknown variable use Fs to view it without disturbing the stack Choosing Initial Guesses for SOLVE The two initial guesses come from B The number currently stored in the unknown variable WB The number in the X register the display These sources are used for guesses whether you enter guesses or not If you enter only one guess and store it in the variable the second guess will be the same value since the display also holds the number you just stored in the variable If such is the case the calculator changes one guess slightly so that it has two different guesses Entering your own guesses has the following advantages W By narrowing the range of search guesses can reduce the time to find a solution W there is more than one mathematical solution guesses can direct tote SOIVE procedure to the desired answer or range of answers For example the equation of linear motion d vot 1 2 gf
295. ven here Example Entering a Program with an Equation The following program calculates the area of a circle using an equation rather than using RPN operation like the previous program Keys Display Description Ex EX PRGM TOP Activates Program entry mode J sets pointer to top of memory ER E E81 LEL E Labels this program routine E for equation R Eaz STOR Stores radius in variable R Wes Wes Selects Equation entry mode R enters the equation returns to 2 EAS gxR Zz Program entry mode r3 CK ESFD 3 Checksum and length of equation r3 Ea4 RTH Ends the program Ex PGM LEL E 613 5 Displays label E and the length of the program in bytes r3 CK 1352 813 5 Cancels program entry Running a Program To run or execute a program program entry cannot be active no program line numbers displayed PRGM off Pressing will cancel Program entry mode 12 8 Simple Programming File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Executing a Program XEQ Press label to execute the program labeled with that letter If there is only one program in memory you can also execute it by pressing EX J run stop The PRGM annunciator blinks on and off while the program is running If necessary enter the data before executing the program Example Run the programs labeled A and E to find the areas of three ditferent circles with radii of 5 2 5 and 2m Remember to enter
296. verted matrix Press M to multiply the inverted matrix by the column vector and to see the value of X Press to see the value of Y then press again to see the value of Z For a new case go back to step 2 Variables Used A through Coefficients of matrix J through L Column vector values W Scratch variable used to store the determinant X through Z Output vector values also used for scratch l Loop control value index variable also used for scratch Remarks For 2 x 2 solutions use zero for coefficients C F H G and for L Use 1 for coefficient I Not all systems of equations have solutions 15 18 Mathematics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Example For the system below compute the inverse and the system solution Review the inverted matrix Invert the matrix again and review the result to make sure that the original matrix is returned 23X4 15Y4 17Z 2 31 8X 11Y 6Z 17 4AX 15Y4 12Z 14 Keys XEQ A 23 R S 8 R S 4 R S 15 R S 14 R S XEQ XEQ M R S R S XEQ A AJ A A NI Pad d Ix mM IM IM CA Display H value E value L value Li value E value A723 BBB 4 5995 BBB A 9366 v roqda Z H 13564 H H ld343 Bp H H256i1 L7H H1635 OVE 816 3 EVA A452 F H H52H File name 32sii Manual E O424 Printed Date 2003 4 24 Description Starts input routine Sets first
297. viewing the catalog of variables or programs 2 Press fea EQN The EQN annunciator shows that Equation mode is active and an entry from the equation list is displayed 3 Start typing the equation The previous display is replaced by the equation you re entering the previous equation isn t affected If you make a mistake press as required 4 Press to terminate the equation and see it in the display The equation is automatically saved in the equation list right after the entry that was displayed when you started typing If you press instead the equation is saved but Equation mode is turned off You can make an equation as long as you want you re limited only by the amount of memory available Equations can contain variables numbers functions and parentheses they re described in the following topics The example that follows illustrates these elements Variables in Equations You can use any of the calculator s 28 variables in an equation A through Z i and i You can use each variable as many times as you want For information about i see Indirectly Addressing Variables and Labels in chapter 13 To enter a variable in an equation press variable or variable When you press RCL the A Z annunciator shows that you can press a variable key to enter its name in the equation Number in Equations You can enter any valid number in an equation except fractions and numbers that aren t base 10 numbers
298. y Required 382 0 bytes 268 5 for programs 33 5 for SOLVE 80 for variables Remarks The program accommodates polynomials of order 2 3 4 and 5 It does not check if the order you enter is valid The program requires that the constant term ao is nonzero for these polynomials IF ao is O then O is a real root Reduce the polynomial by one order by factoring out x The order and the coefficients are not preserved by the program Because of round off error in numerical computations the program may produce values that are not true roots of the polynomial The only way to confirm the roots is to evaluate the polynomial manually to see if it is zero at the roots For a third or higher order polynomial if SOLVE cannot find a real root the error DIVIDE BY amp is displayed You can save time and memory by omitting routines you don t need If you re not solving fifth order polynomials you can omit routine E If you re not solving fourth or fifth order polynomials yoga can omit routines D E and F If you re not solving third fourth or fifth order polynomials you can omit routines C D E and F Program Instructions 1 Press EX ALL to clear all programs and variables This program requires all but 2 bytes of memory while running 15 28 Mathematics Programs File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Key in the program routines press when done Press P to start the polynomia
299. y the inaccuracy in the calculated function f x always provide an exact answer Evaluating the function at an infinite number of sample points would take forever However this is not necessary since the maximum accuracy of the calculated integral is limited by the accuracy of the calculated function values Using only a finite number of sample points the algorithm can calculate an integral that is as accurate as is justified considering the inherent uncertainty in f x The integration algorithm at first considers only a few sample points yielding relatively inaccurate approximations If these approximations are not yet as accurate as the accuracy of f x would permit the algorithm is iterated repeated with a larger number of sample points These iterations continue using about twice as many sample points each time until the resulting approximation is as accurate as is justified considering the inherent uncertainty in f x More about Integration D 1 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 2 As explained in chapter 8 the uncertainty of the final approximation is a number derived from the display format which specifies the uncertainty for the function At the end of each iteration the algorithm compares the approximation calculated during that iteration with the approximations calculated during two previous iterations If the difference between any of these three approximations a
300. your x values were 7776999 7777000 and 7777001 you should enter the data as 1 O and 1 then add 7777000 back to x and x For b add back 7777000 x m To calculate Y be sure to supply an x value that is less QOO Similar inaccuracies can result if your x and y values have greatly different magnitudes Again scaling the data can avoid this problem Effect of Deleted Data Executing EM does not delete any rounding errors that might have been generated in the statistics registers by the original data values This difference is not serious unless the incorrect data have a magnitude that is enormous compared with the correct data in such a case it would be wise to clear and reenter all the data Summation Values and the Statistics Registers The statistics registers are six unique locations in memory that store the accumulation of the six summation values Summation Statistics Pressing 7 gives you access to the contents of the statistics registers m Press n to recall the number of accumulated data sets m Press x to recall the sum of the x values E Press to recall the sum of the y values Statistical Operations 11 11 File name 32sii Manual E O424 Printed Date 2003 4 24 Size 177 x 25 2 cm m Press x8 and xv to recall the sums of the squares and the sum of the products of the x and y values that are of interest when performing other statistical calculations in addition to those provid

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