HP HP-32S, Owner'S Manual

Page 1: ...s s RFIsf Scientific Calcuktor Owners Isfemal HP 32S E9 HEWLETT PACKARD ...

Page 2: ...nu and menu keys 2 Letter keys for variables labels 3 Steps through programs and lists 4 Shift key 5 On cancel display menu program entry 6 Shows all decimal places 7 Run Stop toggle for programs 8 For indirect addressing via 9 Toggles in and out of program entry 10 User memory stored variables and programs 11 Menu keys boxed area 12 Clears all or parts of memory 13 Display formats 14 Angular mode...

Page 3: ...HP 32S RPN Scientific Calculator Owner s Manual m HEWLETT PACKARD Edition 1 March 1988 Reorder Number 00032 90039 ...

Page 4: ...ce or use of this manual or the keystroke programs contained herein Hewlett Packard Co 1988 All rights reserved Reproduction ad aptation or translation of this manual including any programs is prohibited without prior written permission of Hewlett Packard Com pany except as allowed under the copyright laws Hewlett Packard Company grants you the right to use any program contained in this manual in ...

Page 5: ...ife The calculator and its manual have been designed and tested for ease of use We selected spiral binding to let the manual stay open to any page and we added many examples to highlight the varied uses of this calculator Advanced materials and permanent molded in key lettering pro vide a long keyboard life and a positive feel to the keyboard CMOS low power electronics and the liquid crystal displ...

Page 6: ...8 in stead of ERR 21 Data storage in variables A through Z Our traditional RPN logic which saves keystrokes 390 bytes of memory to store data and programs Advanced functionality for statistics base conversions complex number arithmetic integration and solving for the unknown variable of an equation ExtensiveHP programming capability including editing labeled in put and output subroutines looping c...

Page 7: ... Menus 20 Annunciators 21 Keying In Numbers 21 Making Numbers Negative 22 Exponents of Ten 23 Understanding Digit Entry 24 Range of Numbers and OVERFLOW 24 Doing Arithmetic 24 One Number Functions 25 Two Number Functions 26 Chain Calculations 29 Exercises 29 Controlling the Display Format 29 Periods and Commas in Numbers 30 Number of Decimal Places HLdispJ 31 SHOWing Full 12 Digit Precision 32 Mes...

Page 8: ... and Recalling Numbers 49 Reviewing Variables in the VAR Catalog 50 Clearing Variables 50 Arithmetic With Stored Variables 50 Storage Arithmetic 51 Recall Arithmetic 53 The Variable i 4 54 Real Number Functions 55 Exponential and Logarithmic Functions 56 The Power Function y 56 Trigonometry 56 Entering ir 56 Setting the Angular Mode 57 Trigonometric Functions 59 Hyperbolic Functions 59 Percentage ...

Page 9: ...diting a Program 84 Program Memory 84 Viewing Program Memory 84 Memory Usage 85 The Catalog of Programs MEM 85 Clearing One or More Programs 86 The Checksum 87 Nonprogrammable Functions 87 Polynomial Expressions and Horner s Method 6 90 Programming Techniques 90 Routines in Programs 91 Calling Subroutines XEQ RTN 92 Nested Subroutines 93 Branching GTO 95 Conditional Instructions 96 Tests of Compar...

Page 10: ...s for FN 128 Examples Using FN 131 Accuracy of Integration 132 Specifying Accuracy 132 Interpreting Accuracy 134 Using Integration in a Program 136 For More Information 9 137 Operations With Complex Numbers 138 The Complex Stack 139 Complex Operations 142 Using Numbers in Polar Notation 10 144 Base Conversions and Arithmetic 146 Arithmetic in Bases 2 8 and 16 147 The Representation of Numbers 148 ...

Page 11: ...s 161 Summation Statistics 162 The Statistics Registers in Calculator Memory Part 4 Application Programs 12 164 Mathematics Programs 164 Vector Operations 175 Solutions of Simultaneous Equations Determinant Method 183 Solutions of Simultaneous Equations Matrix Inversion Method 191 Quadratic Equation 198 Coordinate Transformations 13 204 Statistics Programs 204 Curve Fitting 215 Normal and Inverse ...

Page 12: ...nsactions in the United Kingdom 249 If the Calculator Requires Service 250 Obtaining Service 250 Service Charge 251 Shipping Instructions 251 Warranty on Service 251 Service Agreements 252 Regulatory Information 252 Radio Frequency Interference B 253 User Memory and the Stack 253 Managing Calculator Memory 254 Resetting the Calculator 255 Clearing Memory 256 The Status of Stack lift 257 Disabling ...

Page 13: ... About Integration 273 How the Integral Is Evaluated 274 Conditions That Could Cause Incorrect Results 279 Conditions That Prolong Calculation Time 281 Messages 286 Function Index 299 Subject Index Contents 11 ...

Page 14: ...3 3 3 3 3 3 3 3 3 3 30 3 3 3 3 3 3 3 3 3 3 3 3 3 DO DO 33 3 3 ...

Page 15: ...Basic Operation Page 14 1 Getting Started 35 2 The Automatic Memory Stack 47 3 Storing Data Into Variables 54 4 Real Number Functions ...

Page 16: ...ect any information you ve stored To conserve energy the calculator turns itself off after about 10 min utes of no use Under most conditions the calculator s batteries last wellover a year If you see the low power indicator C3 in the display replace the batteries as soon as possible See appendix A for details and instructions Adjusting the Display s Contrast Thedisplay sbrightness depends on light...

Page 17: ... you press the next key To cancel just press again J2 i Shifted function TV Jx SE Letter for alphabetic key The Letter Keys Mostof the keys have a letter written next to them as shown above Whenever you need to type in a letter which is used to identify a variableor a label the A Z annunciator appears in the display indi cating that the letter keys are active Variables are covered in chapter 3 Bac...

Page 18: ... a catalog or program entry The CLEAR menu Gives you options for clearing data x VRRS ALL and 2 These clear the current num ber called x allvariables allof memory and statistical data During program entry the menu includes PGM which erases all of program memory Using Menus There is a lot more power to the HP 32S than what you see printed on the keyboard This is because almost half of the shifted k...

Page 19: ...S TESTS ZJ CD CjO GD SOLVE STAT PROB MEM ICT lX CD lZI uw iwvii miuw khum view CD ZKZDSCZ Menu choices Menu pointers Redefined top row keys matched to menu choices Menu keys boxed area Those shifted functions printed with lighter backgrounds on the cal culator such as ICLEflRl are menu keys Pressinga menu key produces a menu in the display a series of choices 1 Getting Started 17 ...

Page 20: ...s for root solving and integration 7 8 STAT Statistical functions 11 PROB Probability functions Programming Instructions 4 LBL RTN Label return end and pause 5 LOOP Conditional looping and counting functions 6 FLAGS Functions to set clear and test flags 6 TESTS Conditional tests Other Functions 6 MODES Angular modes and decimal point convention 4 1 DISP Display formats 1 CLEAR Functions to clear d...

Page 21: ...ll of the many functions available on the HP 32S nor to search through many names printed on the keyboard Exiting Menus Wheneveryou execute a function in a menu the menu automatically disappears as in the example above If you wish to leave a menu without executing a function you have three options Pressing 4 backs out of the menu one step at a time 123 123_ Hi PROB I Cn r Pn r x R R RANDOM SEED f4...

Page 22: ...ciator Meaning A PRGM INPUT 0 12 3 RAD GRAD HEX OCT BIN V and HB are active for stepping through a pro gram or a list pages 33 76 Shift D is active page 15 Program entry is active pages 72 75 Program is waiting for input enter number and press IR Sl to resume the program page 77 Specifies which flags are set page 98 Radians or Grads angular mode is set page 57 Specifies which number base is active...

Page 23: ...at has up to 12 digits plus a 3 digit expo nent 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 back space and delete the last digit or press c to clear the whole number Making Numbers Negative The key changes the sign of a number To key in a negative number type that number the...

Page 24: ...g entered 0 0001 Rounds number to fit display format 4 2000E 5 Automatically uses sci entific notation because otherwise no significant digits would appear Keying In Exponents of Ten Use T exponent to key in numbers multiplied by powers of ten For example take Planck s constant 6 6262 xlO 34 1 Key in the mantissa the non exponent part of the number If this part is negative press F 6 6262 6 6262 2 ...

Page 25: ...lay Description 123 123 Digit entry is not ter minated the number is not completed If you execute a function to calculate a result then the cursor disap pears because the number is complete Digit entry has been terminated Hxl 11 0905 Digit entry terminated PressingIenter Ialso terminates digit entry This is why you must sep arate two numbers with Ienter I to terminate one number before starting to...

Page 26: ...arning Doing Arithmetic When you press a function key the calculator immediately executes the function written on that key Therefore all operands numbers must be present before you press the function key All calculations can be broken down into one number functions and two number functions One Number Functions To use a one number function such as 11 xI W mfxH and P l 1 Key in the number You do not...

Page 27: ...I 4 Press the function key Fora shifted function press the shift key first Remember to enter both numbers before executing the function For example To Calculateb Press Display Is 12 3 12 ENTER 3 15 0000 12 3 12 ENTER 3 9 0000 12 x 3 12 ENTER I 3 I X 36 0000 12 3 12 ENTER 3 Ul 4 0000 The order of entry is of course essential for noncommutative func tions such as Q and If the numbers have been enter...

Page 28: ...working it out on paper but the calculator does the hard part For example solve 12 3 x 7 Work From the Parentheses Out If you were working this prob lem out on paper you would first calculate the intermediate result of 12 3 15 12 i 3 x 7 and then you would multiply the intermediate result by 7 15 x 7 105 Solve the problem in the same way on the HP 32S starting inside the parentheses Keys Display D...

Page 29: ...ent numbers and save intermediate results The last result saved is the first one retrieved as needed to carry out the calculation First calculate 2 3 10 Keys Display 2 ENTER I 3 IT 10 T 0 5000 2 Now calculate 3 10 Keys 3 IENTER I10 0 2HB Display 13 0000 0 1538 Calculate 14 7 3 2 Keys Display 14 ENTER 7 13 2 0 22 0000 4Q 5 5000 Description 2 3 h 10 Description Calculates 3 10 first Puts 2 before 13...

Page 30: ...3 4 x 5 6 on paper you would first calculate the quantity inside these parentheses 3 4 x 5 6 and then the quantity inside these parentheses and then you would multiply the two intermediate answers together You work throughthe problem the sameway with the HP 32S except that you don t have to write down intermediate answers the calcu lator remembers them for you Keys 3 IENTER I 40 5 IENTER I 6 0 0 D...

Page 31: ...e calculation the last result stored is the first to come back out You can calculate in the same order as you would with pencil and paper Exercises VO6 3805 x 5 Calculate 181 000 0 05 Solution 16 3805 Ienter I5 0 Q 05 0 Calculate V 2 3 x 4 5 V 6 7 x 8 9 21 5743 Solution 2 Ienter I3 0 4 Ienter I5Q0H6 Ienter I708 ClNTCR 900 0 Calculate 10 5 f 17 12 x 4 0 2500 Solution 17 Ienter 112 0 4 010 Ienter I5...

Page 32: ...pt FIX _ specify the number of decimal places to be displayed For 10 or 11 places press G 0 orQ 1 Decimal places 123 456 0000 Any number that is too large or too small to display in the current setting will automatically be displayed in scientific format Scientific Format SC SCI format displays a number in scien tific notation one number before the decimal point with up to 11 decimal places if the...

Page 33: ... first significant digit Power of 10 multiple of 3 Mantissa ALL Format RLL ALL format displays a number as preciselyas possible 12 digits maximum If not all digits 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 representatio...

Page 34: ...ent Temporarily shows full precision Messages The calculator responds to certain conditions or keystrokes by dis playing a message TheJL symbol comes on to call your attention to the message To clear a message press Pel or 4 To clear the message and perform another function press any other key If no message appears but Jk does then youhavepressed an inactive key a key that has no meaning in the cu...

Page 35: ...Memory Pressing Hi mem Ishows you the amount of memory still available 216 0 WAR PGM Jf 4 Bytes of memory s Catalog of variablesV Catalog of programs available See chapter 3 See chapter 5 page 49 page 85 1 Toenter the catalog of variables press VflR Toenter the cata log of programs press PGM 2 To review the catalogs press QF or JUTl 3 To delete a variable or a program press H clear Iwhile viewing ...

Page 36: ...s not affect settings modes and formats To clear settings as well as data see Clearing Memory in appendix B To clear all of memory 1 Press Ml clear I ALL You will then see the confirmation prompt CLR ALL Y N which safeguards against the unin tentional clearing of memory 2 Press Y yes 34 1 Getting Started ...

Page 37: ...heses The key to automatic storage is the automatic RPNmem ory stack The memory stack consists of four storage locations called registers which are stacked on top of each other It is a work area for calcula tions These registers labeled X Y Z and T store and manipulate four current numbers The oldest number is the one in the T top register 1HP s operating logic is based on an unambiguous parenthes...

Page 38: ...ple Hi 10 1 raises ten to the power of the number in the X register the displayed number Hi clear I x versus c Pressing Hi clear I always clears the X register to zero and it is also used to program this instruction The I c1 key in contrast is context sensitive It either clears or cancels the current display depending on the situation it acts like Ml clear I x only when the X register is displayed...

Page 39: ...at manipulates the stack contents is x y xexchange y It swaps the contents of the X and Y registers without affecting the rest of the stack Pressing x y twice of course restores the original order of the contents The x y function is used primarily for two purposes To view y and then return it to the Y regjster press fxiyl twice Some functions yield two results one into the X register and one into ...

Page 40: ...ter replicates its contents 2 The stack lifts its contents The top contents are lost 3 The stack drops Notice that when the stack lifts it pushes the top contents out of the T register and that number is lost You can see therefore that the stack s memory is limited to four numbers for calculations When the stack drops it replicates the contents of the T register Because of the automatic movement o...

Page 41: ...rites over the copy of the first number left in the X register The effect is simply to separate two se quentially entered numbers Youcan use the replicating effect of Ienter Ito clear the stack quickly press 01enter I enterICenter I All registers now contain zero Note however that you don t need to clear the stack before doing calculations Using a Number Twice in a Row You can use the replicating ...

Page 42: ...opulation 3 Calculates the population after 1 day 4 Calculates the population after 2 days 5 Calculates the population after 3 days How CLEAR x Works 1 5 1 5 1 5 150 0 4 1 5 1 5 1 5 225 0 5 1 5 1 5 1 5 337 5 Clearing the display X register puts a zero in the X register The next number you key in or recall writes over this zero There are three ways to clear the number in the X register that is to c...

Page 43: ...ates the X register 3 Overwrites the X register 4 Clears x by overwriting it with zero 5 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 exe cuted A numeric function is an operator that produces a result from another number or numbers such as QD Pressing Hi LASTx I...

Page 44: ... cor rect it by using M lastx Iand the inverse of the two number function 0 or 0 0 or 0 w or fg 1 Press Hll lastx 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 Xregister Then If you had used the wrong function press Hi lastx Iagain to restore the original stack conten...

Page 45: ...onstant in a calculation Remember to enter the constant second just before exe cuting the arithmetic operation so that the constant is the last number in the X register and therefore can be saved and retrieved with ILLASJxJ Example Calculate 96 704 52 3947 52 3947 T Z 96 704 Y Ienter I X LASTX f 52 3947 f 0 t z z t 96 704 96 704 z 96 704 52 3947 149 0987 I 52 3947 T Z Y LASTxl X t 0 f z t 149 0987...

Page 46: ...tars into meters to Rigel Centaurus 4 3 yr x 9 5 x 1015 m yr to Sirius 8 7 yr x 9 5 x 1015 m yr Keys Display 4 3080 Description 4 3 1ENTER Light years to R Centaurus 9 5 0 15 9 5E15 Speed of light c 0 4 085E16 9 5O00E15 Distance to R Centaurus 8 7 til LASTx Retrieves c 0 8 2650E16 Distance to Sirius Chain Calculations The automatic lifting and dropping of the stack s contents let you re tain inter...

Page 47: ...additional keystroke Notice that the first intermedi ate 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 x yl to reposition operands for noncommutative functions 0 and 0 The first method starting with the innermost parentheses is often preferred because It takes fewer keystrokes It requires fewer registers in the stack ...

Page 48: ... do to practiceusing RPN Calculate 14 12 x 18 12 _j 9 7 78 0000 A Solution 141enter 1120181 enter 11200 91enter I7 00 Calculate 232 13 x 9 V 412 1429 A Solution 23 BEE 13 Ienter I9 00 7 Qa 0 Calculate V 5 4 x 0 8 12 5 0 73 0 5961 A Solution 5 4 Ienter 1 8 0 7 Ienter I3 12 5 x Q0 1 or 5 4 I ENTER I 8 0 12 5 I ENTER I 7 I ENTER I30G0H W8 33 x 4 5 2 K8 33 7 46 x 0 32f_ V 4 3 x 3 15 2 75 1 71 x 2 01 A...

Page 49: ...lance and C for the speed of light 3ZS SCIENTIFIC ST0_ 3 II I k 2 0 0 0 E o0iGil CMPLX TT HYP ASM ACQS ATAN B 0 BiBB PARTS MOOES CliD GD CD CD 3 BASE CD GTO IXEQ Q urr D vi P RECT H HMS D HAI QD CID CD CD QD CD CD SOLVE S STAT PROB CD CD CD INPUT SHOW CD CD PRGM R S CD CD Cursor prompts for input Indicates letters are active Letter keys 1Note that the variables X Y Z and T are different storageloc...

Page 50: ...tter key To recall a copy of a number from a variable to the display press FrcTI letter key Example Storing Numbers Store Avogadro s number approxi mately 6 0225 X 1023 in A Keys 6 0225 D 23 STO A d key m RCL Display Description 6 0225E23_ STO _ Prompts for variable STO fl Displays function as long as key is held down 6 9225E23 Stores a copy of Avogadro s number in A This also terminates digit ent...

Page 51: ...les in the VAR Catalog The Hi mem I memory function provides information about memory Number of bytes available in memory nhn n VflR PGM Catalog of variables Catalog of programs To review the values of any or all non zero variables 1 Press HFmImI VflR 2 Press or a3 to move the list and display the desired vari able Note the va annunciator indicating that the arrow keys are active To see all the si...

Page 52: ... 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 rsTOllTI fsToFn fsrolPn or fSTOllTl to do arithmetic in the variable itself and to store the result there It uses the value in the ...

Page 53: ...ected all other stack registers are unaffected 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 PressfRCLl f 1 A Now x 0 25 while 12 is still in A iRCLll U 12 T f Z z Y y X 0 25 12 T t Z z Y y X 3 rcOlDla X Result 3 M2 that is x M Recall arithmetic savesmemoryspace in programs Using IRCL I T A oneinstruction uses half ...

Page 54: ...F 1 0000 0 2 0000 E 3 0000 F 4 0000 Adds 1 to D and F Ml view ID Displays the current value of D Ml VIEW I E HI view I F a 1 0000 Clears the VIEW display displays X reg ister again Suppose the variables D 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 RCL l J D 1 5000 Calculates 3 J D 1RCL11x E 4 5000 3 h D...

Page 55: ...es numbers as other variables do it is specialin that it can be used via the QJQ function to refer to other variables a technique called indirect addressing Because this is a programming technique it is covered in chapter 6 under Indirectly Addressing Variables and Labels 3 Storing Data Into Variables 53 ...

Page 56: ...mic functions Trigonometric functions Hyperbolic functions Percentage functions Conversion functions for coordinates angles and fractions Probability functions Parts of numbers number altering functions Arithmetic functions and calculations werecovered in chapters 1 and 2 The advanced numeric operations root finding integrating com plex numbers base conversions and statistics are in part 3 of this...

Page 57: ...LBUHTW LOOP FLAG CD QJ CEMjD SOLVE J STAT PROB MEM j3 3IXIJ GJ y x 6 r 6 r y x Cn r Pn r x RANDOM SEED RAD HMS Exponential and Logarithmic Functions Put the number in the display first then execute the function There is no need to press Ienter I To Calculate Press Natural logarithm base e ran Common logarithm base 10 HITogI Natural exponential El Common exponential antilogarithm mi 10 i 4 Real Num...

Page 58: ... Entering ir PressHIDE to place the first 12 digits of tt into the X register The number displayed depends on the display format Because this is a function ir does not need to be separated from another number by I ENTER I Note that a calculator cannot exactly represent k since ir is an irratio nal number Setting the Angular Mode The angular mode specifies which unit of measure to assume for an gle...

Page 59: ...Functions With x in the display 4 Note To Calculate Press Sine of x Cosine of x Tangent of x Arc sine of x Arc cosine of x Arc tangent of x SIN COS TAN KilASINl W ACQS KilATANl Calculations with the irrational number ir cannot be ex pressed exactly with the 12 digit internal precision of the calculator This is particularly noticeable in trigonom etry for example the calculated sin ir is not zero b...

Page 60: ...ming Note Equations using inverse trigonometric functions to determine an angle 6 often look something like this 6 arctan y x If x 0 then y s x is undefined resulting in the error DIVIDE BY 0 For a program then it would be more reliable to determine 6by a rectangular to polar conversion whichconverts x y to r 6 See Coordinate Conversions later in this chapter Actually thesecalculated results areth...

Page 61: ...0 and T be cause 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 carry out subsequent calculations using both the base number and the result without reentering the base number To Calculate Key In x of y Percentage change from y to x y 0 V 1ENTER X M 1 V 1ENTER 1 X Itil CHG Example Find the sales t...

Page 62: ...rder affects whether the percentage change is consid ered positive or negative Conversion Functions There are three types of conversions coordinate polar rectangular angular degrees radians and fractional decimal minutes seconds Coordinate Conversions P RECT Rectangular coordinates x y and polar coordinates r 6 are mea sured as shown in the illustration Functions in the P RECT polar from to rectan...

Page 63: ...I 3 Execute the conversion you want y x 8 r rectangular to po lar or Q r ytx polar to rectangular The converted coordinates occupy the X and Y registers 4 The resulting display shows either r polar result or x rectangu x y to see 0 or y X Y y 6 X x r Q r y x Example Polar to Rectangular Conversion Find x and y in the right triangle on the left Find r and 0in the right triangle on the right 4 Real ...

Page 64: ...ngineer P C Bord has deter mined that in the RC circuitshown on the next page at left the total impedance is 77 8 ohms and voltage lags current by 36 5 What are 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 ...

Page 65: ...tance Xc For more sophisticated operations with vectors addition subtraction cross product and dot product refer to the Vector Operations pro gram in chapter 12 Mathematics Programs Fractional Conversions H HMS Values for time in hours H or angles in degrees D can be con verted between a decimal fraction form H h or D d and a minutes seconds form H MMSSss or D MMSSss using the H HMS menu hours fro...

Page 66: ...venth as a deci mal fraction Mlh hms I HMS 0 083429 Equals 8 minutes and 34 29 seconds BirDispl FX 4 Restores FIX 4 format Angle Conversions D RAD The D RAD degrees from to radians menu operates independently of the angular mode When converting to radians the number in the X registeris assumed to be degrees Likewise when converting to de grees the number in the X register is assumed to be radians ...

Page 67: ...s played positive integer 0 s x 253 To calculate the gamma function ofa T a key in a 1 and pressBIprobI The x function calcu lates T x 1 The value for x cannot be a negative integer Random number generator Has two options Pressing RANDOM generates a random number in the range 0 x 1 Pressing SEED starts a new ran dom number sequence with the number that is in the X register The random number genera...

Page 68: ...d sbc at a time Probability menu Total number of com binations possible Ifemployees are chosen at random what is the probability that the committee will contain sbc women To find theprobability of an event divide the number of combinations for that event bythetotal number of combinations Description Fourteen women grouped six at a time Number of combina tions of six women on the committee Brings t...

Page 69: ...0 2300 Round RND Rounds x internally to the number of digits specified by the display format If not rounded the internal number is represented by 12 digits Absolute value Replaces x with its absolute value Names of Functions 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 ...

Page 70: ...3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 ...

Page 71: ... JM lHii i iMM w Co Programming Page 70 5 Simple Programming 90 6 Programming Techniques Hi ...

Page 72: ...nal instructions Introduction A Simple Programming Example To find the area of a circle with a radiusof 5 youwould use the formula A tt2 and press 5 IS 10 0 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 puttherepeatable keystrokes into a...

Page 73: ...ng a Program We will continue using the above program for the area of a circle to illustrate programming concepts and methods Program Boundaries LBL and RTN Ifyou want more than one program stored inprogram memory then a program needs a label tomark its beginning such as R01 LBL fl and a return to mark its end such as R05 RTN Notice that the line numbers acquire an fl to match their label Program ...

Page 74: ...n the line number appears with a decimal point instead of the leftmost number such as fl 01 for line 101 in A For more than 199 lines the line number uses a comma such as fl 01 for line 201 Program Returns Programs and subroutines should end with a re turn instruction The keystrokes are Hi LBL RTN RTN When a program finishes running the last RTN instruction returns the program pointer to PRGM TOP ...

Page 75: ... a return instruction which sets the pro gram pointer back to PRGM TOP after the program runs Press I LBL RTN I RTN 6 Press c or WIprgmI to cancel program entry Numbers in program lines are displayed as precisely as you entered them using ALL orSCI format If digits are hidden ina long number by the line number or an exponent press Hi show to view them Data Input and Output For programs that need m...

Page 76: ... previous program for the area of a circle and enter a new one thatincludes a label anda return instruction Ifyou make a mis take during entry press to delete the current program line then reenter it correctly Keys Display PRGM Hi CLEAR I PGM Y PRGM TOP Bl LBL RTN I LBL A fl01 LBL fl a A02 X BGD fl03 tr E J RTN A04 fl05 X IH LBL RTN RTN Lc Description Activates program en try PRGM on Clears all of...

Page 77: ...nter the data before executing the program Example Run the program labeled A to find the areas ofthree dif ferent circles with radii of 5 2 5 and 2ir Remember to enter the radius before executing A Keys 5rxEQl A 2 5fXEQl A 2HHLH Display 78 5398 19 6358 124 0251 Description Enters the radius then starts program A The resulting area is displayed Calculates area of sec ond circle Calculates area of t...

Page 78: ...without starting execution If the program is the first or only program you can press BfGToinFI to move to its beginning 3 Press andhold This displays the current program line When you release Tj 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 canpress Noexecution occurs 4 The program pointer moves to the next line Repeat...

Page 79: ...ables are used to store data input intermediate results and final results Variables as explained in chapter 3 are identified by a letter from Athrough Z but the variables names have nothing to do with program labels Entering Data Into Variables INPUT The INPUT instruction Hi input variable stops a running program and displays a prompt for the given variable This display includes the existing value...

Page 80: ...ney program on page 222 in part 4 The first thing that routine T does iscollect all thenecessary input for the variables N I B P and F lines T02 through T06 Since the INPUT instruction also leaves the value you just entered in the X register you don t have torecall the variable atalater time you could INPUT it and use it when you need it You might beable tosave some memory space this way However i...

Page 81: ...ay digits hiddenby the prompt press Hishow 1 Ifit is a binary number with more than 12 digits use the Qx and s keys to see the rest Displaying Data in Variables VIEW The programmed VIEW instruction JillviEWl variable stops a running program and displays and identifies the contents of the given vari able such as R 78 5398 This is a display only and it does not copy the number to the X register Pres...

Page 82: ...e viewing a VIEW display would have the same effect Example INPUTting and VIEWing Variables in a Program Write anequation tofind thesurface area andvolume ofa cylinder given its radius and height Label the program C for cylinder and use the variables S surface area V volume R radius and H height Use these formulas V irR2H S 2ttR2 2irRH 2 irR2 irRH Keys PRGM lUroJQQ Hi LBL RTN I LBL C C is the W ke...

Page 83: ...C19 VIEW V Will display volume C20 VIEW S and surface area Ends program Cancels program entry LBL C 031 5 Checks memory usage CHKSUM 4602 and checksum A dif ferent checksum means the program was not entered exactly as it is given here Now find the volume and surface area of a cylinder with a radius of 2 5 cm and a height of 8 0 cm Description Starts executing C prompts for R It dis plays whatever ...

Page 84: ... You can interrupt a running program at any time by pressing c or FrTsI The program completes its current instruction before stopping Press rTsI run stop to resume the program If you interrupt a program and then press IXEQ I IGTO I or RTN you cannot resume the program with IR SI Re execute the program instead fxEQl label Error Stops If an error occurs in the course of a running program program exe...

Page 85: ...change by pressing g Thepointer 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 c or Hi prgmI To insert a program line Locate and display the program line that is before the spot whereyouwould liketo inserta line Key in the new...

Page 86: ...st line wraps the pointer around to PRGM TOP while pressing B 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 T or T key Press IGTO 100 to move the program pointer to PRGM TOP Press IGTO 10 label nn to move to a labeled line number 100 If program entryis not active nolines displayed you canalso move the program point...

Page 87: ... list You can use this catalog to Review the labelsin program memoryand the memorycostof each labeled program or routine Execute a labeled program Press fxlcn or rTsI while the label is displayed Display a labeled program Press Hi prgm Iwhile the label is displayed n Delete specific programs Press Hi clear Iwhile the label is displayed See the checksum associated with a given program segment Press...

Page 88: ...omparison 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 the lines of the program Tosee your checksum 1 Press Hi mem 1 PGM for the catalog of program labels 2 Display the appropriate label by using the arrow keys if necessary 3 Press and hold 111 show I...

Page 89: ...e variable several times for their solution For example the expression f x Ax4 Bx3 Cx2 Dx E uses the variable x four different times A program to solve such an equation could repeatedly recall a stored copy of x from a variable A shorter programming method however would be to use a stack which has been filled with the constant see Filling the StackWith a Constant on page 39 in chapter 2 Horner s M...

Page 90: ...x z x then evaluate it for x 7 Keys Display Description HI PRGMI MlGTO QQ PRGM TOP P01 LBL P P02 INPUT X P03 ENTER P04 ENTER P05 ENTER You can skip the 1gto 1 if the display already shows PRGM TOP LBL RTN LBL P 111 INPUT X I ENTER Fills the stack with x then calculates 5x I ENTER 1ENTER 5 P06 5 s P07 X 2 P08 2 P09 P10 X 5x 2 x 0 Pll P12 P13 X X RTN Sx 2 x3 Ml LBL RTN RTN c Cancels program entry 88...

Page 91: ... A more general form of this program for any equation Ax B x Qx D x E would be P81 LBL P P02 INPUT fl P03 INPUT B P04 INPUT C P05 INPUT D P06 INPUT E P07 INPUT X P08 ENTER P09 ENTER P10 ENTER Pll RCLx fl P12 RCL B P13 x P14 RCL C P15 x P16 RCL D P17 x P18 RCL E P19 RTN 5 Simple Programming 89 ...

Page 92: ...instructions comparisons and flags to determine which instructions or subroutines should be used in a particular case Using loops with counters to execute a set of instructions a certain number of times Using indirect addressing to access different variables using the same program instruction Routines in Programs A program is composed of one or more routines Aroutine is a func tional unit that acc...

Page 93: ...by another rou tine and returns to that same routine when the subroutine is finished The subroutine must start with a LBLand end with a RTN A subrou tine is itself a routine and it can call other subroutines XEQ must branch to a label LBL for the subroutine It cannot branch to a line number At the very next RTN encountered program execution returns to the line after the originating XEQ For example...

Page 94: ... LBL E XEQ B I4 XEQ C XEQ 0 XEQ E V SIN K 3 1416 K SQRT IN RCL R h RTN RTN V RTN V RTN 7 RTN End of program Attempting to execute a subroutine nested more than seven levels deep causes an XEQ OVERFLOW error Example A Nested Subroutine The following subroutine labeled S calculates the value of the expression Vfl2 b2 c2 d2 as part of a larger calculation in a larger program The subroutine calls upon...

Page 95: ... B1 1 S12 XEQ Q Calculates A2 B2 C2 2 OS 13 XEQ Q Calculates A2 B2 C2 D2 3 S14 SQRT Calculates Va2 B2 C2 r D2 Ends main subroutine returns S15 RTN execution to main program Q01 LBL Q Starts nested subroutine Q02 xOy Squares number and adds it to Q03 X the current sum of squares Q04 Q05 RTN Ends nested subroutine 0 re turns to first subroutine S Branching GTO As we have seen with subroutines it is ...

Page 96: ... For example consider the Curve Fitting program on page 204 in part 4 The GTO Z instruction branches execution from any one of three independentinitializing routinesto LBL Z the routine that is the common entry point into the heart of the program S01 LBL S S05 GTO Z L01 LBL L L05 GTO Z E01 LBL E E05 GTO Z Z01 LBL Z Using IH gto1 From the Keyboard If program entry is not active no program lines dis...

Page 97: ...branching to line A07 This rule is commonly known as Do if true Do if true R01 LBL R Skip if false R05 x G _ R96 GTO B j R07 LN J R08 STO R i to LBL B The example above points out a common technique usedwith condi tional tests theline immediately after thetest which isonly 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...

Page 98: ...ison then press the menu key for the conditional instruction you want The TESTS Menu Keys 0 y for x y 0 for x 0 y for x y for 0 y for x y 0 for x 0 y for x y 0 for x 0 Although you can display these menus outside of program entry these functions have no purpose outside of programs For Example The Quadratic Equation program on page 191 in part 4 uses the x 0 and x 0 conditionals in routine Q Q01 LB...

Page 99: ...flags from the keyboard Flags 0 1 2 3 and 4 haveno preassigned meanings Thatis their status will mean whatever you define it to mean in a given pro gram See the example below Flag 5 when set willinterrupt a program whenan overflow occurs within the program displaying OVERFLOW and A If flag 5 is clear a program with an overflow is not interrupted though OVERFLOW is displayedbriefly when the program...

Page 100: ...uction See Test ing Flags FS below Functions ffor Flags Pressing M flags Idisplays the RAGS menu SF CF FS After selecting the function you want you will be prompted for the flag number 0 6 For example to set flag 0 pressM flags I SF 0 The FLAGS Menu Menu Key Description SF n CF n FS n Set flag Sets flag n Clear flag Clears flag n Is flag set Tests the status of flag n Testing Flags FS Aflag testis...

Page 101: ...son to remember the signof B Note that line Qll clears flag 0 to makesure that it will be set for only the condition desired Qll CF 0 Makes sure that flag 0 is clear Q12x 0 IsB in X register negative Q13 SF 0 Sets flag 0 if B is negative Q23 FS 0 Is flag 0 set is B negative Q24 If yes change sign Q25 In either case add Other programs in part 4 that make use of flags are Curve Fitting and UnitConve...

Page 102: ...m 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 instruction For example the following routine uses a loop to diminish a value A by aconstant amount Buntil the resulting Ais less than or equal to B Program Lines fl01 LBL fl A02 INPUT fl fl03 INPUT B 501 LBL S 502 RCL fl 503 RCL ...

Page 103: ...g as a FOR NEXT loop in BASIC FOR variable initial value TO final value STEP increment NEXT variable A DSE instruction is like a FOR NEXT loop with a negative increment After pressing the menu key for DSE or ISG you will be promptedfor a variable that will contain the loop control number de scribed below The Loop Control Number The specified variable should contain a loop control number ccccccc ff...

Page 104: ...t value final value continue loop W01 LBL N W09 DSE W10 GTO Mil XEQ X X I U01 LBL W W09 ISG W10 GTO Wll XEQ X 3 I If current value s final value exit loop If current value 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 ...

Page 105: ...iable A through Z GJO is a programming function that directs Use the number in i to determine which variable or label to address This is an indirect address A through Z are direct addresses Both J and Qjj are used together to create an indirect address See the examples below By itself i is just another variable By itself QjQ is either undefined no number in i or uncontrolled using whatever number ...

Page 106: ...hen 0 will address 1 variable A or label A 26 variable Z or label Z 27 or 27 or 0 error INUflLID i Only the absolute value of the integer portion of the number in i is used for addressing Following are the functions that can use i as an address For GTO XEQ and FN i refers to a label for all other functions it refers to a variable Functions That Use 0 for Indirect Addressing STO i INPUT i RCL i VIE...

Page 107: ...f The Curve Fitting pro gram on page 204 in part 4 uses indirect addressing to determine which model to use to compute estimated values for x and y Differ ent 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 fittingmodelthat willbe used...

Page 108: ...ions Determinant Method on page 175 in part 4 This program uses the looping in structions ISG i and DSE i in conjunction with the indirect instructions RCL i and ST0 i to fill and manipulate a matrix The first part of this program is routine A which puts the initial loop control number in i Program Lines R01 LBL R R02 1 012 R03 STO i Description The starting point for data input Loop control numbe...

Page 109: ...n 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 exe cution branches back to A 6 Programming Techniques 107 ...

Page 110: ...cccccccccccccccccccccccccccccccce ...

Page 111: ...ced Operation Page 110 7 Solving for an Unknown Variable in an Equation 126 8 Numerical Integration 137 9 Operations With Complex Numbers 144 10 Base Conversions and Arithmetic 153 11 Statistical Operations ...

Page 112: ...Markup x Cost Price Markup x Cost Price 0 If 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 the variables except one then to solve for x is to find the root s of the equation A root of an equation occurs where the graph of the function crosses the x axis because at that point the ...

Page 113: ... the unknown variable beforestarting the calculation step3 This can speed up the calculation direct the answer toward a realistic solution and find more than one solution if appropriate See Choosing Initial Guesses for SOLVE on page 120 Results The X register and the variable itself contain the final esti mate of the root the Y register contains the previous estimate and theZ register contains the...

Page 114: ... equal to zero yields Length x Width x Height Volume 0 or LxWxH V 0 To write a program evaluating a function 1 Begin with a label so that the program can be called by SOLVE 2 Include an INPUT instruction for each variable including the unknown If there is only one variable in the function omit the INPUT instruction since it is ignored for the unknownanyway t SOLVE worksonlywith real numbers Howeve...

Page 115: ...tion has been found for the unknown variable Examples Using SOLVE Example Solving for the Dimensions of a Box Use the following program to evaluate the dimensions of a box L x Wx H V Note that the program uses recall arithmetic which takeslessmemory than recalling a variable and doing arithmetic as separate operations B81 LBL B B02 INPUT L B83 INPUT W B04 INPUT H B05 INPUT y B06 RCL L B07 RCL W B0...

Page 116: ... will use the same function to solve for a dif ferent variable SOLVE 1 FN B SOLVE SOLVE V 25 IPflTsI 8 5 R S r7s FN _ Prompts for the label of the program that de fines the function Specifies program B SOLVE _ Prompts for the un known variable L value W value H value Starts program B prompts for all data ex cept V the variable being solved SOLVING The volume is 2 125 V 2 125 0080 cm3 Now solve for...

Page 117: ... g is the acceleration due to gravity Setting the equation equal to zero and simplifying it yields 0 n 0 2 d The following program evaluates this function M01 M02 1183 FI04 M05 1186 M07 108 1109 N10 Mil Ml 2 Ml 3 LBL M INPUT INPUT INPUT INPUT RCL G 2 RCLx T RCL V RCLx T RCL D RTN The acceleration due to gravity g is included as a variable to allow you to change it for working with different units ...

Page 118: ...ong does it take an object to fall 500 meters Since v0 and g are already stored there is no need to reenter them MSOLVE 1 S0LVE T R Sl rTsI 500 rTs V 0 0000 G 9 8000 D 122 5000 T 10 1015 Specifies a different unknown prompts for V Result in seconds Example Finding the Roots of an Equation Consider the single variable equation x3 5x2 lOx 20 Rearranging the equation so one side is zero yields x3 5x2...

Page 119: ...ulator can find all three roots if you run SOLVE three times and supply different initial guesses each time For more information see Choosing Initial Guesses for SOLVE Enter theabove program LBL R The graph shows that thefirst root is somewhere between x 3 and x 2 the second root is be tween 1 and 2 and the third root is between 6 and 7 Put each set of guesses in the variable Xand in the X registe...

Page 120: ... it to or not Understanding and Controlling SOLVE SOLVE uses an iterative repetitive procedure to solve for the un known variable The procedure starts by substituting two initial guesses for the unknown into the function defined in the program Based on the result withthose twoguesses SOLVE generates another better guess Through successive iterations SOLVE finds a value that makes the function equa...

Page 121: ...ro then the root given was only an approxima tion and this number should be close to zero If a calculation ends with NO ROOT FND this means that the cal culation couldnot converge on a root so the values in the X and Y registers areprobably not close together You canseethe value in the X register the final estimate of the root by pressing 51 or RTI to clearthe message These twovalues bracket the i...

Page 122: ...e equation of motion d d0 v0t Vigt2 can have two solutions for t You can direct the answer to the only meaningful one t 0 by entering appropriate guesses If an equation does not allow certain values for the unknown guesses can prevent these values from occurring For example the equation y t log results in an error if x 0 LOG 0 L0G NEG The example in the previous section Finding the Roots of an Equ...

Page 123: ... the box that is the amount to be folded up along each of the four sides that gives the specified volume A taller box is preferred to a shorter one I ro i r 80 If H is the height then the length of the box is 80 2H and the width is 40 2H The volume V is V 80 2H x 40 2H x H and the function equal to zero is 0 80 2H x 40 2H xH V 4H 40 H 20 H V 7 Solving for an Unknown Variable in an Equation 121 ...

Page 124: ...physically possible because the metal sheet is only 40 centimeters wide Initial estimates of 10 and 20 centimeters are therefore appropriate Keys Display H SOLVE JFN V 10 STO H 20 10 0000 20_ IM SOLVE fSOLVEi H V va i e 7500 R S SOLVING H 15 0000 Description Selects program V as the function to solve Stores upper and lower limits Prompts for volume This is the desired height Now check the quality ...

Page 125: ...d 10 cm you would obtain a height of 2 9744 cm pro ducing an undesirably short flat box Using Graphs to Select Initial Guesses As an aid to understand ing the behavior of a particular function you can graph it Use your program routine to evaluate the function for several values of the un known For each point on the graph store the value for the x coordinate in the variable and then obtain the corr...

Page 126: ...ing it If you do want this result displayed add a VIEW variable instruction after the SOLVE instruction Conditional Execution if No Solution If no solution is found for the unknown variable then the next program line is skipped in ac cordance with the Do if True rule explained in chapter 6 The program should then handle the case of not finding a root such as by choosing new initial estimates or ch...

Page 127: ...n that is it cannot be used recursively S0LVE S0LVE error Nor can SOLVEcall a routine that contains a FN label instruction SOLVE ACTIVE error SOLVE cannot call a routine that contains an FN instruction SOLVECfFN error just as FN cannot call a routine that contains a SOLVE instruction SOLVE error The SOLVE variable instruction in a program uses one of the seven pending subroutine returns in the cal...

Page 128: ... The quantity I can be interpreted geometrically as the area of a region bounded by the graph of the function fix the x axis and the limits x a and x b provided that fix is nonnegative throughout the in terval of integration The FN operation integrates a specified function with respect to a specified variable The function must be defined beforehand in a la beled program and it may have more than o...

Page 129: ...tion about the integration is available until the calculation finishes normally To resume the calculation press Ir s I Accuracy The display format setting affects the level of accuracy as sumed for your function and used for the result Integration is more precise but takes much longer in the ALL and higher FX SC and EN settings The uncertainty of the result ends up in the Y register pushing the li...

Page 130: ... is only one variable in the function you can omit the INPUT instruction 3 Enter the instructions to define the function Use a RCL instruc tion any place a variable s value is needed for a calculation 4 End the program with a RTN The program should end with the value of the function in the X register Examples Using FN Example Bessel Function The Bessel function of the first kind of order 0 can be ...

Page 131: ...ODES RD J02 RAD IHI INPUT X J03 INPUT X Ml INPUT IT J04 INPUT T 1RCL I T 1SIN I J06 SIN 1RCL 11 x X ICOS I J08 COS At this point the X m LBL RTN I RTN JQ9 RTN regjster will contain the value of the function c Now integrate this function with respect Hi SOLVE I FN FN _ 0 IENTER I Hm 3 1416 Bl SOLVE J I FN XFN d _ T X va we Ends program entry to t from zero to ir x 2 Selects routine J for the functi...

Page 132: ... HI SOLVE FN T Starts integration prompts for x 3 R S T 0 8170 Integral of fit 10 0 0 2601 Result for 0 3 Example Sine Integral Certain problems in communications the ory for example pulse transmission through idealized networks require calculating an integral sometimes called the sine integral of the form Si t X fr Find Si 2 Key in the following program to evaluate the function fix sinx 5 x If th...

Page 133: ... integral exactly it approximates it The accuracy of this approximation depends on the accuracy of the integrand s function itself as calculated by your pro gram 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 likel...

Page 134: ...vel of accuracy and precision will be reflected in the result of integration Interpreting Accuracy After calculating the integral the calculator places the estimated un certainty of that integral s result in the Y regjster Press y 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...

Page 135: ...ainty of an integration calculation decreases by a factor of 10 for each additional digit specified in the display format Example Changing the Accuracy For the integral of Si 2 just cal culated specify that the result be accurate to four decimal places instead of only two Keys Display EBl DISP SC 4 1 0000E 3 ED LIE 2 0000E0 SOLVE XFN X X 1 6054E0 1 0000E 5 L idJSP FX 4 Description Specifies accura...

Page 136: ...ccuracy and execution time are controlled by the display format at the time the program runs The two integration in structions appear in the program as FN label FN d variable Labeling Output The programmed FN instruction does not produce a labeled display S value since this might not be the significant out put for your program that is you might want to do further calculations with this number If y...

Page 137: ... FN d D Integrates the normal function for the vari able D Limitations The FN variable instruction cannot call a routine that contains another FN instruction that is it cannot be used recursively so you cannot calculate multiple integrals X XFN error Nor can FN call a routine that contains a FN label instruction JFN ACTIVE error FN cannot call a routine that contains a SOLVE in struction S SOLVE e...

Page 138: ...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 136 8 Numerical Integration ...

Page 139: ...are complex numbers Complex numbers in the HP 32S are handled by entering each part imaginary and real of a complex number as a separate entry To en ter two complex numbers you enter four separate numbers To do a complex operation press1H cmplx I before the operator For example to do 2 i4 3 f5 press 41enter 121 enter 151 enter 13Hl cmplx I The result is 5 i 9 Press x y to see the imaginary part 9 ...

Page 140: ...ry and real parts of a complex number are entered and stored separately you can easily work with or alter either part by itself Ki 1 2 2 Complex function displayed imaginary part real part Complex input z or z1 and z2 Complex result z Always enter the imaginary part the y part ofa number first The real por tion of the result z is displayed press x y to view the imaginary portion Zy 138 9 Operation...

Page 141: ... z Inverse 1 z Natural log In z Natural antilog e2 Sin z Cos z Tan z Ml CMPLX _ HI CMPLX 11 x ftll CMPLX LN Ml CMPLX 16 Ml CMPLX SIN HI CMPLX COS Mil CMPLX TAN To do an arithmetic operation with two complex numbers 1 Enter the first complex number Zj composed of X iy by keyingin y21 enter IXj Ienter I For zfr key in the base part zv first 2 Enter the second complex number z2 by keying in y21 enter...

Page 142: ...amples Here are some examples of trigonometry and arithmetic with complex numbers Evaluate sin 2 z 3 Keys Display 3 I ENTERI 2 Hi CMPLX fslN 9 1545 4 1689 Description Real part of result Result is 9 1545 4 1689 Evaluate the expression zi 22 zi where zx 23 i 13 z2 2 i z3 4 z 3 Since the stack can retain only two complex numbers at a time per form the calculation as i x 1 fe Za 140 9 Operations With...

Page 143: ...part of a complex number Keys Display 0 4000 4 0000 8 6667 11 7333 Description 2 IENTER 5 I M Al Calculates imaginary part using real operations 4 I ENTER I Enters real part of first complex number 2 1ENTER I 3 I II I Calculates imaginary part of second complex number 3 CMPLX x Completes entry of second number and then multiplies the two complex numbers Result is 11 7333 i3 8667 Lxuj 3 8667 Evalua...

Page 144: ...lex numbers so you can do arithmetic with these numbers by using the complex opera tions Since the HP 32S s complex operations work on numbers in rectangular form convert polar form to rectangular form using 111 p REcf before executingthe complexoperation then convert the result back to polar form a to r cos 0 i sin 6 rei r L 0 Polar or phasor form imaginary j 4 real Example Vector Addition Add th...

Page 145: ...f l P RECT etr y x Hi cmplx I m Hi P RECT y x Q r J Zl 135 7680 48 9158 15 6434 64 5592 178 9372 111 1489 185 LB A 62 Description Sets Degrees mode Enters Lj and converts it to rectangular form Enters and converts L2 Adds vectors Enters and converts L3 Adds Lj L2 L3 Converts vector back to polar form displays r Displays 9 Operations With Complex Numbers 143 ...

Page 146: ...ow keys become digits t through fTl Octal mode OCT annunciator on Converts numbers to base 8 uses integers only TheQT QD and unshifted top row keys are inactive Binary mode BIN annunciator on Converts numbers to base 2 uses integers only Digit keys other than Qj and T and the unshifted top row functions are inactive If a number is longer than 12 digits then the outer top row keys Q Jand IS l are a...

Page 147: ...t Convert 24FF16 to binary base The binary number will be more than 12 digits the maximum display long HrBASEl HX 24FF fifBASEl BN GD 1UASE DEC 24FF_ Use the s key to type F 010011111111 The entire binary num ber does not fit The annunciator indi cates that the number continues to the left the V annunciator points to Qx 10 Displays the rest of the number The full number is 100100111111112 01001111...

Page 148: ...e number in the X register If the result of an operation cannot be represented in 36 bits the dis play shows OVERFLOW and then the largest positive or negative number possible Examples Here are some examples of arithmetic in Hexadecimal Octal and Binary modes Keys ariASE hx 12F IENTER I E9A 12F16 E9A16 Display Description Sets base 16 HEX an nunciator on FC9 Result The only function keys that are ...

Page 149: ...or on Changes to base 2 BIN 1001100_ annunciator on This terminates digit entry so no Ienter Iis needed between the numbers 10U110U00 Result in binary base 5EC Result in hexadecimal base 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...

Page 150: ...gnificant 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 0 positive A negative number is the 2 s complement of its positive binary number Keys 546HrBAsT HX W BASE BN GDGU BASE DEC Display Description 222 Enters a positive deci mal number then converts it to hexadecimal FFFFFFDDE 2 s com...

Page 151: ... 34 359 738 368 When you key in numbers the calculator will not accept more than the maximum number of digits for each base Forexample if you at tempt to keyin a 10 digit hexadecimal number digit entryhalts and the A annunciator appears 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 cause...

Page 152: ...ow 000000000880 111111111111 t 7 Press to display IBHElDgiE right window SHOWing Partially Hidden Numbers The ill view 1and Bl input functions work with non decimal numbers as theydo with decimal numbers However if the full octal or binary number does not fit in the display the leftmost digits are replaced with ellipses Press Si show Ito view the digits obscured by the fl or fl labels Keys WfBASEl...

Page 153: ...Program Insert a BIN OCT or HEX instruction into the beginning of the pro gram 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 how input is interpreted and how output looks during and after pro gram execution but it does not...

Page 154: ... program lines below in the left and right columns Notice that the hexadecimal number like all non decimal numbers is right justified Decimal mode set PROM R99 HEX PROM R1Q 23 Hexadecimal mode set PROM R09 HEX PROM R10 Program line numbers are always decimal HEX H HEX 1 Current base mode set 152 10 Base Conversions and Arithmetic ...

Page 155: ...ear estimation x and y Weighted mean x weighted by y Summation statistics n 2x Sy 2x2 Sy2 and Sxy I I I I I I n x y x2 y2 xy T y STAT r sx xw 1 sy L R n n x y r m b Entering Statistical Data I s N lUfs17 One and two variable statistical data are entered in similar fashion The data values are accumulated as summation statistics in six statis tics registers whose values are displayed under Hi stat I...

Page 156: ...cal data 2 Key in the y value first and press Ienter I 3 Key in the corresponding x value and press Is l 4 The display shows n the number of statistical data pairs now accumulated 5 Continue entering x y pairs The n value is updated with each entry To recall an x value to the display immediately after it has been en tered press Si last This procedureactually enters two variables into the statistic...

Page 157: ...astx to retrieve them then BUEI to delete them The in correct y value was still in the Y register and its x value was saved in the LASTx register Example Key in the x y values on the left then make the correc tions shown on the right Keys Initial x y Corrected x y 20 4 400 6 20 5 40 6 Display 111CLEAR m 4 1ENTER120 fS 1 6 1ENTER 1400 IH l 1 8888 2 8888 HI LASTx 488 8888 Description Clears previous...

Page 158: ...ummation menu n 2x 2y 2x2 2y2 2xy See Sum mation Statistics The mean menu x y and weighted x xw See Mean and Standard Deviation s The standard deviation menu sx and sy See Mean and Standard Deviation L R The linear regression menu curve fitting r m b and linear estimation x y See Linear Regression Mean and Standard Deviation The Mean x y Menu Press Bl stat I x y x for the arithmetic mean average o...

Page 159: ... process and records the number of min utes required 15 5 9 25 10 0 12 5 12 0 8 5 Calculate the mean and standard deviation of the times Treat all these data as x values Keys Display Description 1 CLEAR Zr Clears the statistics registers 15 5 2 1 1 0000 Enters the first time 9 25 2 1 10 2 1 12 5 2 12 2 8 5 U 3 0000 5 0000 6 0000 11 2917 Enters the remaining data ISTATI x y x Calculates mean This c...

Page 160: ...Display Description Clears the statistics registers 1 0000 2 0000 3 0000 4 0000 Enters the data and their weights 4 4314 Calculates mean price weighted for quantity purchased Linear Regression linear regression also called linear estimation is a statistical method for finding a straight line that best fits a set of z y data Be sure to enter your data values before using these functions To find an ...

Page 161: ...ng The yield of a new variety of rice depends on its rate of fertilization with nitrogen For the following data deter mine the linear relationship the correlation coefficient the slope and the y intercept X Nitrogen Applied kg per 0 00 20 00 40 00 60 00 80 00 hectare Y Grain Yield metric tons 4 63 5 78 6 61 7 21 7 78 per hectare Keys CLEAR 2 4 63 5 78 ENTERI 0 I 2 1 ENTER I 20 2 1 6 61 7 21 7 78 E...

Page 162: ...e rice field Pre dict the grain yield based on the above statistics Keys 70 Display 70_ Hi STAT I L R y 7 5615 Description Enters hypothetical x value 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 160 11 Statistical Operat...

Page 163: ...s can result if your x and y values have greatly dif ferent magnitudes Again scaling the data can avoid this problem Effect of Deleted Data Executing BCED does not delete any rounding errors that might have been generated in the statistics regis ters 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...

Page 164: ...d if it doesn t existalready when you press 12 1 or 12 L v The registers are deleted and the memory deallocated when you exe cute CL AR 2 O If not enough calculator memory is available to hold the statistics reg isters when you first press I2 1 or 12 1 the calculator displays f MEMORY FULL You will need to clear variables or programs or both to make room for the statistics registers before you can...

Page 165: ... 5P Application Programs Page 164 12 Mathematics Programs 204 13 Statistics Programs 222 14 Miscellaneous Programs ...

Page 166: ... Vector Operations This program performs the basic vector operations of addition sub traction cross product and dot or scalar product The program uses three dimensional vectors and provides input and output in rectangu lar or polar form Angles between vectors can also be found Vector Coordinate Systems 164 12 Mathematics Programs ...

Page 167: ...P arctan VX2 Y2 Vector addition and subtraction vi v2 X U i Y V j Z W k v2 Vl U X i V Y j IV Z k Cross product vx x v2 YW ZV i ZU XW j XV YU k Dot product D XU YV ZW Angle between vectors 7 G arccos J j x K2 where vx Xi Yj Zk and v2 lii Vj Wk The vector displayed by the input routines LBL P and LBL R is Vj 12 Mathematics Programs 165 ...

Page 168: ...ular input display routine Displays or accepts input of X Displays or accepts input of Y Displays or accepts input of Z 006 0 80FB Defines beginning of rectangular to polar conversion process Calculates V X2 Y2 and arctan Y X Saves T arctan Y X Gets V X2 Y2 back Calculates V X2 Y2 Z2 and P Saves R Saves P 018 0 D6D5 Defines the beginning of the polar input display routine Displays or accepts input...

Page 169: ...06 RCL Z E07 STO w E08 GTO Q Loops back for polar conversion and display input Bytes and Checksum 012 0 7137 XOl LBL X Defines beginning of vector exchange routine X02 RCL X Exchanges X Y and Z with U V and W respectively X03 RCL U X04 STO X X05 xOy X06 STO U X07 RCL Y X08 RCL V X09 STO Y X10 xOy Xll STO V X12 RCL Z X13 RCL W X14 STO Z X15 xOy X16 STO W XI7 GTO Q Loops back for polar conversion an...

Page 170: ...LBL S Defines the beginning of the vector subtraction routine 502 1 Multiplies X Y and Z by 1 to change the sign 503 STOx x 504 STOx Y 505 STOx Z 506 GTO fl Goes to the vector addition routine Bytes and Checksum 017 0 250B C01 LBL C Defines the beginning of the cross product routine C02 RCL Y C03 RCLx W C04 RCL Z C05 RCLx V C06 Calculates YW ZV which is the X component C07 RCL Z C08 RCLx U C09 RCL...

Page 171: ... LBL D Defines beginning of dot product and vector angle routine D02 RCL X 003 RCLx U 004 RCL Y 005 RCLx y D06 007 RCL Z 008 RCLx W D09 D10 STO D 011 VIEW D D12 RCL D 013 RCL R 014 T D15 RCL W 016 RCL V 017 RCL U 018 y x 8 r D19 xOy 020 R 021 y x 9 r 022 xOy 023 R Stores the dot product of X17 YV ZW Displays the dot product Dividesthe dot product by the magnitude of the X Y Z vector Calculates the...

Page 172: ...instead of the proper three dimensional terms of spherical and Cartesian This stretch of terminology allows the la bels 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 QT when done 2 If your vectoris i...

Page 173: ...ted the cross product vj has been replaced by the result v2 is not altered To continue cal culations based on the result remember to press IxeqI E before keying in a new vector 10 Go to step 2 to continue vector calculations Variables Used X Y Z u V W KT P D G The rectangular components of vj The rectangular components of v2 The radius the angle in the x y plane 8 and the angle from the Z axis of ...

Page 174: ... ir s R 17 3388 Sets Z equal to 0 76 and calculates R the radius R S T 65 6631 Calculates T the angle in the x y plane R S P 92 5134 Calculates P the angle from the z axis 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 172 12 Mathematics Programs ...

Page 175: ...qual to 215 17 R S R 17 0000 Sets P equal to 17 xeq E R 17 0908 Enters vector by copy ing it into v2 23 R S T9 145 0000 Sets radius of vj equal to 23 80 R S P 17 0000 Sets T equal to 80 74 IR SI R 23 0000 Sets P equal to 74 XEQ A R729 4741 Adds the vectors and displays the resultant R iTsI T990 7032 Displays T of resultant vector 12 Mathematics Programs 173 ...

Page 176: ...R sl XEQ C R S IrTs rXEQlR rR S R S Display T790 7032 P739 9445 R71 0700 R 18 0209 T955 3719 P 124 3412 X 8 4554 Y 12 2439 Z9 10 1660 Description Sets R equal to 1 07 Sets T equal to 125 Sets P equal to 63 Calculates cross prod uct and displays R of result Displays T of cross product Displays P of cross product Displays rectangular form of cross product The dot product can be used to resolve the f...

Page 177: ...culates angle be tween resultant force vector and lever R S R71 0000 Gets back to input routine Solutions of Simultaneous Equations Determinant Method Thisprogramsolvessimultaneouslinear equationsin two or three un knowns The program uses Cramer s method also know as the method of determinants Given a system of three linear equations AX DY GZ BX EY HZ K CX FY IZ L the three unknowns X Y and Z may ...

Page 178: ...i Description Starting point for input of all known values Loop control value loops from 1 to 12 1 at a time Stores control value in index variable 012 5 7878 Starts the input loop Prompts for and stores the variable pointed to by i Adds one to i If i is less than 13 goes back to LBL L and gets the next value Returns to LBL A to review values 007 5 C1DE Starting point for simultaneous equation sol...

Page 179: ...es determinant to original form Calculates determinant of original coefficients Divides by original determinant S05 XEQ D S06 STO 2 S07 XEQ E S08 6 S89 STO i S10 XEQ E Sll XEQ D S12 STO Y S13 XEQ E S14 3 S15 STO i S16 XEQ E S17 XEQ D S18 STO X S19 XEQ E S20 XEQ D S21 STO X S22 STO Y S23 STO 2 S24 RCL X S25 VIEW X S26 RCL Y S27 VIEW Y S28 RCL Z S29 VIEW 2 S30 RTN Recalls and displays results for X ...

Page 180: ...terminant E14 RCLCi Gets top element from column of determinant El5 RCL J Gets top element from vector E16 ST0 i Saves vector element in determinant E17 xOy Gets the determinant element back E18 STO J Saves the determinant element in the vector E19 2 E20 STO i Restores i to its original value when routine started E21 RTN Returns to the calling program or to PRGM TOP Bytes and Checksum 031 5 8420 D...

Page 181: ...es press c when done 2 PressfxEQl Ato input coefficients that is A through L of linear equations 3 Key in coefficient A through L at each prompt and pressIR s I 4 Optional to compute determinant of a 3 x 3 system IXEQI D 5 Compute solution to system of equations by pressing IXEQI S 6 See value of X and press IR SI to see the value of Y 7 Press IR S I to see the value of Z 8 For a new case go back ...

Page 182: ... the system solution Then substitute the values back into the first equa tion to verify that the left side of the equation is actually equal to the right side 1 23X 15Y 17Z 1 8X 11Y 6Z 1 4X 15Y 12Z 1 Keys IXEQIA 23fR7s 8 r7s 4 r7s 15 fR Si 1 rTsI ICEQl D Display Description fl va ae Starts input routine B value Sets first coefficient A equal to 23 C value Sets B equal to 8 D value Sets C equal to ...

Page 183: ...ys Y Displays Z Description Multiplies X by 23 Multiplies Y by 15 Adds the last two results Multiplies Z by 17 Completes the left side of the equation Since the left and right sides are both equal to one to 11 significant dig its the solution is correct Example 2 Solve for the loop currents in the circuit below en vVW Loop 2 r Loop 1 4Q VVW in NA S V Loop 3 J ion U NAA V i5n 40V 12 Mathematics Pro...

Page 184: ...0 15X 10Y 26Z 0 Keys Display Description XEQ A Revalue Starts input routine 19 R S B value Sets first coefficient A equal to 19 4 L y R S C value Sets B equal to 4 i5by R s D value Sets C equal to 15 Continues entry for D through L 0 R S fi 19 8898 Enters L and returns to first coefficient entered XEQ S X 7 8601 Solves system of equa tions and displays X R S Y 4 2298 Displays Y IR SI Z 6 1615 Disp...

Page 185: ...of three linear equations AX DY GZ BX EY HZ K CX FY IZ L can be represented by the matrix equation below A D G X V B E H Y K C F I Z L The matrix equation may be solved for X Y and Z by multiplying the result matrix by the inverse of the coefficient matrix A U G Y X B E H K Y C F r L Z Specifics regarding the inversion process are given in the comments for the inversion routine I 12 Mathematics Pr...

Page 186: ...o i L04 GTO L If i is less than 13 goes back to LBL L and gets the next value L05 GTO fl Returns to LBL A to review values Bytes and Checksum 007 5 C1DE erts a 3 x 3 matrix 101 LBL I This routine 102 XEQ D Calculates d the division 103 STO W 104 RCL fl I05 RCLx I 106 RCL C 107 RCLx G 108 109 STO X Calculates Ef 110 RCL C 111 RCLx D 112 RCL fl 113 RCLx F 114 115 STO Y Calculates F 116 RCL B 117 RCL...

Page 187: ... B 147 RCL F 148 RCLx G 149 RCL D 150 RCLX I 151 152 RCL D 153 RCLx H 154 RCL E 155 RCLx G 156 157 STO G 158 R 159 STO D I60 RCL i 161 STO I 162 RCL X 163 STO E Calculates V x determinant AE BD Calculates A x determinant EI FH Calculates B x determinant CH BL Calculates C x determinant BF CE Stores B Calculates D x determinant FG Dl Calculates G x determinant Stores D Stores Stores E DE EG 12 Math...

Page 188: ...alling program or to PRGM TOP Bytes and Checksum 007 5 A354 M01 LBL M This routine multiplies a column matrix and a 3 x 3 matrix M02 7 Sets index value to point to last element in first row M03 XEQ N M04 8 Sets index value to point to last element in second row 1105 XEQ N M06 9 Sets index value to point to last element in third row Bytes and Checksum 009 0 0A85 NOl LBL N This routine calculates pr...

Page 189: ...nd 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 PRGM TOP 021 0 BBBF This routine multiplies and adds values within a row Gets next column value Sets index value to point to next row value Multiplies column value by row value Adds product to previous sum Returns to the calling program 012 0 520E This...

Page 190: ...I A to input coefficients of matrix and column vector 3 Key in coefficient or vector value A through L at each prompt and press IR s I 4 Optional press IxeqI Dto compute determinant of 3 x 3 system 5 Press IXEQ 11 to compute inverse of 3 x 3 matrix 6 Optional press Ixeq IA and repeatedly press IR s Ito review the values of the inverted matrix 7 Press Ixeq IMto multiply the inverted matrix by the c...

Page 191: ...are common to this program and to the Solutions of Simultaneous Equations Determinant Method program Example For the system below compute the inverse and the system solution Review the inverted matrix Invert the matrix again and re view the result to make sure that the original matrix is returned Keys fXEQlA 23QVS 8 rTs 4QJ SJ 15rR7s 23X 15Y VIZ 31 8X 11Y 6Z 17 4X 15Y 12Z 14 Display Description fl...

Page 192: ...irst coef ficient entered Calculates the inverse and displays the determinant Multiplies by column vector to compute X Calculates and displays Y Calculatesand displays Z Begins review of the inverted matrix Displays next value Displays next value Displays next value Displays next value Displays next value Displays next value Displays next value Displays next value Inverts inverse to pro duce origi...

Page 193: ...For real roots the program always calculates the root of the greatest absolute value first It does this to rninimize inaccuracies that can be introducedif the square root of the discriminant is nearly equal to b Once the first root xlf is found the second root x2 is computed using the relationship x _ c ax1 Numerical errors like the one avoided by this program are common in computer software Anyco...

Page 194: ...the beginning of the quadratic equation routine Prompts for and stores the value of A If A is zero goes back and asks for A again Prompts for and stores the value of B Prompts for and stores the value of C If Cis zero goesback and asks for all inputs again Recalls B B Clears flag 0 Assumes that B is positive Is B negative Sets flag 0 if it is Calculates B2 Calculates B2 4AC Tests to see if the roo...

Page 195: ...ulates absolute value of V B2 4AQ 5 2A Stores the imaginary part Retrieves 2A Stores the real part in R Retrieves the imaginary part of X Retrieves the real part of X Displays the real part Displays the imaginary part Goes back for a new case 025 5 DA3B Flags Used Flag 0 is used to remember the sign of B If B is negative then flag 0 is set Flag 0 is tested later in the program to assure that the f...

Page 196: ...ess IXEQI Q to start the quadratic equation routine 3 Key in A and press IR SI 4 Key in B and press IR s I 5 Key in C and press IR SI 6 Seethe first value of X if the rootsare real or see the real part R if the roots are imaginary 7 Press IR sIto see the secondvalue of X or to see the imaginary part J if the roots are imaginary 8 For a new case press IR S Iand go back to step 3 Variables Used A Co...

Page 197: ...ve already run example 1 all you have to do is change the sign ofC Keys Display Description R S A73 0000 Resumes the program IR Sl B 5 0000 Keeps A r s C7 3 0000 Keeps B B r s R 0 8333 Changes the sign of C and calculates the real part of the complex root R SJ 1 0 5528 Calculates the positive value of the imaginary root Example 3 A ball is thrown straight up at a velocity of 20 meters per second f...

Page 198: ...time has no meaning in the context of this problem the first result 4 1751 seconds is the meaningful answer Example 4 Find the roots of the following second degree polyno mial using the program as it is listed Then change the sense of the comparison at line Q12 so that the second root is computed first and then the results are compared Remember to restore the original line or clear the program whe...

Page 199: ...r of calcula tion can be quite significant Ifyousubstitute the first values calculated backintothe equation you will find that the left hand side of the equation is zero for the root of smaller absolute value as it theoretically should be and 1 for the root of larger absolute value Does this mean that the result of 3 000 000 0000 is incorrect The answer to this question is a quali fied no If you i...

Page 200: ...m to the pair u v in the new translated rotated system u x m cos0 y n sin0 v y n cos0 y n sin0 The inverse transformation is accomplished with the formulas below x cos0 v sin0 m y u sin0 v cos0 n The HP 32S complex and polar to rectangular functions make these computations straightforward Old coordinate system v co cn New coordinate system A Two Dimensional Rotation About the Axis 198 12 Mathemati...

Page 201: ...the old system to the new system Prompts for and stores X the old in 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 Changes the sign of T because sin T equals sin T Sets radius to 1 for computation of co...

Page 202: ...s N Pushes up results and recalls M Completes calculation by adding M and N to previous results Stores the x coordinate in variable X Swaps the positions of the coordinates Stores the y coordinate in variable Y Swaps the positions of the coordinates back Halts the program to display X Halts the program to display Y Goes back for another calculation 027 0 9AE6 Memory Required 119 bytes 63 for progr...

Page 203: ...n V they coordinate in the new system and press IR SI to see X 15 Press Ir sI to see Y 16 For another new to old transformation press IR S Iand go to step 13 For an old to new transformation go to step 7 Variables Used M The x coordinate of the origin of the new system N The y coordinate of the origin of the new system T The rotation angle 0 between the old and new systems X The x coordinate of a ...

Page 204: ...n M MODES TDGi Sets Degrees mode since T is given in degrees XEQ D W value Starts the routine that defines the transformation 7 1R S1 N va i e Stores 7 in M 4 by ir s i T va ue Stores 4 in N 27 R S I M 7 0000 Stores 27 in T 202 12 Mathematics Programs ...

Page 205: ... 1461 X l 1 0401 Y 5 9818 Starts the old to new routine Stores 9 in X Stores 7 in Y and cal culates 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 cal culates li Calculates V Starts the new to old routine Stores 2 7 in U Stores 3 6 in V and calculates X Calculate...

Page 206: ...tial curve and the power curve Theprogram accepts two or more x y data pairs and then calculates the correlation coefficient r and the two regression coefficients mand b Theprogram 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 function...

Page 207: ...alues of y must be positive To fit power curves both x and y must be positive A LOG NEG 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 13 Statistics Programs 205 ...

Page 208: ...indicator for lnX L04 CF 1 Clears flag 1 the indicator for lnY L05 GTO Z Branches to common entry point Z Bytes and Checksum 007 5 6047 EO1 LBL E This routine sets the status for the exponen tial model E02 3 Enters index value for later storage in i for indirect addressing E03 CF 6 Clears flag 0 the indicator for lnX E04 SF 1 Sets flag 1 the indicator for lnY E05 GTO Z Branches to common entry poi...

Page 209: ...efines 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 ap pear with the prompt for X Displays counter with prompt and stores X input If flag 0 is set takes the natural log of the input Stores that value for the correction routine Prompts for and stores Y If flag 1 is set takes the natural log of the input Accumulates B an...

Page 210: ...efficient b If flag 1 is set takes the natural antilog of b Stores b in B Displays value Calculates coefficient m Stores minM Displays value 018 0 7492 Defines the beginning of the estimation projection loop Displays prompts for and if changed stores x value in X Calls subroutine to compute y Stores y value in Y Displays prompts for and if changed stores y value in Y Adjusts index value to address...

Page 211: ...culates y M lnX B B06 RTN Returns to the calling routine Bytes and Checksum 009 0 1B06 HO 1 LBL H This subroutine calculates x for the logarith mic model H02 STO i Restores index value to its original value H03 RCL Y H04 RCL B H05 RCL M H06 e Calculates x eV B M H07 RTN Returns to the calling routine Bytes and Checksum 010 5 C783 C01 LBL C This subroutine calculates y for the ex ponential model C0...

Page 212: ...s Y B XM D06 RTN Returns to the calling routine Bytes and Checksum 009 0 B4D4 JOI LBL J This subroutine calculates x for the power model J02 STO i Restores index value to its original value J03 RCL Y J04 RCL B J05 RCL M J06 1 x J07 y Calculates x Y B l M J08 RTN Returns to the calling routine Bytes and Checksum 012 0 FAA4 Flags Used Flag 0 is set if a natural log is required of the X input Flag 1 ...

Page 213: ...press Ixeq IU to undo remove the last data pair If you discover that you made an error after step 4 press IXEQI U In either case continue at step 3 6 After all data are keyed in press Ixeq IR to see the correlation coefficient R 7 Press IR SI to see the regression coefficient B 8 Press IR SIto see the regression coefficient M 9 Press IR SI to see the X va ue prompt for the x y estimation routine 1...

Page 214: ...en a hypothetical x Index variable used to indirectly address the cor rect x y projection equation Statistical accumulation and computation Statistics registers Example 1 Fit a straight line to the data below Make an intentional error when keyingin 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 Keys fXEQl S 40 5 fRTS X ...

Page 215: ...last pair Now proceed with the correct data entry 37 9 R S Y 102 0000 Enters correct x value of data pair 100 R S X 4 0000 Enters pair y value of data 36 2 R s Y7100 0000 Enters pair x value of data 97 5 R S X 5 0000 Enters pair y value of data 35 1 R S Y797 5000 Enters pair x value of data 95 5 R S X 6 0000 Enters pair y value of data 34 6 R S Y 95 5000 Enters pair x value of data 94 R S X77 0000...

Page 216: ...tial and power curve fits The table below gives you the start ing execution label and the results the correlation and regression coefficients and 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 Logarithmic Exponential Power To start XEQ L XEQ E IXEQIP R 0 9965 0 9945 0 9959 B 139 0088 51 1312 8 9730 M 65 ...

Page 217: ...his 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 Q x 0 5 V27 X e 2 ix This program uses the built in integration feature of the HP 32S to integrate 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 prob...

Page 218: ... I This routine calculates X given Q X 102 INPUT Q Prompts for and stores Q X 103 RCL M Recalls the mean 104 STO X Stores the mean as the guess for X called Y guess Bytes and Checksum 006 0 ED6E T01 LBL T This label defines the start of the iterative loop Calculates Q Xguess Q X T02 XEQ Q T03 RCL Q T04 RCL X T05 STO 0 T06 R T07 XEQ F T08 RCL 5 T T09 T10 ST0 X Til FIBS T12 0 0001 T13 x y T14 GTO T ...

Page 219: ...using the dummy variable D Q06 2 Q07 ir Q08 X Q09 SQRT Q10 RCL S Qll X Q12 STO T Q13 f Q14 Q15 0 5 Q16 F02 RCL D F03 RCL M F04 RCL r S F05 X F86 2 F07 r F08 F09 e F18 RTN Calculates S x V2tt Stores result temporarily for inverse routine Adds half the area under the curve since we integrated using the mean as the lower limit Q17 RTN Returns to the calling routine Bytes and Checksum 033 5 4B20 F01 L...

Page 220: ...ructions 1 Key in the program routines press c when done 2 Press fxEQl S 3 After the prompt for M key in the population mean and press IR SI If the mean is zero just press IR s I 4 After the prompt for S key in the population standard deviation and press IR SI If the standard deviation is 1 just press IR SI 5 To calculate X given Q X skip to step 9 of these instructions 6 To calculate Q X given X ...

Page 221: ...ore 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 3a band Since this problem is stated in terms of standard deviations use the default values of zero for M and 1 for S Keys XEQl S R S R S IXEQID 3 r7s Display Description M70 0000 Starts the initialization routine S71 0000 Accepts th...

Page 222: ...rogram 2 R S Q 0 0227 Enters X value of 2 and calculates Q X 10000 0 227 4937 Multiplies by the population for the re vised estimate Example 2 The mean of a set of test scores is 55 The standard devi ation is 15 3 Assuming that the standard normal curve adequately models the distribution what is the probability that a randomly se lected student scored 90 What is the score that only 10 percent of t...

Page 223: ...for X 90 R S Q 0 0111 Enters 90 for X and calculates Q X Thus we would expect that only about 1 would do better than score 90 percent of the students Keys Display Description XEQ 1 Q70 0111 Starts the inverse routine 1 R S X 74 6078 Stores 0 1 10 percent in Q X and calculates X R S Q70 1000 Resumes the inverse routine 8 IR S I X 42 1232 Stores 0 8 100 percent minus 20 percent in Q X and calculates...

Page 224: ...lues of the time value of money equation this program solves for the fifth It is useful in a wide variety of finan cial applications such as consumer and home loans and savings accounts The equation used to solve problems for the time value of money is P SL Z Z I f 1 z n b 0 Balance B a Payments P i t t t N l N Future Value F w A Cash Flow Diagram 222 14 Miscellaneous Programs ...

Page 225: ...L I This routine calculates the interest rate I 102 9 Enters the number that corresponds to I for indirect addressing 103 GTO L Branches to the common control routine L Bytes and Checksum 004 5 DA04 B01 LBL B This routine calculates the initial balance B B02 2 Enters the number that corresponds to B for indirect addressing B03 GTO L Branches to the common control routine L Bytes and Checksum 004 5...

Page 226: ... the equation for SOLVE Solves for the variable indirectly addressed by i Displays the result addressed by i Goes back for another calculation 009 0 7878 This routine contains the equation defining the time value of money Prompts for and stores N Prompts for and stores I Prompts for and stores B Prompts for and stores P Prompts for and stores F Recalls the interest rate in percent If 7 0 then uses...

Page 227: ...ired 145 bytes 89 for program 56 for variables Remarks Since all of the computation for the program is done in routines T and K it is possible to shorten the program by eliminating the other user interface routines Torun the program in this shortened form select the function defined by LBL T Bl solve 1 FN T and then solve for the variable you need Bl solve jI SOLVE variable Program Instructions 1 ...

Page 228: ...c interest rate as a percentage rate Forexample if the annual interest rate is 15 but there are 12 payments per year then the periodic interest rate is 15 5 12 1 25 Z The periodic interest rate as a decimal B The initial balance of loan or savings account P The periodic payment F The future value of a savings account or balance of a loan l The index variable used here for indirect addressing Examp...

Page 229: ...hly rate R S B value B 5 750 00 Stores the monthly in terest rate in I 72501 ENTER I 15001 1 Calculates the begin ning loan balance R S F va ue Sets B equal to the be ginning balance 01R S1 P 186 89 Stores zero in F the fu ture or ending balance and calculates the pay ment of the loan The answer is negative since the loan has been viewed from the borrower s perspective Money received by the borrow...

Page 230: ...ent in P9 176 89 F70 00 1 0 56 6 75 stack so that you can calculate with it The X register will be over written by the next number entered Reduces the monthly payment by 10 00 Stores the modified payment value Accepts zero as the fu ture balance and calculates 1 the monthly interest rate Calculates the annual interest rate Part 3 Using the interest rate of 6 75 assume that you sell the car after 2...

Page 231: ...alue and calculates the future balance Again the sign is neg ative indicating that you must pay out this money Unit Conversions This program consists of two routines that convert one type of unit to another One routine converts among Celsius Fahrenheit Rankine and Kelvin temperatures The other routine converts among inches feet and meters and among square inches square feet and square meters The p...

Page 232: ...played with the prompt would be the temperature in degrees Fahrenheit To end the program press l c l input output JT 273 15 input output n P CI 0 Rl jjff 32 Fl input output 459 67 input output Ferris Wheel Structure for Temperature Conversion The program has been designed to minimize the use of the stack When the program is terminated the values you had in the X and Y registers are left in the Y a...

Page 233: ...t temperature in F Drops stack so that only one level is used Displays temperature in F or requests and stores Fahrenheit input Converts from Fahrenheit to Rankine Stores Rankine temperature in R Drops stack so that only one level is used Displays temperature in R or requests and stores Rankine input Converts Rankine to Kelvin Stores Kelvin temperature in K Drops stack so that only one level is us...

Page 234: ...put Enters conversion factor for inches to feet Tests whether this is an area conversion If yes squares the conversion factor Calculates result Stores feet or square feet Drops stack so that only one level is used Displays feet or square feet or accepts input Enters conversion factor for feet to meters Tests whether this is an area conversion If yes squares the conversion factor Calculates the res...

Page 235: ...en in the display when the routine was started 5 Press IR SI until the prompt with a result corresponds to the units you want to find 6 Go to step 3 for another conversion 7 Press cj to clear the prompt and end the program Variables Used C Temperature in degrees Celsius F Temperature in degrees Fahrenheit or feet R Temperature in degrees Rankine K Temperature in kelvins 7 Inches M Meters Example 1...

Page 236: ...nversion routine Rolls down from the Y register the value you previously calcu lated for in2 Calculates the square feet Cancels the prompt and ends the program R S F795 2500 m 95 2500 Example 3 Suppose that the result of a lengthy calculation is 3 787 and that it is currently in the display of your calculator Further sup pose that this value must be divided by a length specified in meters to compl...

Page 237: ... any odd positive integer greater than 3 If the number is a prime number not evenly divisible by integers 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 not prime the program ad...

Page 238: ...236 Note x is the value in the register Start Prime Number Flow Chart 14 Miscellaneous Programs ...

Page 239: ...3 Stores 3 in test divisor D P04 STO D Bytes and Checksum 006 0 9E38 X01 LBL X This routine tests P to see if it is prime X02 RCL P X03 RCL D X04 FP Finds the fractional part of P D X05 0 Tests for a remainder of zero number not prime X06GTOZ If the number is not prime tries next possibility X07 RCL P X08 SQRT X09 RCL 0 X10 x y Tests to see whether all possible factors have been tried X11GT0Y If a...

Page 240: ...layed 4 To see the next prime number press IR SI Variables Used P Prime value and potential prime values D Divisor which is being used to test the current value of P Remarks No tests are made to assure that the input is an odd posi tive integer greater than 3 Example What is the first prime number after 789 What is the next prime number Keys 789rxEQ P R S Display P 797 0000 P 809 0000 238 14 Misce...

Page 241: ...s and Reference Pm Page 240 A Assistance Batteries and Service 253 B User Memory and the Stack 259 C More About Solving an Equation 273 D More About Integration 281 Messages 286 Function Index 299 Subject Index ...

Page 242: ...ny of our customers have similar questions about our products If you don t find an answer to your question you can contact us using the address or phone number listed on the inside back cover Answers to Common Questions Q How can I determine if the calculator is operating properly A Refer to page 246 which describes the diagnostic self test Q How do I change the number of decimal places in the dis...

Page 243: ...ou must clear a portion of memory before proceeding See ap pendix B Q Why does calculating the sine or tangent of ir radians display a very small number instead of 0 A k cannot be represented exactly with the 12 digit precision of the calculator Q Why do I get incorrect answers when I use the trigonometric functions A You must make sure the calculator is using the correct angular mode Hi modes I Q...

Page 244: ...and silver oxide batteries last about twice as long as alkaline batteries Use only fresh button cell batteries Do not use rechargeable batteries The following batteries are recommended for use Not all batteries are available in all countries Alkaline Panasonic LR44 Eveready A76 Varta V13GA Mercury Panasonic NP675 Eveready EP675E Toshiba NR44 or MR44 Radio Shack NR44 or MR44 Duracell LR44 Duracell ...

Page 245: ...te to save Continuous Memory Have the new batteries readily at hand before opening the battery compartment Also make sure the calcu lator is off during the entire process of changing batteries To install batteries 1 Have three fresh button cell batteries at hand 2 Make sure the calculator is off Do not press cj again until the entire procedure ffor changing batteries is completed Chang ing batteri...

Page 246: ...ardous chemicals 5 Hold the calculator as shown and stack the batteries one at a time in the battery compartment Orient the batteries according to the diagram inside the battery compartment Be sure the raised and flat ends match the diagram 6 Insert the tab of the battery compartment door into the slot in the calculator case as shown 244 A Assistance Batteries and Service ...

Page 247: ... observe the following temperature and humidity limits Operating temperature 0 to 45 C 32 to 113 F Storage temperature 20 to 65 C 4 to 149 F Operating and storage humidity 90 relative humidity at 40 C 104 F maximum Determining if the Calculator Requires Service Use these guidelines to determine if the calculator requires service Then if necessary read If the Calculator Requires Service on page 249...

Page 248: ... malfunctioning 1 Do the self test described below If the calculator fails the self test it requires service 2 If the calculator passes the self test it is likely that you ve made a mistake in operating the calculator Tryrereading por tions of the manual and check Answers to Common Questions at the beginning of this chapter 3 You can communicate with an expert on calculator operation by contacting...

Page 249: ... 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 The calculator displays 32S OK if it passed the self test Go to step 5 The calculator displays 32S FAIL 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 you should...

Page 250: ...d you return the product shipping prepaid to a Hewlett Packard ser vice 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 Covered Batteries and damage caused by the batteries are not covered by the Hew...

Page 251: ...s are sold on the basis of specifications applicable at the time of manufacture Hewlett Packard shall have no obligation to modify or update products once sold Consumer Transactions 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 transac tions the rights and obligations of Seller and Buyer shal...

Page 252: ...r 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 All shipping reimportation arrangements and customs costs are your responsibility Service Charge There is a standard repair charge for out of warranty service The Calculator Service Center listed on the inside...

Page 253: ... pay in advance Ship the calculator in adequate protective packaging to prevent damage Such damage is not covered by the warranty so we rec ommend that you insure the shipment Pay the shipping charges for delivery to the Hewlett Packard ser vice center whether or not the calculator is under warranty Warranty on Service Service is warranted against defects in materials and workmanship for 90 days f...

Page 254: ...he 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 Fed eral Communications 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 printi...

Page 255: ...gram lines SOLVE FN and statistical calculations also require user memory The FN opera tion 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 Clear the contents of a...

Page 256: ...tries For an exam ple see page 86 To manually deallocate the memory allocated for a SOLVE or FN calculation that has been interrupted press Hi lbl rtn RTN 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 be having unusually attempt to reset it Rese...

Page 257: ... a more powerful clearing procedure that resets additional information and is useful if the keyboard is not functioning properly If the calculator fails to respond to keystrokes and you are unable to restore operation by resetting it or changing the batteries try the fol lowing procedure These keystrokes clear all of memory reset the calculator and restore all formats and modes to their original d...

Page 258: ...o zero Variables Cleared to zero Memory may inadvertently be cleared if the calculator is dropped or if power is interrupted The Status of Stack Lift The four 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 dis abled regarding its behavior when the next number is placed in the X regjster Refer to chapter 2 The Autom...

Page 259: ...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 alter the previous status of the stack lift DEG RAD FIX SCI DEC HEX CLVARS GRAD ENG ALL OCT BIN PSE SHOW RADIX RADIX CL2 OFF inary R s and STOP GTO QQ Errors C IMEMKURR MEM PGM t Digit entry IGTOM l abe rm Switching b 1prgm and pro windows gram entr...

Page 260: ...ASINH ACOSH ATANH IP FP RND ABS y x 0 r 0 r y x HR HMS DEG RAD Cn r Pn r x CMPLX CMPLX x CMPLX e LN yx 1 x CMPLX SIN COS T Note that the recall arithmetic sequence x IRCL T variable stores a different value in the LAST X register than the sequence xIRCL Ivariable T does The former stores x in LAST X the latter stores the recalled number in LAST X 258 B User Memory and the Stack ...

Page 261: ...e x axisin at least one place between the two estimates This interval is sys tematically 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 conditio...

Page 262: ...tween adjacent roots of fa figure d below Functions 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 fa 0 However a very small non zero value for fa is often acceptable because it might result from approximating num bers with limited 12 digit precision 260 C More Abo...

Page 263: ... the 12th digit and the function s value is positive for one esti mate and negative for the other In most cases fa will be relatively close to zero fCxJ ffxJ Cases Where a Root Is Found To obtain additional information about the result press IR Ito see the previous estimate of the root x which was left in the Y register PressFrT again to see the value of fa which was left in the Z regis ter If fa ...

Page 264: ...m R81 LBL R R02 2 AQ3 RCLx X 004 4 fl05 A06 RCLx X fl07 6 R08 R09 RCLx X R10 8 fill R12 RTN Keys II SOLVE J FN A OlsTolX 10 Hi SOLVE J S0LVE X Lm fRTI Display X 1 6586 1 6586 1 0000E 11 262 C More About Solving an Equation Description Calculates x using guesses 0 and 10 Final two estimates are the same to four deci mal places fa is very small so the approximation is a good root ...

Page 265: ...s 0 and 10 nri 2 0000 0 00000000000 Final two estimates are the same IFUI Ml SHOW fix 0 OlSTOlX 10I I IHI SOLVE J S0LVE X X 3 0000 0 00000000000 Calculates the negative root using guesses 0 and 10 IR IIR I Ml SHOW fa o Certain cases require special consideration If the function s graph has a discontinuity that crosses the x axis then the SOLVE operation returns a value adjacent to the disconti nui...

Page 266: ...hboring values of x it returns the possible root However the value for fa 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 xJ a fCxJ A a b Special Cases A Discontinuity and a Pole Example A Discontinuous Function Find the root of the equation IP x 1 5 0 264 C More About...

Page 267: ...previous estimate is slightly bigger fa is relatively large Note the difference between the last two estimates as well as the rel atively large value for fa The problem is that there is no value of x for which fa equals zero However at x 1 99999999999 there is a neighboring value of x that yields an opposite sign for fa Example A Pole Find the root of the equation r 1 0 As x approaches f6 ffa beco...

Page 268: ...4495 IR JLR 81 649 658 092 0 Description Calculates the root using guesses that bracket y fa is relatively large Thereis a pole betweenthe final estimates The initialguesses yielded opposite signs for fa and the interval between successive estimates was narrowed until two neighbors were found Unfortunately these neighbors made fix approach a pole instead of the x axis The func tion does have roots...

Page 269: ...in the unknown variable might be a 12 digit num ber very close to a theoretical root The search halts because SOLVE is working on a horizontal asymp tote an area where fa is essentially constant for a wide range of x see figure b below The ending value of fa is the value of the potential asymptote The search is concentrated in a local flat region of the function see figure c below The ending value...

Page 270: ...e to see the value that pro duced the error Example A Relative Minimum Calculate the root of this parabolic equation x2 6x 13 It has a minimum at x 3 Enter the function as the program G01 LBL G G02 RCL X G03 x G64 6 G65 RCLx X G06 G07 13 G08 G09 RTN Keys ill SOLVE J FN G ofsfolx 10 HI SOLVE J S0LVE X 4l II SHOW FrTI 111 SHOW LED Display NO ROOT FND 3 00000010001 3 00000468443 4 0000 0 Description ...

Page 271: ...sing guesses 0 005 and 5 LIE 0 1000 999999999999 Previous estimate is the same fRT SHOW m o Watch what happens when you use negative values for guesses Keys Display Description 1 raisT0ix2ra HISOLVE Jl S0LVE X NO ROOT FND No root found for fix a 46 666 666 692 1 Displays last estimate of X HE 5 7750E15 Previous estimate was much larger in magnitude HE 10 0000 fix for last estimate is rather large ...

Page 272: ...First attempt to find a positive root Keys Display I SOLVE J FN I orsToix 10 11 SOLVE J SOLVE X X 0 1000 0 Description Calculates the root us ing guesses 0 and 10 Now attempt to find a negative root by entering guesses 0 and 10 Notice that the function is undefined for values of x between 0 and 0 3 since those values produce a positive denominator but a nega tive numerator causing a negative squar...

Page 273: ...E J FN J rn 8 F i fsToi x 1 EHE8E Hi solve J I SOLVE HE LIE Display NO ROOT FND 1 0000E 8 0 0025 1 0000 Description No root found using very small guesses near zero thereby re stricting the search to the flat region of the function The last two estimates are far apart and the final value of fix is large If you use larger guesses then SOLVE can find the roots which are outside the flat region at x ...

Page 274: ...ver no 12 digit number exactly equals ff so the calculator can never make the function equal to zero Further more the function never changes sign SOLVE returns the message NO ROOT FND However the final estimate of x press T 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 calculato...

Page 275: ...lways provide an exact answer Evaluating the function atan infinite number of sample points would take forever However this is not necessary since the maximum accu racy 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 anintegral that isas accurate asis justified considering the inherent u...

Page 276: ...e displayed uncertainty ofthe approximation Inother words the uncertainty esti mate 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 32S is one of the best available in certain situations it like allother algorithms for numeri cal integrat...

Page 277: ... function atmore and more points Ifa fluctuation ofthe function in one region is not unlike the behavior over the restof the interval of integration at some iteration the algorithm will likely de tect the fluctuation When this happens the numberof sample points is increased until successive iterations yieldapproximations that take into account the presence of the most rapid but characteristic fluc...

Page 278: ... Specifies accuracylevel and limits of integration Approximation of integral The answer returned by the calculator is clearly incorrect since the actual integral off x xe x from zero to oo is exactly 1 But the problem is not that oo wasrepresented by 10499 since the actual inte gral of this function from zero to 10499 is very close to 1 The reason for the incorrect answer becomes apparent from the...

Page 279: ...val of integration Basically the more rapid the varia tion 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 respect to the width of the in terval ...

Page 280: ...valuating the function using the subroutine 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 subdi vide theinterval ofintegration into two ormore adjacent subintervals integrate the function over each subinterval then add the resulting approximations This causes the function to be sampled a...

Page 281: ... very quickly asxapproaches oo thecontribution tothe integral ofthe function at large values ofxis negligible Therefore you canevaluate theintegral byreplacing oo theupper limit ofintegration bya num ber not so large as 10499 say 10 Re run the previous integration problem with this new limit of inte gration If you have notrun anyother integrations in the meantime you do not have to re specify FN F...

Page 282: ...ns are required over the larger interval toachieve an ap proximation 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 inter esting the calculation of the integral of any function will be prolonged if the interval ofintegrat...

Page 283: ...hile an integration calculation was running FN A running program attempted to calculate an integral FN d variable while another integration calculation was running S0LVE A running program attempted a SOLVE operation while an integra tion calculation was running ALL VARS 0 The catalog of variables mem VAR indicates no values stored CALCULATING The calculator is executing a function that might take ...

Page 284: ... Attempted a factorial or gamma operation with x as a negative integer INVALID y Exponentiation error Attempted to raise 0 to the 0th or to a negative power Attempted to raise a negative number to a non integer power Attempted to raise the complex number 0 iO to a number with a negative real part INVALID i Attempted an operation with an indirect address but the number in the index register is inva...

Page 285: ...ot produce this error the same condition causes it instead to skip the next program line the line following the instruc tion SOLVE variable NO STAT DATA Attempted to do a statistics calculation with no statistics data stored OVERFLOW 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 form...

Page 286: ...LVE operation while another SOLVE operation was running SOLVE FN Arunning program attempted tocalculate anintegral while a SOLVE operation was running SOLVING The calculator is solving an equation for its root This might take a while SQRT NEG Attempted to calculate the square root of a negative number STAT ERROR Statistics error Attempted to calculate sv sy x y m r or bwith n 1 Attempted to calcul...

Page 287: ...EX OCT or BIN base The number must be in the range 34 359 738 368 n 34 359 738 367 XEQ OVERFLOW A running program attempted an eighth nested XEQ label Up to seven subroutines can be nested Since SOLVE and FN each use a level they can also generate this error Messages 285 ...

Page 288: ... as TJ Non letter characters and Greek letters are alphabetized before all the letters function names precededby arrows e g DEG are alphabet ized as if the arrow were not there Function Name Keys and Description Page Changes the sign of a number 21 Addition Aeturns y x 25 E Subtraction Returns y x 25 X 0 Multiplication Returns y x x 25 r s Division Returns y 4 x 25 a Deletes the last digit keyed i...

Page 289: ...Returns y x x e 100 Bl CHG Percent change Returns x y 100 y HE Returns the approximation 3 14159265359 US Accumulates y x into statistics registers HE Removes y x from statistics registers BirSTAfl 2 x Returns the sum of x values swim Returns the sum of squares of x values HrSTAfl 2 xy Returns the sum of products of x and y values HrSTATl 2 y Returns the sum of y values igrSTAfl 2 y Returns the su...

Page 290: ...COS Hyperbolic arc cosine Returns cosh 1 rrJispl ALL Selects display of all significant digits Arc sine Returns sin 1 x HYP LASIN Hyperbolic arc sine Returns sinh 1 x JfATANl Arc tangent Returns tan 1 x Thy SfATAN Hyperbolic arc tangent Returns tanh 1x rsTAfl L R b Returns the y intercept of the regression line y mx Displays the menu for base conversions HfBAsTl BN Selects Binary base 2 mode Turns...

Page 291: ...ars all programs WW CLEAR M CLEAR JRLL M CLEAR fPGfn CL2 CLVARS CLx W CLEAR f2 Clears statistics registers HI CLEAR fVARSl Clears all variables to zero HII CLEAR IW Clears x to zero Displays the CMPLX_ prefix for complex functions M CMPLX CMPLX CMPLX CMPLX CMPLX x m CMPLX _ Complex change sign Returns zx izy Mil CMPLX I T Complex addition Returns zu iz z iz2y IMCMPLX IP Complex subtraction Returns...

Page 292: ...zx izy Ml CMPLX lie Complex natural exponential Returns ezx zy Ifll CMPLX LN Complex natural log Returns loge zx izy till CMPLX I SIN I Complex sine Returns sin zx izy lillCMPLXMTANl Complex tangent Returns tan zx izy Ml CMPLX f l Complex power Returns z iz Z2x V 1x y lill prob Cn r Combinations of n items taken r at a time Re turns n r r n r COS Cosine Returns cos x Ill HYP COSI Hyperbolic cosine...

Page 293: ...s entry of exponents and adds E to the number being entered Indicates that a power of ten follows a Natural exponential Returns e raised to the x power Brblspl EN n Selects Engineering display with n digits following the first digit 0 s n 11 ENTER Separates two numbers keyed in sequen tially copies x into the Y register lifts y into the Z register lifts z into the T regis ter and loses t Urmspl FX...

Page 294: ...tions Displays the menu to convert between frac tional hours and hours minutes seconds HI HYP till H HMS HMS HR GID INPUT variable IP H HMS HNS Hours to hours minutes seconds Converts x from a decimal fraction to minutes sec onds format HllH HMS HR Hours minutes seconds to hours Converts x from minutes seconds format to a decimal fraction The indirect parameter Addresses indi rectly the variable o...

Page 295: ...s Displays the menu for LBL RTN and PSE flNl Natural logarithm Returns loge x HogI Common logarithm Returns log10 x Displays the menu for DSE and ISG iHrSTATl L R Displays menu for linear regression HI STAT L R m Returns the slope of the regression line 2 x x y y 2fo x 2 Displays the amount of available memory and the catalog menu Begins catalog of programs Begins catalog of variables Displays the...

Page 296: ...am execution briefly to dis play x then resumes Used only in programs lillSTATKLR 1 ir Returns the correlation coefficient between the x and y values 2 x x y y Vz x 2 x 2 y p 2 HlD RAD RAD Degrees to radians Returns 2 360 x WPROBl fR Displays random number menu IM MODES fRD Selects Radians angular mode HlMODESli l Selects the comma as the radix mark decimal point H MODES f Selects the period as th...

Page 297: ...g routine Run stop Begins program execution at the current program line or stops a running program IRJJ Roll down Moves f to Z register z to Y register y to X register and x to T register Ml dispI SC n Selects Scientific display with n decimal places 0 n s 11 PROBl R SEED Restarts the random number sequence with the seed Ixl HI FLAGS I SF Sets flag n 0 s n s 6 indicating true Shows the full mantis...

Page 298: ...le Stores variable x into variable STO ED variable Stores variable x into variable STO QcJ variable Stores variable x x into variable STO L J variable Stores variable s x into variable R S Halts program execution and displays the X register 1111 STAT S SX Returns the standard deviation of x values V2 x x 2 n 1 Ml STAT S sy Returns the standard deviation of y values Vzflf yf n 1 TAN Tangent Returns...

Page 299: ...or T x 1 HII STAT I y xw Returns the weighted mean of x values 2y x s 2y x exchange y Moves x to the Y register and y to the X register ImilTESTSl 0 0 If x 0 executes the next program line if x 0 skips the next program line HI TESTS x y y Ifx y executes the next program line if x 2 y skips the next program line HI TESTSI 0 0 If x 0 executes the next program line if x 0 skips the next program line ...

Page 300: ...e next program line if x 0 skips the next program line Ml TESTS ix y y If x y executes the next program line if x y skips the next program line HI STAT x y y Returns the mean of y values 2y 4 n W STAT L R y Given an x value in the X register re turns the y estimate based on the regression line mx b HlP RECTl y 8 r Rectangular to polar Converts x y to r d ED Power Returns y raised to the x power 29...

Page 301: ...ode 56 57 Annunciators 20 21 flag 98 Arc cosine 57 Arc sine 57 Arc tangent 57 Area conversions 229 235 Area of a circle 70 74 78 Arithmetic 24 29 38 46 complex 139 140 nondecimal See Base arithmetic in stack 38 with stored variables 50 52 vector 164 175 Assistance 240 Average See Mean Backspace 16 19 23 32 40 73 Balance 226 Base arithmetic 146 148 conversions 144 145 modes programming 151 152 Batt...

Page 302: ...c 191 Compounding periods 226 Conditional instructions 95 99 100 SOLVE 124 FN 134 300 Index Constant using 39 40 43 Constant growth 40 Continuous Memory 14 243 Contrast 14 Conversions angular 64 coordinate 60 62 fractional 63 64 Coordinate transformations 198 203 Coordinates converting 60 62 Copying numbers See Storing numbers Copying variables from catalog 49 Correcting errors using LAST X 41 42 ...

Page 303: ...7 in SOLVE 272 in statistics 161 205 in trigonometry 57 Exponent 22 23 30 digits in 21 keying in 22 Exponential common 55 natural 55 curve 204 205 211 Exponentiation See y fix 126 in integration 273 in SOLVE 259 Factorial 19 65 Fahrenheit conversion 229 235 Feet conversion 229 235 Ferris wheel principle 230 Financial calculations See Time value of money FIX format 30 Fixed decimal format 30 Flag c...

Page 304: ... with nondecimal numbers 150 with SOLVE 112 302 Index Input program 78 Inserting program lines 82 Integer part 67 in nondecimal arithmetic 146 Integral approximating 131 Integrand 127 131 Integration 126 136 accuracy of 127 131 134 algorithm 130 272 274 anomalies 275 277 approximations 273 274 calculation time 279 280 conditional 134 errors 274 function for 128 how it works 273 280 interrupting 12...

Page 305: ...ower 242 243 M Magnitude 24 Mantissa 22 30 31 49 Matrices solving See Simultaneous equations Matrix coefficient 183 formulas 175 176 183 inverse 183 190 inversion 183 190 result 183 Mean 156 157 population 219 weighted 157 158 MEM 33 49 85 Memory available 33 49 checking 33 MEMORY CLEAR 243 245 255 Memory clearing 34 50 253 clearing all 255 256 deallocating 254 MEMORY FULL 85 162 253 Memory loss l...

Page 306: ...9 size of 21 too large 21 22 49 too small 22 Octal numbers 144 149 Off 14 304 Index On 14 One variable data 154 Operation checking 245 247 help with 240 Operations index of 286 298 Order of calculation 26 45 46 of entry 25 of numbers 37 Output program 78 Overflow 24 flagged 97 98 in nondecimal arithmetic 146 program 98 P RECT 60 62 Parentheses 26 28 45 PARTS menu 67 Parts of numbers functions 25 6...

Page 307: ...2 84 87 names See Program labels pointer 76 84 94 resuming 78 82 returns 72 73 running a 75 76 85 stepping through 76 stopping 82 testing 75 76 writing a 71 74 Programming 70 89 Programming with base modes 151 152 Programs clearing 85 86 Prompt for variable 77 79 Q R Quadratic equation 191 197 Questions 240 241 Rl 36 37 RAD 57 Radians converting 64 Radians mode 57 Radius vector 174 Radix mark 29 R...

Page 308: ...racts 251 international 250 Shift canceling 15 Shift key 15 Shipping 251 Shorting 246 306 Index SHOW 31 49 79 nondecimal numbers 150 Sign bit 148 Significant digits 22 31 49 Simultaneous equations determinant method of 175 182 matrix inversion method of 183 190 Sine 57 integral 130 131 Slope 159 204 211 212 Solutions See SOLVE results SOLVE 259 272 asymptote 267 269 calculation interrupting 119 co...

Page 309: ...62 Statistics registers 161 162 allocating 162 clearing 162 STO 48 Storage arithmetic 50 51 Stored data 253 Storing numbers 48 Subroutines 91 nested 92 Sum of products 162 of squares 162 of x values 161 of y values 161 Summation values statistical 156 161 162 Support customer 240 Surface area of a cylinder 80 81 Swapping niunbers X and Y regis ters 25 37 T register 35 36 38 40 47 Tangent 57 Temper...

Page 310: ...48 249 service 251 United Kingdom 249 Weighted mean See Mean weighted Windows 149 150 Word size 149 Wrong function correcting 42 Wrong numbers correcting 42 x z x estimate 158 159 212 X register 35 40 47 clearing 40 41 clearing in a program 73 exchanging with Y register 37 and integration 128 in programming 70 with SOLVE 113 120 for statistical data 154 308 Index testing 95 96 with Y register comp...

Page 311: ...orvallis OR 97330 U S A 503 757 2004 8 00 a m to 3 00 p m Pacific time Monday through Friday ForService If your calculatordoesn t seem to work prop erly see appendbc A to determine if the calculator requires service Appendix A also contains important information about obtaining service If your calculator does require ser vice mail it to the Calculator Service Center Hewlett Packard Calculator Serv...

Page 312: ...umerical Integration Operations With Complex Numbers Base Conversions and Arithmetic Statistical Operations 163 Part 4 Application Programs Mathematics Programs Statistics Programs Miscellaneous Programs 239 Part 5 Appendixes and Reference Assistance Batteries and Service User Memory and the Stack More About Solving an Equation More About Integration Messages Function Index Subject Index m HEWLETT...