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HP 35s scientific calculator

1. To Calculate Press Display 123 02 G7 GB ENTER 123 1 725 668 ATA akena AMM xroore3 64 gt ENTER 4 0088 Percentage Calculations The Percent Function The Ce key divides a number by 100 To Calculate Press Display 27 of 200 Wey 2 OJOJL V2 xteee er2 7 ENTER 54 0008 200 less 27 L2 LO LO Wes 2 2 288 40 288 27 MD IZITWENTER 146 8888 25 plus 12 2059 2 295 25te 25 123 L gt LL CZ ENTER 25 6686 To Calculate Press x of y We y J x ENTER Percentage change from y to x y 0 ECHC y gt x ENTER Example Suppose that the 15 76 item cost 16 12 last year What is the percentage change from last year s price to this year s Keys Display EH CHG 1 TE ponme xcHG 16 12 15 7 7 6 ENTER 2 2333 Description This year s price dropped about 2 2 from last year s price ALG Summary C 3 Permutations and Combinations Example Combinations of People A company employing 14 women and 10 men is forming a six person safety committee How many different combinations of people are possible Keys Display Description EW oc 2 4 2 nCreed 63 Total number of 6 ENTER 134 596 0008 combinations possible Quotient and Remainder Of Division You can use EWJUNTG 2 21NTG and EUNTG 3 3Rmdr to produce either the quotient or remainder of division operations involving two integers ES INTG 2 2 INT
2. Page 11 4 13 18 13 19 12 7 4 15 3 7 Operation Index G 11 Name Keys and Description Page RCL variable RCL variable 3 7 Returns x variable RCL variable RCL variable 3 7 Returns x variable RCLx variable RCL LX variable 3 7 Returns x x variable RCL variable RCL LE variable 3 7 Returns x variable RMDR ENTO 3 SR mar Produces 6 16 the remainder of a division operation involving two integers RND EW RND Round 4 18 Rounds x to n decimal places in FIX n 5 8 display mode to n 1 significant digits in SCI n or ENG n display mode or to decimal number closest to displayed fraction in Fraction display mode MODE 5 SRPHM Activates Reverse 1 9 Polish notation RTN E RIN Return 13 Marks the end of a program the 14 1 program pointer returns to the top or to the calling routine RV Roll down 2 3 Moves tto the Z register z to the Y C 7 register y to the X register and x to the T register in RPN mode Displays the X Y Z T menu to review the stack in ALG mode RA a Roll up 2 3 Moves t to the X register z to the T C 7 register y to the Z register and x to the Y register in RPN mode Displays the X Y Z T menu to review the stack in ALG mode B Displays the standard deviation 12 4 Menu G 12 Operation Index Name Keys and Description Page SCI n SEED SF n S
3. ccccccessseeeeeeeenteeeeeeeeaes B 7 ALG SUMMATY ssciiscsschcias descr isccercaaancets de ceenetansaateonsteane C 1 POUT AG do Medea O tea ote conan n ated does St C1 Doing Two argument Arithmetic in ALG ccceeeeeeeeeeeeeeeeneeees C2 Simple Arithimen ej cisesiesvacteasuis sate ctw tues E C2 Power F nchions erie on car eseannatsventoatn a E mind a T C3 Percentage Calculations cccccceeseseseceeeeseneeeeeeeseteeeeeenees C 3 Permutations and Combinations ccccccseceeeeeeeeeteeeeeeeees C4 Quotient and Remainder Of Division cccceceeesseeeeeees C 4 Parentheses Calculations i gest cece eA aaa sab eiehtiaustacan deans torah caae s C4 Exponential and Logarithmic Functions sseeceeeeeteeeeeeneeeees C5 Trigonometric Functions 20 0 ec eeeeeecececceeecececeeeeeeeeeeeeeneeteeeeeeeeeees C46 Hyperbolic TUMCHONS tss ce nsec W ait eee reneeedtan hn teaae eels C 6 Pans of HOMbELS iis vedi ecirtsceascheaduoecenatauagsaseeudhignentedciveussueuziss C 7 Reviewing the Stack lt a ivehinashac iaatimenvesthaedunwwiy nein rolumiedssaaiats C 7 Integrating an Equation ccccceecsssecceeeeeseeeeseeeeeeeeececeeeeeeeeess C8 Operations with Complex Numbers 0 ccccceeeeecteeeeeesteeees C 8 Arithmetic in Bases 2 8 and 16 assssessnsessesssererssressrernse C10 Entering Statistical Two Variable Data cceeceeeeeeeeeeetteeeees C11 More about Solving scsscs
4. Keys Display Description EQN R 2xCxiT A 25 Displays the current equation in the equation list OJ R 2xCx T A2 25 Activates cursor to the left of the equation ENTER X lt 2xCx T A 25 Activates cursor to the right of the 7 equation KA Leaves Equation mode Entering and Evaluating Equations 6 7 Editing and Clearing Equations You can edit or clear an equation that you re typing You can also edit or clear equations saved in the equation list However you cannot edit or clear the two built in equations 2 2 lin solve and 3 3 lin solve If you attempt to insert a equation between the two built in equations the new equation will be inserted after 3 3 lin solve To edit an equation you re typing 1 Press or to move the cursor allowing you to insert characters before the cursor 2 Move the cursor and press repeatedly to delete the unwanted number or function Pressing LJ when the equation editing line is empty has no effect but pressing on an empty equation line causes the empty equation line to be deleted The display then shows the previous entry in the equation list 3 Press ENTER or LC to save the equation in the equation list To edit a saved equation 1 Display the desired equation press to activate the cursor at the beginning of the equation or press to activate the cursor at the end of the equation See Displaying and Selecting Equations above 2 When the cursor is active in the equatio
5. 147 If x 0 executes next program line if x40 skips next program line XOR ER COGIC 2 2xa0R 11 4 Logic operator xiy ES DISPLAY EA 2x 4 1 Changes display of complex numbers x yi memi iti 1 25 Changes display of complex numbers ALG mode only y 3 12A Returns the mean of y values Lyj n G 16 Operation Index Name Keys and Description Page A A 12 11 y Given an x value in the X register returns the y estimate based on the regression line y mx b yx Power 4 2 1 Returns y raised to the xth power Notes 1 Function can be used in equations Operation Index G 17 Index Special Characters J FN See integration functions 4 6 1 15 O in fractions 1 26 n 4 3 A 2 4 v annunciator in fractions 5 2 in fractions 5 3 annunciators equations 6 7 binary numbers 11 8 equations 13 7 E See backspace key _ See digit entry cursor 2 See integration Kal fed annunciators 1 3 annunciator 1 1 A 3 A A Z annunciator 1 3 3 2 6 4 absolute value real number 4 17 addressing indirect 14 20 14 21 14 23 ALG 1 9 compared to equations 13 4 in programs 13 4 Algebraic mode 1 9 ALL format See display format in equations 6 5 in programs 13 7 setting 1 23 alpha characters 1 3 angles between vectors 10 5 converting format 4 13 converting units 4 13 implied units 4 4 A 2 angular mode 4 4 A 2 B 4 annunciators alpha
6. If current value lt final value continue loop Wee ISG A O Q Weis GTO Weel Hii XEQ xeei 0 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 If the loop control number is a complex number or vector it will use the real part or first part to control the loop The following program uses ISG to loop 10 times in RPN mode The loop counter 1 010 is stored in the variable Z Leading and trailing zeros can be left off Programming Techniques 14 19 Legi LBLL L G2 1 61 L amp G STE Z L 64 ISG Z LEGS GTO L b4 L G6 RTH Press ENTER then press to see that the loop control number is now 11 0100 Indirectly Addressing Variables and Labels Indirect addressing is a technique used in advanced programming to specify a variable or label without specifying beforehand exactly which one This is determined when the program runs so it depends on the intermediate results or input of the program Indirect addressing uses four different keys 1 1 1 and WD These keys are active for many functions that take A through Z as variables or labels a land J are variables whose contents can refer to another variable It holds a number just like any other variable A through Z a I and J are programming functions that directs Use the number in or J to determine which variable or label to address This is an indirect
7. Keys Display Description Wea SOLVE SOLVE Prompts for unknown variable DI we Selects D prompts for V value LO R S T Stores O in V prompts for T value 5 R S G Stores 5 in T prompts for value G AAIR SOLVING Stores 9 8 in G solves for D D 122 5006 Try another calculation using the same equation how long does it take an object to fall 500 meters from rest Solving Equations 7 3 Keys EQN rea 5 0 LO R S R S R S Display D VxT 8 SxGxT ee Oo 122 5 We G G 3 8 SOLVING 16 1615 Example Solving the Ideal Gas Law Equation Description Displays the equation Solves for T prompts for D Stores 500 in D prompts for V Retains O in V prompts for G Retains 9 8 in G solves for T The Ideal Gas Law describes the relationship between pressure volume temperature and the amount moles of an ideal gas PxV NxRxT where P is pressure in atmospheres or N m2 V is volume in liters N is the number of moles of gas R is the universal gas constant 0 0821 liter atm mole K or 8 314 J mole K and T is temperature Kelvins K C 273 1 Enter the equation Keys EQN RCL PX RCL LV aH RCL NJ x RCL R X RCL T ENTER EN SHOW 7 4 Solving Equations Display PxVSHeRxT_ PxV HxRxT CK EDCS LH 3 Description Selects Equation mode and starts the equation Terminates and displays th
8. Percentage Functions The percentage functions are special compared with X and because they preserve the value of the base number in the Y register when they return the result of the percentage calculation in the X register You can then carry out subsequent calculations using both the base number and the result without reentering the base number To Calculate Press x OF y y Paka Percentage change from y to x y 0 y ENTER x EW 4CHG Example Find the sales tax at 6 and the total cost of a 15 76 item Use FIX 2 display format so the costs are rounded appropriately 4 6 Real Number Functions Keys Display ESN DISPLAY L1 iF I 2 GICITICIENTER 15 76 L6 Wea 4 95 E3 16 71 Description Rounds display to two decimal places Calculates 6 tax Total cost base price 6 tax Suppose that the 15 76 item cost 16 12 last year What is the percentage change from last year s price to this year s Keys Display COCCI 2 ENTER 16 12 MGICIZI 4 ey 2 23 CHG EaN DISPLAY LA i FTX 2 2333 4 Description This year s price dropped about 2 2 from last year s price Restores FIX 4 format Note The order of the two numbers is important for the CHG function The order affects whether the percentage change is considered T positive or negative Real Number Functions 4 7 Physics Constants There are 41 physic
9. C and MEMU MEM 2 GTO LILLJ GTO LJ label nnn MAR 2PGM EQN FDISP Errors PROM and program entry Switching binary Digit entry xiy ra UNDO windows x Except when used like Clx x Including all operations performed while the catalog is displayed except VAR and FGM XEQ which enable stack lift User Memory and the Stack B 5 The Status of the LAST X Register The following operations save x in the LAST X register in RPN mode X LN LOG SIN COS TAN SINH COSH TANH CHG nCr nPr CMPLX x gt kg gt lb gt gt gal Vx x2 yx Ay ASIN ACOS ATAN ASINH ACOSH ATANH 2 HMS gt gt HMS CMPLX ex LN yx 1 x 23 C gt F gt KM MILE Notice that c does not affect the LAST X register ex 10x I x INT Rmdr A A x OM IP FP SGN INTG RND ABS RCL x gt DEG gt RAD ARG CMPLX SIN COS TAN gt cm gt in The recall arithmetic sequence variable stores x in LASTx and variable LE stores the recalled number in LASTx In ALG mode the LAST X register is a companion to the stack it holds the number that is the result of last expression It supports using the previous expression result in ALG mode B 6 User Memory and the Stack Accessing Stack Register Contents The values held in the four stack registers X Y Z and T are accessible in RPN mode in an equation or program using th
10. If you know there is an error in a program but are not sure where the error is then a good way to test the program is by stepwise execution It is also a good idea to test a long or complicated program before relying on it By stepping through its execution one line at a time you can see the result after each program line is executed so you can verify the progress of known data whose correct results are also known 1 As for regular execution make sure program entry is not active PRGM annunciator off 2 Set the program pointer to the start of the program that is at its LBL instruction The instruction moves the program pointer without starting execution 3 Press and hold L This displays the current program line When you release Lv the line is executed The result of that execution is then displayed it is in the X register To move to the preceding line you can press LA No execution occurs 4 The program pointer moves to the next line Repeat step 3 until you find an error an incorrect result occurs or reach the end of the program If Program entry mode is active then or simply changes the program pointer without executing lines Holding down a cursor key during program entry makes the lines roll by automatically Example Testing a Program Step through the execution of the program labeled A Use a radius of 5 for the test data Check that Program entry mode is not active before you start Keys Display
11. Polynomial Expressions and Horner s Method Some expressions such as polynomials use the same variable several times for their solution For example the expression Ax4 Bx3 Cx2 Dx E uses the variable x four different times A program to calculate such an expression using RPN operations could repeatedly recall a stored copy of x from a variable Example Write a program using RPN operations for 5x4 2x3 then evaluate it for x 7 13 26 Simple Programming Keys In RPN mode Wea erem GTO CIC Wea LBL A E UNPUT LX E RoK E BGHHNREREBE T by a B T fo OQA Display PRGM TOP ABEL LBL A RABE INPUT amp AGBS 3 RABE4 REL amp AGES 4 RAGGE vY ABB x AGES RCL AGES 3 AGIA ABL1 2 AGIZ x AGLS Aid RTH LEL A LN 46 CK EAI9 LN 46 Now evaluate this polynomial for x 7 Keys In RPN mode KEQ A ENTER 7 J R S Display a value 12 691 6868 Description x4 5x4 x3 2x3 5x4 2x3 Displays label A which takes 46 bytes Checksum and length Cancels program entry Description Prompts for x Result Simple Programming 13 27 A more general form of this program for any equation Ax4 Bx3 Cx2 Dx E would be ABBI LELA Rese INPUT A ABS INPUT B Reed INPUT C ReeS INPUT O ABBE INPUT E Ree INPUT amp RBBS RCL amp ReeS RCL A A616 RCL E RAB1i RCL RABi2 RCL C RBI
12. amp BEB F 26 BEBE H 3 BEBE 4 5 6 15 22 37 43 73 115 Description Prompts for the first xj Stores 5 in X prompts for first fj Stores 17 in F displays the counter Prompts for the second x Prompts for second fi Displays the counter Prompts for the third xj Prompts for the third fi Displays the counter You erred by entering 14 instead of 13 for x3 Undo your error by executing routine U XEQ U ENTER R S 1 3 R S R S R S 1 5 R S H 2 BEBE a 14 6686 F a7 BEBE H 3 BEBE a 13 6686 F 37 BEBE 16 22 Statistics Programs Removes the erroneous data displays the revised counter Prompts for new third xi Prompts for the new third fj Displays the counter Prompts for the fourth xj Prompts for the fourth fi WARS R S AALE 7B RZ R S BIT RS WAAR XEQ G ENTER R S H 4 66668 a 13 8686 F 43 6668 H T BEEBE a 22 BEEBE FY 7s BEBE H 6 68668 g 11 4115 f 23 4664 23 4664 Displays the counter Prompts for the fifth xj Prompts for the fifth fj Displays the counter Prompts for the sixth xj Prompts for the sixth fj Displays the counter Calculates and displays the grouped standard deviation sx of the six data points Calculates and displays weighted mean x Clears VIEW Statistics Programs 16 23 17 Miscellaneous Programs and Equations Time Value of Money
13. 7 so the calculator can never make the function equal to zero Furthermore the function never changes sign SOLVE returns the message HO ROOT FHD More about Solving D 13 More about Integration This appendix provides information about integration beyond that given in chapter 8 How the Integral Is Evaluated The algorithm used by the integration operation J FM 4x calculates the integral of a function f x by computing a weighted average of the function s values at many values of x known as sample points within the interval of integration The accuracy of the result of any such sampling process depends on the number of sample points considered generally the more sample points the greater the accuracy If f x could be evaluated at an infinite number of sample points the algorithm could neglecting the limitation imposed by the inaccuracy in the calculated function f x always provide an exact answer Evaluating the function at an infinite number of sample points would take forever However this is not necessary since the maximum accuracy of the calculated integral is limited by the accuracy of the calculated function values Using only a finite number of sample points the algorithm can calculate an integral that is as accurate as is justified considering the inherent uncertainty in f x The integration algorithm at first considers only a few sample points yielding relatively inaccurate approximations If these appr
14. MODE 4 4ALG Switches to ALG mode FS LU 2 2 ey C 2 4 _ Enters 2 4 AIWA Ha C 2 41 2 Enters 5 as a scalar ENTER C 2 41 2 Performs division C 1 6666 2 6666 Absolute value of the vector The absolute value function ABS when applied to a vector produces the magnitude of the vector For a vector A A1 A2 An the magnitude is defined as A 4 4 A tert A 1 Press ABS 2 Enter a vector 3 Press ENTER For example Absolute value of vector 5 1 2 Wes ABS Wes 11 5 EW 1 LZ J ENTER The answer is 13 In RPPN mode MODE 5 3R FH We 5 LZ ee 485 Vector Arithmetic 10 3 Dot product Function DOT is used to calculate the dot product of two vectors with the same length Attempting to calculate the dot product of two vectors of different length causes an error message INVALIO DATR For 2 D vectors A B C D dot product is defined as A B C D A x C B x D For 3 D vectors A B X C D Y dot product is defined as A B X C D Y A x C B x D X xY Enter the first Vector Press X Enter the second vector Press LENTER Note The sign here means dot product instead of cross product For cross ea Mes product see chapter 17 Calculate the dot product of two vectors 1 2 and 3 4 Keys Display Description MODE 4 4ALG Switches to ALG mode FSV WBC Eil Enters the first vector 1 2 R
15. Some of these input and output techniques are described in the following topics 13 12 Simple Programming Using INPUT for Entering Data The INPUT instruction amp Variable stops a running program and displays a prompt for the given variable This display includes the existing value for the variable such as R amp 6666 where R is the variable s name 2 is the prompt for information and 0 0000 is the current value stored in the variable Press run stop to resume the program The value you keyed in then writes over the contents of the X register and is stored in the given variable If you have not changed the displayed value then that value is retained in the X register The area of a circle program with an INPUT instruction looks like this RPN mode ALG mode AGGI LBL A AGGI LELA ABG INPUT R AGEZ INPUT R PEGI 2 ABBS SOCK x7 ABE 7 Age4 RTH AGES x REGE RTH To use the INPUT function in a program 1 Decide which data values you will need and assign them names In the area of a circle example the only input needed is the radius which we can assign to R Simple Programming 13 13 2 In the beginning of the program insert an INPUT instruction for each variable whose value you will need Later in the program when you write the part of the calculation that needs a given value insert a variable instruction to bring that value back into the stack Since the INPUT instruction
16. by storing the equation you get the HP 35s to remember the relationship between diameter length and volume so you can use it many times Put the calculator in Equation mode and type in the equation using the following keystrokes Entering and Evaluating Equations 6 1 Keys Display EQN EQH LIST TOP line 2 RCL WV ey W dw y a 25 RARU Yee 25xgx0 2xL_ ENTER VEG 25xq xKOe2xL Lal CK 49CA LH 14 EJLA IEA ES MEBs 25x7Tx_ ROMA VEG Z5xgx0 2 Description Selects Equation mode shown by or the current equation in the EQN annunciator Begins a new equation RCL turns on the A Z annunciator so you can enter a variable name RELI types Digit entry uses the entry cursor x ends the number RA types Terminates and displays the equation Shows the checksum and length for the equation so you can check your keystrokes By comparing the checksum and length of your equation with those in the example you can verify that you ve entered the equation properly See Verifying Equations at the end of this chapter for more information Evaluate the equation to calculate V Keys Display D value wW p 2 172 R S L value 1 6 R S y r 5395 Description Prompts for variables on the right hand side of the equation Prompts for D first value is the current value of D Enters 2 1 2 inches as a fraction Stores D prompts for L valu
17. EN acos Arc tangent of x E ATN Note Colculations with the irrational number r cannot be expressed exactly by the 15 digit internal precision of the calculator This is acl particularly noticeable in trigonometry For example the a calculated sin x radians is not zero but 2 0676 x 10 13 a very small number close to zero 4 4 Real Number Functions Example Show that cosine 5 7 radians and cosine 128 57 are equal to four significant digits Keys Display Description MODE 2 2RAD Sets Radians mode RAD annunciator on CJC ZZ ENTER 7143 5 7 in decimal format EN Zz a COs 6 6235 Cos 5 7 r MODE 1 1 DEG 6 6235 Switches to Degrees mode no annunciator OMB 6 6235 Calculates cos 128 57 which is Cos the same as cos 5 7 n Programming Note Equations using inverse trigonometric functions to determine an angle 9 often look something like this 6 arctan y x If x 0 then yx is undefined resulting in the error DIVIDE BY 8 Real Number Functions 4 5 Hyperbolic Functions With x in the display To Calculate Press Hyperbolic sine of x SINH HYP SIN Hyperbolic cosine of x COSH YP COS Hyperbolic tangent of x TANH YP TAN Hyperbolic arc sine of x ASINH YP Wea ASIN Hyperbolic arc cosine of x ACOSH HYP Fes acos Hyperbolic arc tangent of x ATANH HYP Fea ATAN Danae BEB
18. Example Using Guesses to Find a Root Using a rectangular piece of sheet metal 40 cm by 80 cm form an open top box having a volume of 7500 cm3 You need to find the height of 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 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 xH which you can simplify and enter as V 40 H x 20 H x4xH Type in the equation Keys Display Description EQN v Selects Equation mode and starts RCL V EW the equation LOI IIE ROD W C4B H gt _ 7 10 Solving Equations ESKER 2 LO RCL H C40 H9x 2B H _ COGIC RCIG Hixi20 Hix4xH_ ENTER W C4 H x 2 H Terminates and displays the equation Ev SHOW CK 49R4 Checksum and length LH 12 It seems reasonable that either a tall narrow box or a short flat box could be formed having the desired volume Because the taller box is preferred larger initial estimates of the height are reasonable However heights greater than 20 cm are not physically possible because the metal sheet is only 40 cm wide Initial estimates of 10 and 20 cm are therefore appropriate Keys Display Description Ke Leaves Equation mode 1 0 fea STO LH Stores lower and upper limit ENTER 2 0 ze guesses EQN W C48 H3x 28 H Displays current
19. Given any four of the five values in the Time Value of Money equation TVM you can solve for the fifth value This equation is useful in a wide variety of financial applications such as consumer and home loans and savings accounts The TVM equation is Pl 1 1 100 1 100 et anooy 8 0 Balance B Payments P Future Value F The signs of the cash values balance B payment P and future balance F correspond to the direction of the cash flow Money that you receive has a positive sign while money that you pay has a negative sign Note that any problem can be viewed from two perspectives The lender and the borrower view the same problem with reversed signs Miscellaneous Programs and Equations 17 1 Equation Entry Key in this equation PeiBGxti CitT iBea Hosi Fxcit 1 1i6es H B Keys In RPN mode EQN Rep PILIAN auma WWA Re UWHA ES JEA KA H RAOL Re Ea LO COE Rev EOI 2 PACA E3 ENTER ey hold Remarks Display Description EQH LIST TOP Selects Equation or current equation mode Px 166_ Starts entering equation PxilBG xci 3 PxeiB xci citas exci citi i66 m ci citizieess gt m lt 1 I 1603 H _ 1G8 HOFItFx_ e HosItFe citi ltFuti 1 i6e xC1 1 1882 H_ i 1 1869 H B_ Fxi x i i I m Terminates the equation CK CEFA Checksum and length LH 41 The TVM equation requires that I must be non zero to avoid a DIM
20. LBL letter Choose a letter that will remind you of the program such as A for area If the message DUPLICAT LEL is displayed use a different letter You can clear the existing program instead press EW MEM 2 2F GM use or to find the label and press Wea CLEAR and LC 4 To record calculator operations as program instructions press the same keys you would to do an operation manually Remember that many functions don t appear on the keyboard but must be accessed using menus To enter an equation in a program line see the instructions below 13 6 Simple Programming 5 End the program with a return instruction which sets the program pointer back to PRGM TOF after the program runs Press EW RIN 6 Press LC or fea PRGM to cancel program entry Numbers in program lines are stored precisely as you entered them and they re displayed using ALL or SCI format If a long number is shortened in the display press EN SHOW to view all digits To enter an equation in a program line 1 Press to activate Equation entry mode The EQN annunciator turns on 2 Enter the equation as you would in the equation list See chapter 6 for details Use to correct errors as you type 3 Press to terminate the equation and display its left end The equation does not become part of the equation list After you ve entered an equation you can press Et to see its checksum and length Hold the key to keep the va
21. RMDR nCr and nPr Separate the two arguments with a comma In an equation the XROOT function takes its arguments in the opposite order from RPN usage For example 8 ENTER 3 to is equivalent to FROOT 3 82 All other two argument functions take their arguments in the Y X order used for RPN For example 28 ENTER 4 EW nCr is equivalent to NCR t2824 For two argument functions be careful if the second argument is negative These are valid equations 6 16 Entering and Evaluating Equations ACHGC K 23 CHGS C Y Eight of the equation functions have names that differ from their equivalent operations RPN Operation Equation function x2 SQ Jx SQRT ex EXP 10x ALOG 1 x INV xy XROOT y INT IDIV Example Perimeter of a Trapezoid The following equation calculates the perimeter of a trapezoid This is how the equation might appear in a book Perimeter a b TEE sin sing a 0 b b The following equation obeys the syntax rules for HP 35s equations Entering and Evaluating Equations 6 17 Parentheses used to group items P A B Hx 1 SIN T 1 SIN F d Single letter Optional explicit Division is done before name multiplication addition The next equation also obeys the syntax rules This equation uses the inverse function IHYESIMET3 2 instead of the fractional form 1 4SIM T3 Notice that the SIN function is nested inside the INV function INV is typed by
22. Stores result temporarily for inverse routine Adds half the area under the curve since we integrated using the mean as the lower limit Returns to the calling routine Checksum and length 8387 52 Fegi LEL F Feee RCL O FB3 RCL M This subroutine calculates the integrand for the normal f DE function e X M S 2 16 14 Statistics Programs Program Lines Description In RPN mode Fe 4 RCL 5 FBES x2 FBG 2 Feary FEBS 7 Fee es Fei RTH Returns to the calling routine Checksum and length B3EB 31 Flags Used None Remarks The accuracy of this program is dependent on the display setting For inputs in the area between 3 standard deviations a display of four or more significant figures is adequate for most applications At full precision the input limit becomes 5 standard deviations Computation time is significantly less with a lower number of displayed digits In routine Q the constant 0 5 may be replaced by 2 and UZ You do not need to key in the inverse routine in routines and T if you are not interested in the inverse capability Program Instructions 1 Key in the program routines press when done 2 Press XEQ CS ENTER 3 After the prompt for M key in the population mean and press RZS If the mean is zero just press R S Statistics Programs 16 15 4 After the prompt for S key in the population standard deviation and press R S If the standard deviation
23. Y Z T registers Functions to clear different portions of memory refer to FER CLEAR in the table on page 1 5 14 14 14 1 3 6 12 To use a menu function 1 Press a menu key to display a set of menu items 2 Press 2 LC LA LY to move the underline to the item you want to select 3 Press while the item is underlined With numbered menu items you can either press while the item is underlined or just enter the number of the item Getting Started 1 7 Some menus like the CONST and SUMS have more than one page Entering these menus turns on the or annunciator In these menus use the and cursor keys to navigate to an item on the current menu page use the and keys to access the next and previous pages in the menu Example In this example we use the DISPLAY menu to fix the display of numbers to 4 decimal places and then compute 6 7 The example closes using the DISPLAY menu fo return to full floating point display of numbers Keys Display Description B Initial display z Ev DISPLAY IF Ix 2SCI Enter the DISPLAY menu SEHG 4ALL A or FIR The Fix command is pasted to line 2 4 6 BEGG Fix to 4 decimal places 6 BEBE 6 ENTER I B 6868 Perform the division B 85r1 ESN DISPLAY 4 5 Return to full precision 8 5ri42857143E Menus help you execute dozens of functions by guiding you to them You don t have to remember the names of all the functions buil
24. press LC 1 28 Getting Started Clearing All of Memory Clearing all of memory erases all numbers equations and programs you ve stored It does not affect mode and format settings To clear settings as well as data see Clearing Memory in appendix B To clear all of memory 1 Press 4 ALL You will then see the confirmation prompt CLR ALL Y H which safeguards against the unintentional clearing of memory 2 Press t ENTER Getting Started 1 29 RPN The Automatic Memory Stack This chapter explains how calculations take place in the automatic memory stack in RPN mode You do not need to read and understand this material to use the calculator but understanding the material will greatly enhance your use of the calculator especially when programming In part 2 Programming you will learn how the stack can help you to manipulate and organize data for programs What the Stack Is Automatic storage of intermediate results is the reason that the HP 35s easily processes complex calculations and does so without parentheses The key to automatic storage is the automatic RPN memory stack HP s operating logic is based on an unambiguous parentheses free mathematical logic known as Polish Notation developed by the Polish logician Jan Lukasiewicz 1878 1956 While conventional algebraic notation places the operators between the relevant numbers or variables Lukasiewicz s notation places them before the numbe
25. responding to 13 14 integer part function 4 17 integration accuracy 8 2 8 6 E 1 difficult functions E 2 E 7 display format 8 2 8 6 8 7 evaluating programs 15 7 how it works E 1 in programs 15 10 limits of 8 2 15 8 C 8 E 7 memory usage 8 2 purpose 8 1 restrictions 15 11 results on stack 8 2 8 6 stopping 8 2 15 8 subintervals E 7 time required 8 6 E 7 transforming variables E 9 uncertainty of result 8 2 8 6 E 2 using 8 2 C 8 variable of 8 2 C 8 intercept curve it 12 8 16 1 interest finance 17 3 intermediate results 2 12 inverse function 9 3 inverse hyperbolic functions 4 6 inverse trigonometric functions 4 4 C 6 inverse normal distribution 16 11 ISG 14 18 J 3 9 14 20 14 21 i 14 20 K keys alpha 1 3 letters 1 3 shifted 1 3 L LAST X register 2 8 B 6 LASTx function 2 8 lender finance 17 1 length conversions 4 14 letter keys 1 3 limits of integration 8 2 15 8 C 8 linear regression estimation 12 8 16 logarithmic curve fitting 16 1 Index 5 logarithmic functions 4 1 9 3 C 5 logic AND 11 4 NAND 11 4 NOR 11 4 NOT 11 4 OR 11 4 XOR 11 4 loop counter 14 18 14 23 looping 14 16 14 17 tukasiewicz 2 1 M MEM program catalog 1 28 13 22 reviews memory 1 28 variable catalog 1 28 mantissa 1 25 mass conversions 4 14 math complex number 9 1 general procedure 1 18 intermediate results 2 12 long calculations 2 12 order of calculation 2 14 real number 4 1
26. the sign is 2 847 85 negative indicating that you must pay out this money Ey Os OD Sets FIX 4 display format 1F 1X Prime Number Generator This program accepts any 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 adds 2 assuring that the value is still odd and tests to see if it has found a prime This process continues until a prime number is found Miscellaneous Programs and Equations 17 7 VIEW Prime Note x is the value in the X register t4 e ox ov o yes 2 no no D 2 gt D 17 8 Miscellaneous Programs and Equations Program Listing Program Lines In ALG mode 661 LEL Y BE2 VIEW F Checksum and length 2661 LEL Z 2662 2 F Checksum and length P61 LEL F PeB2 LAST P PGES FPOP 2 PGE4 xib PRBS amp FEBO x Pe 1 PRP FoB SFO Checksum and length KBBI LBL amp HeB2 FPCP O3 EBS x 87 4EG4 GTO 2661 EBS SORTCP3 KEBE xd hy ee O SEBS xv KEE GTO Yael S616 2 0hO 4611 GTO 661 Description This routine displays prime number P 2CC5 6 This routine adds 2 to P EFB2 9 This routine sto
27. variables in 13 12 15 1 15 7 prompts affect stack 6 14 13 14 clearing 1 4 6 14 13 15 equations 6 13 INPUT 13 12 13 14 15 2 15 8 programmed equations 14 11 15 1 15 9 responding to 6 13 13 14 showing hidden digits 6 14 PSE pausing programs 13 19 15 10 preventing program stops 14 11 Q questions A 1 quotient and remainder of division 4 2 R ending prompts 6 11 6 14 7 2 13 15 interrupting programs 13 19 resuming programs 13 16 13 19 running programs 13 22 stopping integration 8 2 15 8 stopping SOLVE 7 8 15 1 RV and R 2 3 C 7 radians angle unit 4 4 angle units A 2 converting to degrees 4 14 radix mark A 1 random numbers 4 15 B 4 RCL 3 2 13 14 RCL arithmetic 3 7 real numbers operations 4 1 real part complex numbers 9 1 recall arithmetic 3 7 rectangular to polar coordinate conver sion 4 10 9 5 regression linear 12 7 16 1 resetting the calculator A 4 B 2 return program See programs Reverse Polish Notation See RPN rolling the stack 2 3 C 7 root functions 4 3 roots See SOLVE checking 7 7 D 3 in programs 15 6 multiple 7 9 none found 7 8 D 8 of equations 7 1 of programs 15 1 rounding fractions 5 8 13 18 numbers 4 18 round off fractions 5 8 integration 8 6 SOLVE D 13 statistics 12 10 trig functions 4 4 routines calling 14 1 nesting 14 2 15 11 parts of programs 14 1 RPN compared to equations 13 4 in programs 13 4 origins 2 1 running programs 13 10 S SHOW equation c
28. 1 and 2 this is what you should do to correct your error RPN The Automatic Memory Stack 2 7 lt x lt N Ho Lifts the stack Lifts the stack and replicates the X register Overwrites the X register Clears x by overwriting it with zero ee PY Overwrites x replaces the zero The LAST X Register The LAST X register is a companion to the stack it holds the number that was in the X register before the last numeric function was executed A numeric function is an operation that produces a result from another number or numbers such as J Pressing Wea returns this value into the X register This ability to retrieve the last x has two main uses 1 Correcting errors 2 Reusing a number in a calculation See appendix B for a comprehensive list of the functions that save x in the LAST X register 2 8 RPN The Automatic Memory Stack Correcting Mistakes with LAST X Wrong Single Argument Function If you execute the wrong single argument function use WB LAST to retrieve the number so you can execute the correct function Press first if you want to clear the incorrect result from the stack Since M and ACHO don t cause the stack to drop you can recover from these functions in the same manner as from single argument functions Example Suppose that you had just computed In 4 7839 x 3 879 x 105 and wanted to find its square root but pressed by mistake You don t have to start over To find the
29. 12 X 0 25 that is x 12 Storing Data into Variables 3 7 Example Suppose the variables D E and F contain the values 1 2 and 3 Use storage arithmetic to add 1 to each of those variables Keys Display Description operon i BGEB Stores the assumed values into the mmeo 2 8866 variable Big ee 1 Fea STO Adds to D E and F 0 Wea STO onago 1 6666 WA LA D Displays the current value of D 2 BEEBE muma 3 BBB EW VIEW LE 4 6666 E3 i GGBB Clears the VIEW display displays X register again Suppose the variables D E and F contain the values 2 3 and 4 from the last example Divide 3 by D multiply it by E and add F to the result Keys Display Description WRUHA 1 5866 Calculates 3 D RECAE 4 5000 3 Dx E RoE 5 5006 3 DxE F Exchanging x with Any Variable The EY key allows you to exchange the contents of x the displayed X register with the contents of any variable Executing this function does not affect the Y Z or T registers 3 8 Storing Data into Variables Example Keys Display Description 1 2 fe STO 12 6668 Stores 12 in variable A AJ ENTER 3 a Displays x EEN x5 A 12 6666 Exchanges contents of the X register and variable A ESN x5 A 3 BGG8 Exchanges contents of the X register and variable A lt x lt N The Variables
30. 3 There is a maximum of 800 variables 14 24 Programming Techniques 15 Solving and Integrating Programs Solving a Program In chapter 7 you saw how you can enter an equation it s added to the equation list and then solve it for any variable You can also enter a program that calculates a function and then solve it for any variable This is especially useful if the equation you re solving changes for certain conditions or if it requires repeated calculations To solve a programmed function 1 Enter a program that defines the function See To write a program for SOLVE below 2 Select the program to solve press label You can skip this step if you re re solving the same program 3 Solve for the unknown variable press a SOLVE variable Notice that FN is required if you re solving a programmed function but not if you re solving an equation from the equation list To halt a calculation press or and the message INTERRUPTED will appear in line 2 The current best estimate of the root is in the unknown variable use EN to view it without disturbing the stack To resume the calculation press R S To write a program for SOLVE The program can use equations and ALG or RPN operations in whatever combination is most convenient Solving and Integrating Programs 15 1 1 Begin the program with a label This label identifies the function that you want SOLVE to evaluate F H abel 2 Include an IN
31. 33 8668 Intermediate result a B 1212 Final result More Exercises Practice using RPN by working through the following problems Calculate 14 12 x 18 12 9 7 78 0000 A Solution CL 4Y ENTER 29 EC CS ENTER CO 2 9 JEENTER ZI E A Calculate 237 13 x9 1 7 412 1429 A Solution DOAANDERRMOmAMm A Calculate 5 4 x 0 8 12 5 0 7 0 5961 Solution DOR OMAOMRROwAMMAOOene am or HEaAmRATAQTACQCORmRMQAmnMWAA A a Calculate 4 5728 8 33x 4 5 2 8 33 7 46 x 0 32 4 3x 3 15 2 75 1 71x 2 01 2 16 RPN The Automatic Memory Stack A Solution ARR AMNMAEMOMMAETsAnNOMAwea OADMAwAADOMORAOMAewAnwAz OMOEA a RPN The Automatic Memory Stack 2 17 3 Storing Data into Variables The HP 35s has 30 KB of memory in which you can store numbers equations and programs Numbers are stored in locations called variables each named with a letter from A through Z You can choose the letter to remind you of what is stored there such as B for bank balance and C for the speed of light Example This example shows you how to store the value 3 in the variable A first in RPN mode and then in ALG mode Keys Display Description MODE 5 5 FFH Switch to RPN mode if necessary 3 8 8688 Enter the value 3 a F53 STO The Store command prompts for a STO_ letter note the A Z annunciator A 8 6668 The v
32. 4D Integrates the normal function using the dummy variable D Restrictions on Solving and Integrating The SOLVE variable and FN d variable instructions cannot call a routine that contains another SOLVE or J FN instruction That is neither of these instructions can be used recursively For example attempting to calculate a multiple integral will result in an f FH error Also SOLVE and J FN cannot call a routine that contains an FH abel instruction if attempted a SOLVE ACTIVE or FM ACTIVE error will be returned SOLVE cannot call a routine that contains an J FN instruction produces a SOLVE FN error just as J FN cannot call a routine that contains a SOLVE instruction produces an f SOLVE error The SOLVE variable and J FN d variable instructions in a program use one of the 20 pending subroutine returns in the calculator Refer to Nested Subroutines in chapter 14 Solving and Integrating Programs 15 11 16 Statistics Programs Curve Fitting This program can be used to fit one of four models of equations to your data These models are the straight line the logarithmic curve the exponential curve and the power curve The program accepts two or more x y data pairs and then calculates the correlation coefficient r and the two regression coefficients m and b The program includes a routine to calculate the estimates X and y For definitions of these values see Linear Regression in chapter 12 Samples of
33. 7 4 0 0 466 y Display shows n the number of data E 2 8888 pairs you entered Wes LASTx LAST x Brings back last x value Last y is still 466 6668 in Y register Ey c 466 5 Deletes the last data pair 1 6666 L6 4 LO 4 y Reenters the last data pair 2 6666 4 2 0 Ey 20 Deletes the first data pair PA 1 8888 EERS 2 LO 2B y Reenters the first data pair There is 2 8808 still a total of two data pairs in the C 12 ALG Summary statistics registers Linear Regression Linear regression or L R also called linear estimation is a statistical method for finding a straight line that best fits a set of x y data m To find an estimated value for x or y key in a given hypothetical value for y or x press ENTER then press x or Ex m To find the values that define the line that best fits your data press amp followed by r m or E ALG Summary C 13 D More about Solving This appendix provides information about the SOLVE operation beyond that given in chapter 7 How SOLVE Finds a Root SOLVE first attempts to solve the equation directly for the unknown variable If the attempt fails SOLVE changes to an iterative repetitive procedure The iterative operation is to execute repetitively the specified equation The value returned by the equation is a function f x of the unknown variable x f x is mathematical shorthand for a function defined i
34. 8 solving programs 15 1 fractional part function 4 17 Fraction display mode affects rounding 5 8 affects VIEW 13 15 setting 5 1 A 2 fractions accuracy indicator 5 2 5 3 and equations 5 9 and programs 5 10 13 15 14 9 denominators 1 26 5 4 14 10 14 14 displaying 5 2 5 4 A 2 flags 14 9 formats 5 6 not statistics registers 5 2 reducing 5 2 5 6 rounding 5 8 round off 5 8 setting format 5 6 14 10 14 14 typing 1 26 functions in equations 6 5 6 16 list of G 1 names in display 13 8 nonprogrammable 13 24 real number 4 1 single argument 1 18 2 9 two argument 1 19 2 9 9 3 future balance finance 17 1 G GTO finds PRGM TOP 13 6 13 21 14 6 finds program labels 13 10 13 22 14 5 finds program lines 13 22 14 5 gamma function 4 15 go to See GTO grads angle units 4 4 A 2 Grandma Hinkle 12 7 Greatest integer 4 18 grouped standard deviation 16 18 GTO 14 4 14 17 guesses for SOLVE 7 2 7 7 7 8 7 12 15 6 H help about calculator A 1 HEX annunciator 11 1 hex numbers See numbers arithmetic 11 4 converting to 11 2 range of 11 7 typing 11 1 hexadecimal numbers See hex numbers Horner s method 13 26 humidity limits for calculator A 2 hyperbolic functions 4 6 C 6 i 3 9 14 20 i 14 20 14 21 14 23 imaginary part complex numbers 9 1 C8 indirect addressing 14 20 14 21 14 23 INPUT always prompts 14 11 entering program data 13 12 in integration programs 15 8 in SOLVE programs 15 2
35. 8 314 J mole K T Temperature kelvins K C 273 1 15 2 Solving and Integrating Programs To begin put the calculator in Program mode if necessary position the program pointer to the top of program memory Keys Display Description In ALG mode a Sets Program mode GTO CIE FEGM TOP Type in the program Program Lines Description In ALG mode GEBI LEL G Identifies the programmed function CBZ IHFUT P Stores P for pressure Gees INPUT W Stores V for volume GeeG4 IMPUT H Stores N for number of moles of gas GAGS INPUT R Stores R for gas constant CEBE INPUT T Stores T for temp GOB PxV NxRxT Press EQN Pressure x volume Moles x gas constant x temp GEBS RTH Ends the program Checksum and length F425 33 Press to cancel Program entry mode Use program G to solve for the pressure of 0 005 moles of carbon dioxide in a 2 liter bottle at 24 C Keys Display Description In ALG mode EW FN G Selects G the program SOLVE evaluates to find the value of the unknown variable We SOLVE Ce We Selects P prompts for V value 2 R S H Stores 2 in V prompts for N value Solving and Integrating Programs 15 3 C 0 0 5 R S R Stores 005 in N prompts for R value OMB T Stores 0821 in R prompts for T R75 value moon T Calculates T 3 JL ENTER 297 1888 R S SOLVING Stores 297 1 in T solves for P P Pressure is 0 06
36. BEEBE Common logarithm base 10 LOG 1 0 LOGCIB ENTER 1 6666 Natural exponential Wes eE Z ENTER ESPZ r 3591 Common exponential ESN 107 2 ENTER ALOGEZI 166 GEG antilogarithm ALG Summary C 5 Trigonometric Functions Assume the unit of the angle is MODE 1 i0E6 To Calculate Press Display Sine of x SIN L3 LOJIENTER SINC Se 6 56606 Cosine of x COS 6 O ENTER COS oe2 6 5606 Tangent of x TAN 4 5 ENTER TRNS 45 gt 1 8668 Arc sine of x Fes ASIN 171 ASIHC1 gt ENTER 38 BEBE Arc cosine of x Fes ACOS 0 ACOS ENTER 26 BEBE Arc tangent of x We ATAN 0 ATAHS Ba ENTER 6 6666 Hyperbolic functions To Calculate Press Hyperbolic sine of x SINH B HYP SIN key in a number HYP COS key in a umber press HYP TAN key in a number me a oO n n Hyperbolic cosine of x COSH B Hyperbolic tangent of x TANH B press ENTER Hyperbolic arc sine of x ASINH ESN HYP Wed ASN key ina r press ENTER HYP fea acos key ina ress ENTER e E 3 O oO Hyperbolic arc cosine of x ACOSH B J 3 og oO rp Hyperbolic arc tangent of x ATANH ESN HYP Fed AAN key ina number press ENTER C 6 ALG Summary Parts of numbers To calculate Press Di
37. Cancels program entry Simple Programming 13 9 Running a Program To run or execute a program program entry cannot be active no program line numbers displayed PRGM off Pressing will cancel Program entry mode Executing a Program XEQ Press XEQ label to execute the program labeled with that letter To execute a program from it s beginning press XEQ label ENTER For example press XEQ A ENTER The display will show E ABBI and execution will start at the top of Label A You can also execute a program starting at another position by pressing label Line number for example KEQ A LOLL If there is only one program in memory you can also execute it after moving pointer to the top of the program line and pressing run stop key The PRGM annunciator displays and the E annunciator turns on while the program is running If necessary enter the data before executing the program Example Run the programs labeled A and E to find the areas of three different circles with radii of 5 2 5 and 2r Remember to enter the radius before executing A or E Keys Display Description In RPN mode 5 KEQ A ENTER RUNNING Enters the radius then starts 8 5398 program A The resulting area is displayed GICIGIKEQ E 12 6356 Calculates area of the second ENTER circle using program E aom x Calculates area of the third circle Eel 124 0251 13 10 Simple Programming Testing a Program
38. Checksum and length 042A 18 166i LBL I I662 INPUT Q I663 ECL M 1664 STO X This routine calculates X given Q X Prompts for and stores Q X Recalls the mean Stores the mean as the guess for X called Xguess Checksum and length A970 12 TEBI LEL T TGZ AEG QBBI TEB RCL Q T664 REL amp TBS STOD TEBE Ry TEEF AEG FEBI TBS RCL T TBBS This label defines the start of the iterative loop Calculates Q Xguess Q X Calculates the derivative at Xguess Calculates the correction for Xguess Statistics Programs 16 13 Program Lines In RPN mode TH1B STO amp TH 1ii ABS THlz amp 6681 T LS xiv THi4 GTO Teel TEIS RCL amp Ti VIEW amp Tir GTO 166i Description Adds the correction to yield a new Xguess Tests to see if the correction is significant Goes back to start of loop if correction is significant Continues if correction is not significant Displays the calculated value of X Loops to calculate another X Checksum and length EDF4 57 GEG1i LEL peZ RCL M GEES RCL GEG4 FH F QES FH aD GEG6 2 BEEF 7 QBBE x GEES J GBE1iG RCL iii STOT GBi2 QBI 7 G614 6 5 BBi5 GBEG16 RTH This subroutine calculates the upper tail area Q x Recalls the lower limit of integration Recalls the upper limit of integration Selects the function defined by LBL F for integration Integrates the normal function using the dummy variable D Calculates S x 27r
39. Cross Product in VECIOIS s sinsacsaeind vanes nckinnean eacus crenvaidpneddooagens 17 11 Part 3 Appendixes and Reference A Support Batteries and Service sscsssccsssceseeceees A 1 Calculator S ppors waynes ranges aaa ae A Answers to Common Questions c sseeeeeeereeeeeeeeeeeeeeeeees A 1 Environment l LITMUS ssnipe aR a seus EEE EE A 2 Changing the Batteries 5 sissisinvactoserenbudasousstoadnta tusdian thaws Waa vane A 3 Testing Calculator Operation s 43 d0stiaiiociacmainn mien wanes A 4 Wiis S el Testiin a A a e a A 5 Wairany eenen a e e T e E TEE A 7 A axe Vacs E A tues knee anaes A 8 Regulatory information ssnnssseeseseseseoessotsreorseersserrsssersseees A 12 Federal Communications Commission Notice esceeeeeeeeeees A 12 Contents 9 D 10 User Memory and the Stack ssccssscsssscsscceseeceees B 1 Managing Calculator Memory csccccceeeeeeeceeeeeeeeeteeeeeeeenseeeees B 1 Resetting the Calculator ax ivwu ie tiger meen mGhera ees B 2 CIEGIIFgEMEMGIY vinvivecetinnnssucesueiasiagesich duaiedies usisy euity enti veaiirnseligebues B 3 The Status of Stae OUP cinceveeerarounmmninnnscntare men mae vee ree B 4 Disabling Qperctionss ys iiss vents verasdacessddas oossdee sueoessovsveadesuneodis B 5 Neutral Operations se usiiastaciar ire asunus aera agene tue B 5 The Status of the LAST X Register ccecccseeseceeteceeseeeeeseseees B 6 Accessing Stack Register Contents
40. Description In RPN mode 5 GTO TA 2 BBBE Moves program counter to label A ENTER LY hold release F881 LEL A 2 BEBE C hold release ABBE x2 Squares input 25 BEBE Simple Programming 13 11 hold release FEES x Value of z 3 1416 hold release P284 257 To 3395 hold release F285 RTH End of program Result is correct TS 3393 Entering and Displaying Data The calculator s variables are used to store data input intermediate results and final results Variables as explained in chapter 3 are identified by a letter from A through Z but the variable names have nothing to do with program labels In a program you can get data in these ways From an INPUT instruction which prompts for the value of a variable This is the most handy technique From the stack You can use STO to store the value in a variable for later use From variables that already have values stored From automatic equation prompting if enabled by flag 11 set This is also handy if you re using equations In a program you can display information in these ways With a VIEW instruction which shows the name and value of a variable This is the most handy technique On the stack only the values in the X and Y registers are visible You can use PSE for a 1 second look at the X and Y registers In a displayed equation if enabled by flag 10 set The equation is usually a message not a true equation
41. Description Wes CLEAR The CLEAR menu VARS ALL E STK CLVAR contains options for clearing x the number in the X register all direct variables all of memory all statistical data all stacks and indirect variables If you press 3 4ALL a new menu CLR ALL Y His displayed so you can verify your decision before erasing everything in memory During program entry RLL is replaced by 3PGM If you press 3PGM a new menu CLR PGMS Y H is displayed so you can verify your decision before erasing all your programs During equation entry SALL is replaced by 3E N If you press EGH the CLR EQN YH menu is displayed so you can verify your decision before erasing all your equations When you select 6 GL YAR the command is pasted into the command line with three placeholders You must enter a 3 digit number in the placeholder blanks Then all the indirect variables whose addresses are greater than the address entered are erased For example CLVARO56 erases all indirect variables whose address is greater than 56 Getting Started 1 5 Using Menus There is a lot more power to the HP 35s than what you see on the keyboard This is because 16 of the keys are menu keys There are 16 menus in all which provide many more functions or more options for more functions HP 35s Menus Menu Name Menu Description Chapter L R s 0 CONST SUMS BASE INTG LOGIC Numeric Functions
42. E 3 SF i Sets flag 1 the indicator for In Y Es 4 GTO Z661 Branches to common entry point Z Checksum and length D6F1 12 Pegi LEL F This routine sets the status for the power model Page SFB Sets flag O the indicator for In X P B3 SF i Sets flag 1 the indicator for In Y Checksum and length 3800 9 2661 LEL Z Defines common entry point for all models 29 2 CLE Clears the statistics registers Press Wea CLEAR 4 4 gt 2883 B Sets the loop counter to zero for the first input Checksum and length 8611 10 H i LBL H Defines the beginning of the input loop HeBe i Adjusts the loop counter by one to prompt for input WEES Hee4 STO Stores loop counter in X so that it will appear with the prompt for X He65 INPUT Displays counter with prompt and stores X input Statistics Programs 16 3 Program Lines Description In RPN mode WEG6 FS B It flag O is set Waa LH takes the natural log of the X input Hees STO B Stores that value for the correction routine Wee9 TMPUT Y Prompts for and stores Y WEiB FS 1 It flag 1 is set Wait LH takes the natural log of the Y input Heiz STOR His RCL E Heid E Accumulates B and R as x y data pair in statistics registers Heis CTO HEGI Loops for another X Y pair Checksum and length 9560 46 uggi LBL U Defines the beginning of the undo routine Weee REL R Recalls the most recent data pair UBES RCL E UBe4 E Deletes this pair from the statistic
43. I and J There are two variables that you can access directly the variables and J Although they store values as other variables do and J are special in that they can be used to refer to other variables including the statistical registers using the I and J commands I is found on the LO key while J is on the LJ key This is a programming technique called indirect addressing that is covered under Indirectly Addressing Variables and Labels in chapter 14 Storing Data into Variables 3 9 A Real Number Functions This chapter covers most of the calculator s functions that perform computations on real numbers including some numeric functions used in programs such as ABS the absolute value function These functions are addressed in groups as follows m Exponential and logarithmic functions m Quotient and Remainder of Divisions m Power functions L and EN EZ m Trigonometric functions m Hyperbolic functions m Percentage functions m Physics constants Conversion functions for coordinates angles and units Probability functions Parts of numbers number altering functions Arithmetic functions and calculations were covered in chapters 1 and 2 Advanced numeric operations root finding integrating complex numbers base conversions and statistics are described in later chapters The examples in this chapter all assume the HP 35s is in RPN mode Exponential and Logarithmic Funct
44. IDE BY amp error If you re solving for and aren t sure of its current value press MQ fea STO LL before you begin the SOLVE calculation E SOLVE LL 17 2 Miscellaneous Programs and Equations The order in which you re prompted for values depends upon the variable you re solving for SOLVE instructions 1 If your first TVM calculation is to solve for interest rate press UJ Wa STO LL 2 Press EQN If necessary press or to scroll through the equation list until you come to the TVM equation 3 Do one of the following five operations a Press M SOLVE to calculate the number of compounding periods b Press WE3 SOLVE LL to calculate periodic interest For monthly payments the result returned for is the monthly interest rate i press 12 to see the annual interest rate c Press GOLE B to calculate initial balance of a loan or savings account d Press Fea SOLVE LP to calculate periodic payment e Press P SOLVE LE to calculate future value or balance of a loan 4 Key in the values of the four known variables as they are prompted for press after each value 5 When you press the last R S the value of the unknown variable is calculated and displayed 6 To calculate a new variable or recalculate the same variable using different data go back to step 2 SOLVE works effectively in this application without initial guesses Miscellaneous Programs and Equat
45. ROOT FOUND See Verifying the Result later in this chapter and Interpreting Results and When SOLVE Cannot Find a Root in appendix D For certain equations it helps to provide one or two initial guesses for the unknown variable before solving the equation 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 later in this chapter Example Solving the Equation of Linear Motion The equation of motion for a free falling object is d vot 1 2gt2 where d is the distance vg is the initial velocity t is the time and g is the acceleration due to gravity Type in the equation 7 2 Solving Equations Keys Display Description Wes CLEAR 3 ALL Clears memory C lt ENTER EQN 343 lin solve Selects Equation mode EQN LIST TOP RCL D_ EH RCL Starts the equation WY Gx RELI D VxT _ QAI RCL GI T SxGxT 2 RCL 1 7 2 ENTER O VxT O 5xGxT 2 Terminates the equation and displays the left end Ev SHOW CK FB3C Checksum and length LH 15 g acceleration due to gravity is included as a variable so you can change it for different units 9 8 m s2 or 32 2 ft s2 Calculate how many meters an object falls in 5 seconds starting from rest Since Equation mode is turned on and the desired equation is already in the display you can start solving for D
46. SOLVE operation was running The calculator is solving an equation or program for its root This might take a while Attempted to calculate the square root of a negative number STAT ERROR SYHTAS ERROR TOO BIG SEQ OVERFLOW YES Self Test Messages 355 OK 355 FRIL n Statistics error m Attempted to do a statistics calculation with n O m Attempted to calculate sx sy Y m r or b with n m Attempted to calculate r or xw with x data only all y values equal to zero m Attempted to calculate x Y r m or b with all x values equal A syntax error was detected during evaluation of an expression equation SOLVE or LZ Pressing or clears the error message and allows you to correct the error The magnitude of the number is too large to be converted to HEX OCT or BIN base the number must be in the range 34 359 738 368 lt n lt 34 359 738 367 A running program attempted an 215 nested E label Up to 20 subroutines can be nested Since SOLVE and J FN each uses a level they can also generate this error The condition checked by a test instruction is true Occurs only when executed from the keyboard The self test and the keyboard test passed The self test or the keyboard test failed and the calculator requires service 2667 HP DEY CO L F Copyright message displayed after successfully completing the self test Messages F 5 Operation Index G This section
47. T016 at the end of the T routine display the result for X Note also that this VIEW instruction in this program is preceded by a RCL instruction The RCL instruction is not necessary but it is convenient because it brings the VIEWed variable to the X register making it available for manual calculations Pressing while viewing a VIEW display would have the same effect The other application programs in chapters 16 and 17 also ensure that the VIEWed variable is in the X register as well Simple Programming 13 15 Using Equations to Display Messages Equations aren t checked for valid syntax until they re evaluated This means you can enter almost any sequence of characters into a program as an equation you enter it just as you enter any equation On any program line press to start the equation Press number and math keys to get numbers and symbols Press before each letter Press to end the equation If flag 10 is set equations are displayed instead of being evaluated This means you can display any message you enter as an equation Flags are discussed in detail in chapter 14 When the message is displayed the program stops press to resume execution If the displayed message is longer than 14 characters the annunciator turns on when the message is displayed You can then use M and 0 to scroll the display If you don t want the program to stop see Displaying Information without Stopping below Example INPUT VIEW
48. The built in equations are 2 2 lin solve Ax By C Dx Ey F and 3 3 lin Solve Ax By Cz D Ex Fy Gz H Ix Jy Kz L If you select one of them the XEQ ENTER and LZ key will have no effect Pressing the fa SOLVE will request 6 variables A to F for the 2 2 case or 12 variables A to L for the 3 3 case and use them to find x y for a 2 2 linear equation system or x y and z for a 3 3 linear equation system The result will be saved in variables x y and z The calculator can detect cases with infinitely many solutions or no solutions x 2y 5 Example solve the x y in simultaneous equations 3x 4y 11 Keys Display Description EQN 343 lin solve Enters equation mode EQH LIST TOP WY EQN LIST TOP Displays the built in 2 2 lin salve equation Fes SOLVE A Prompts for A value NRS B Stores 1 in A prompts for value B CIRS C Stores 2 in B prompts for value C GIRS oO Stores 5 in C prompts for value D BIRS E Stores 3 in D prompts for value E 7 6 Solving Equations 4 R S F Stores 4 in E prompts for F value L1 L1 R S Stores 11 in F and 1 EGGE amp calculates x and y ly v value of y 2 8088 4 Understanding and Controlling SOLVE SOLVE first attempts to solve the equation directly for the unknown variable If the attempt fails SOLVE changes to an iterative repetitive procedure The procedure starts by evaluating the equation using two initial guesse
49. The first CJ separates the integer part of the number from its fractional part 2 Key in the fraction numerator and press LJ again The second LJ separates the numerator from the denominator 3 Key in the denominator then press or a function key to terminate digit entry The number or result is formatted according to the current display format The a b c symbol under the LJ key is a reminder that the LJ key is used twice for fraction entry The following example illustrates the entry and display of fractions 1 26 Getting Started Example Enter the mixed numeral 12 3 8 and display it in fraction and decimal forms Then enter and add it to 12 3 8 This example uses RPN mode Keys va EIER ENTER Wea FDISP EENEN Ez Wea Ese Display B 12 3 8 6668 12 3 8 12 3756 12 3756 12 378 12 378 12 378 B34 G i3 i75 B 13 1256 Description The decimal point is interpreted in the normal way When LJ is pressed the 2nd time the display switches to fraction mode Upon entry the number is displayed using the current display format Switch to fraction display mode Enter 34 Note you start with LJ because there is no integer part you could type in O Add to 12 3 8 Switch back to the current display mode Refer to chapter 5 Fractions for more information about using fractions Messages The calculator responds to error conditions by displaying the A annunciator Usually
50. UZx PHRA Bt HeC IMVC SING Tao T HVC STHCF 3 oo Example Area of a Polygon The equation for area of a regular polygon with n sides of length d is Area 1 cos m n Tia g sin n d You can specify this equation as RRB 25xNxKO 2x COSC tha SINC qth Notice how the operators and functions combine to give the desired equation 6 18 Entering and Evaluating Equations You can enter the equation into the equation list using the following keystrokes EQN RCL A SW 2S RCE LN 2 RCL D2 29x COS 5H 2 RCL ON J SIN a 7 RCL NJ ENTER Syntax Errors The calculator doesn t check the syntax of an equation until you evaluate the equation If an error is detected 3 NTAX ERROR is displayed and the cursor is displayed at the first error location You have to edit the equation to correct the error See Editing and Clearing Equations earlier in this chapter By not checking equation syntax until evaluation the HP 35s lets you create equations that might actually be messages This is especially useful in programs as described in chapter 13 Verifying Equations When you re viewing an equation not while you re typing an equation you can press ES SHOW to show you two things about the equation the equation s checksum and its length Hold the key to keep the values in the display The checksum is a four digit hexadecimal value that uniquely identities this equ
51. X register In RPN mode to enter this program into program memory do the following Keys Display Description In RPN mode r Clears memory 3ALL C METR Fea PRGM ctivates Program entry mode PRGM Acti Prog y mod PRGM annunciator on to FIG PREM TOP Resets program pointer to PRGM TOP BA GGG x2 Radius 2 z alalar x Baas x Area 7x2 Fea PROM Exits Program entry mode Try running this program to find the area of a circle with a radius of 5 Keys Display Description In RPN mode oao This sets the program to its beginning 5 78 5398 The answer In ALG mode to enter this program into program memory do the following Keys Display Description In ALG mode r Clears memory GALL METR Fes PROM Activates Program entry mode PRGM annunciator on 13 2 Simple Programming GTO CG GC PRGM TOP Resets program pointer to PRGM TOP We 2 RCO DID IK BBE1l SECHJE Area m2 et z Wea PROM Exits Program entry mode Try running this program to find the area of a circle with a radius of 5 Keys Display Description In ALG mode Gro FG KER This sets the program to its beginning 5 STO XX ENTER Sie Stores 5 into X T BEBE R S 8 2358 The answer We will continue using the above program for the area of a circle to illustrate programming concepts and methods Designing a Program The following topics show what instructions you
52. an operation equation or program is executing When in Fraction display mode press za EDISP only one of the 4 or w halves of the 4 w annunciator will be turned on to indicate whether the displayed numerator is slightly less than or slightly greater than its true value If neither part of 4 w is on the exact value of the fraction is being displayed Left shift is active Right shift is active Reverse Polish Notation mode is active Algebraic mode is active Program entry is active Equation entry mode is active or the calculator is evaluating an expression or executing an equation Indicates which flags are set flags 5 through 11 have no annunciator Radians or Grad angular mode is set DEG mode default has no annunciator Indicates the active number base DEC base 10 default has no annunciator Hyperbolic function is active 1 2 1 C 13 4 C Getting Started 1 13 HP 35s Annunciators continued Annunciator Meaning Chapter rr tt There are more characters to the left or right in the display of the entry in line 1 or line 2 Both of these annunciators may appear simultaneously indicating that there are characters to the left and right in the display of an entry Entries in line 1 with missing characters will show an ellipsis to indicate missing characters In RPN mode use the and keys to scroll through an entry and see the leading and trailing charac
53. and storage humidity 90 relative humidity at 40 C 104 F maximum A 2 Support Batteries and Service Changing the Batteries The calculator is powered by two 3 volt lithium coin batteries CR2032 Replace the batteries as soon as possible when the low battery annunciator appears If the battery annunciator is on and the display dims you may lose data If data is lost the MEMOR CLEAR message is displayed Once you ve removed the batteries replace them within 2 minutes to avoid losing stored information Have the new batteries readily at hand before you open the battery compartment To install batteries 1 Have two fresh button cell batteries at hand Avoid touching the battery terminals handle batteries only by their edges 2 Make sure the calculator is OFF Do not press ON LC again until the entire battery changing procedure is completed If the calculator is ON when the batteries are removed the contents of Continuous Memory will be erased BK B 3 Turn the calculator over and slide off the battery cover 4 To prevent memory loss never remove two old batteries at the same time Be sure to remove and replace the batteries one at a time Support Batteries and Service A 3 Warning Do not mutilate puncture or dispose of batteries in fire The batteries can burst or explode releasing hazardous 7 chemicals 5 Insert a new CR2032 lithium battery makin
54. calculator generating its own seed Example Combinations of People A company employing 14 women and 10 men is forming a six person safety committee How many different combinations of people are possible Keys Display Description 2 4 JIENTER 6 24 Twenty four people grouped six at 6 a time ey 134 596 8888 Total number of combinations possible If employees are chosen at random what is the probability that the committee will contain six women To find the probability of an event divide the number of combinations for that event by the total number of combinations Keys Display Description 1 4 ENTER 6 i4 Fourteen women grouped six at a time Lal 3 003 000G Number of combinations of six women on the committee we 124 596 8888 Brings total number of combinations back into the X register B 6 B223 Divides combinations of women by total combinations to find probability that any one combination would have all women 4 16 Real Number Functions Parts of Numbers These functions are primarily used in programming Integer part To remove the fractional part of x and replace it with zeros press EW UNTG 6 SIF For example the integer part of 14 2300 is 14 0000 Fractional part To remove the integer part of x and replace it with zeros press EW UNTO 5 SFP For example the fractional part of 14 2300 is 0 2300 Absolute value To replace a number in the x register
55. can put in a program What you put in a program affects how it appears when you view it and how it works when you run it Selecting a Mode Programs created and saved in RPN mode should be edited and executed in RPN mode and programs or steps created and saved in ALG mode should be edited and executed in ALG mode If not the result may be incorrect Simple Programming 13 3 Program Boundaries LBL and RTN If you want more than one program stored in program memory then a program needs a label to mark its beginning such as R amp B1 LBL A and a return to mark its end such as ABES RTH Notice that the line numbers acquire an F to match their label Program Labels Programs and segments of programs called routines should start with a label To record a label press a letter key The label is a single letter from A through Z The letter keys are used as they are for variables as discussed in chapter 3 You cannot assign the same label more than once this causes the message DUPLICAT LEL but a label can use the same letter that a variable uses It is possible to have one program the top one in memory without any label However adjacent programs need a label between them to keep them distinct Programs can not have more than 999 lines Program Returns Programs and subroutines should end with a return instruction The keystrokes are Ey RN When a program finishes running the last RTN instruction returns
56. correct result press Wea LAST x Mistakes with Two Argument Functions If you make a mistake with a two argument operation such as LJ 4 or LEJ you can correct it by using Wea and the inverse of the two argument operation 1 Press Wea 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 X register Then m f you had used the wrong function press Wea LASTX again to restore the original stack contents Now execute the correct function m If you had used the wrong second number key in the correct one and execute the function If you had used the wrong first number key in the correct first number press We LAST to recover the second number and execute the function again Press first if you want to clear the incorrect result from the stack RPN The Automatic Memory Stack 2 9 Example Suppose you made a mistake while calculating 16 x 19 304 There are three kinds of mistakes you could have made Wrong Mistake Correction Calculation ENTERO Weng function Wes AT G 5 Wes LAST x x ENTER 1 Wrong firstnumber 1 6 WES LASTx x U Ea CE ENTER 7 Wong second number yey LASTx IOI x EJ e gt x BENEKE Reusing Numbers with LAST X You can use F LASTX to reuse a n
57. equation Pa SOLVE We Solves for H prompts for V value 7 5 OJ LO R S H Stores 7500 in V solves for H 13 8686 Now check the quality of this solution that is whether it returned an exact root by looking at the value of the previous estimate of the root in the Y register and the value of the equation at the root in the Z register Keys Display Description 15 6888 This value from the Y register is the estimate made just prior to the final result Since it is the same as the solution the solution is an exact root a 6888 This value from the Z register shows the equation equals zero at the root Solving Equations 7 11 The dimensions of the desired box are 50 x 10 x 15 cm If you ignored the upper limit on the height 20 cm and used initial estimates of 30 and 40 cm you would obtain a height of 42 0256 cm a root that is physically meaningless If you used small initial estimates such as O and 10 cm you would obtain a height of 2 9774 cm producing an undesirably short flat box If you don t know what guesses to use you can use a graph to help understand the behavior of the equation Evaluate your equation for several values of the unknown For each point on the graph display the equation and press at the prompt for x enter the x coordinate and then obtain the corresponding value of the equation the y coordinate For the problem above you would always set V 7500 and vary the value of H
58. field Predict the grain yield based on the above statistics Keys Display Description 7100 r TEBE Enters hypothetical x value 76 EN 2 zo F mB The predicted yield in tons per 7 5615 hectare Limitations on Precision of Data Since the calculator uses finite precision it follows that there are limitations to calculations due to rounding Here are two examples Normalizing Close Large Numbers The calculator might be unable to correctly calculate the standard deviation and linear regression for a variable whose data values differ by a relatively small amount To avoid this normalize the data by entering each value as the difference from one central value such as the mean For normalized x values this difference must then be added back to the calculation of X and x and y and b must also be adjusted For example if your x values were 7776999 7777000 and 7777001 you should enter the data as 1 O and 1 then add 7777000 back to X and xX For b add back 7777000 x m To calculate y be sure to supply an x value that is less 7777000 Similar inaccuracies can result if your x and y values have greatly different magnitudes Again scaling the data can avoid this problem Effect of Deleted Data Executing does not delete any rounding errors that might have been generated in the statistics registers by the original data values This difference is not serious unless the incorrect data have a magnitude that is enor
59. find the root of the equation using the current initial guesses see page These conditions include bad guess solution not found point of interest left unequal to right A SOLVE operation executed in a program does not produce this error the same condition causes it instead to skip the next program line the line following the instruction SOLE variable Warning displayed momentarily the magnitude of a result is too large for the calculator to handle The calculator returns 9 99999999999E499 in the current display format See Range of Numbers and Overflow on page This condition sets flag 6 If flag 5 is set overflow has the added effect of halting a running program and leaving the message in the display until you press a key Indicates the top of program memory The memory scheme is circular so PEGM TOP is also the line after the last line in program memory The calculator is running an equation or program other than a SOLVE or JFN routine Attempted to execute SOLVE variable or J FM d variable without a selected program label This can happen the first time that you use SOLVE or J FN after the message MEMORY CLEAR or it can happen if the current label no longer exists A running program attempted to select a program label FH abel while a SOLVE operation was running A running program attempted to solve a program while a SOLVE operation was running A running program attempted to integrate a program while a
60. functions are valid in equations m How equations are checked for syntax errors Operator Precedence Operators in an equation are processed in a certain order that makes the evaluation logical and predictable 6 14 Entering and Evaluating Equations Order Operation Example Parentheses Kel 2 Functions SINCK 12 3 Power Hes 4 Unary Minus G4 A 5 Multiply and Divide ax ASE 6 Add and Subtract P 0 A E 7 Equality B C So for example all operations inside parentheses are performed before operations outside the parentheses Examples Equations Meaning AxB S C ax b3 c CAxXBI S SC ax b 3 c A B C 12 a b c 12 CA B9 0C 12 a b c 12 SCHG T 12 A 63 2 CHG t 12 a 6 2 Entering and Evaluating Equations 6 15 Equation Functions The following table lists the functions that are valid in equations Appendix G Operation Index also gives this information LN LOG EXP ALOG SQ SQRT INV IP FP RND ABS SGN INTG IDIV RMDR SIN COS TAN ASIN ACOS ATAN SINH COSH TANH ASINH ACOSH ATANH DEG RAD HMS gt gt HMS CHG XROOT gt L gt GAL gt MILE gt KM nCr nPr PKG LB SPE F gt CM IN SEED ARG RAND T T x A sx sy ox oy x y Xw x y r m b n xx Ly rx2 Ly2 xxy For convenience prefix type functions which require one or two arguments display a left parenthesis when you enter them The prefix functions that require two arguments are CHG XROOT IDIV
61. i i I i I E 6 More about Integration In many cases you will be familiar enough with the function you want to integrate that you will know whether the function has any quick wiggles relative to the interval of integration If you re not familiar with the function and you suspect that it may cause problems you can quickly plot a few points by evaluating the function using the equation or program you wrote for that purpose If for any reason after obtaining an approximation to an integral you suspect its validity there s a simple procedure to verify it subdivide the interval of integration into two or more adjacent subintervals integrate the function over each subinterval then add the resulting approximations This causes the function to be sampled at a brand new set of sample points thereby more likely revealing any previously hidden spikes If the initial approximation was valid it will equal the sum of the approximations over the subintervals Conditions That Prolong Calculation Time In the preceding example the algorithm gave an incorrect answer because it never detected the spike in the function This happened because the variation in the function was too quick relative to the width of the interval of integration If the width of the interval were smaller you would get the correct answer but it would take a very long time if the interval were still too wide Consider an integral where the interval of integratio
62. in millimeters calculates V in cubic millimeters stores the result in V and displays V Changes cubic millimelers to liters but doesn t change V If an equation is displayed in the equation list you can press to evaluate the equation The entire equation is evaluated regardless of the type of equation The result is returned to the X register 6 12 Entering and Evaluating Equations Example Evaluating an Equation with XEQ Use the results from the previous example to find out how much the volume of the pipe changes if the diameter is changed to 35 5 millimeters Keys Display Description EQN v 6 25xPx0 2xL Displays the desired equation XEQ V Starts evaluating the equation to 19 242 255 8833 find its value Prompts for all variables R S D Keeps the same V prompts for D 35 BOG L Stores new D Prompts for L RS 26 060 R S 553 765 7651 Keeps the same L calculates the value of the equation the imbalance between the left and right sides gow 6 5537 Changes cubic millimeters to liters ENTER The value of the equation is the old volume from V minus the new volume calculated using the new D value so the old volume is smaller by the amount shown Responding to Equation Prompts When you evaluate an equation you re prompted for a value for each variable that s needed The prompt gives the variable name and its current value such as s72 SBE If the unnamed indirect variable I or J is
63. in the equation and variable values The value of the equation is returned to the X register Using ENTER for Evaluation If an equation is displayed in the equation list you can press to evaluate the equation If you re in the process of typing the equation pressing only ends the equation it doesn t evaluate it Entering and Evaluating Equations 6 11 m If the equation is an assignment only the right hand side is evaluated The result is returned to the X register and stored in the left hand variable then the variable is viewed in the display Essentially ENTER finds the value of the left hand variable m If the equation is an equality or expression the entire equation is evaluated just as it is for KEQ The result is returned to the X register Example Evaluating an Equation with ENTER Use the equation from the beginning of this chapter to find the volume of a 35 mm diameter pipe that s 20 meters long Keys Display EQN VEB 25xq_xO 2xL as required ENTER Oo 2 5 3 5 R S L 16 2 LO XL 0 0 0 ENTER Ws 19 242 235 6835 a004 19 2423 ENTER Using XEQ for Evaluation Description Displays the desired equation Starts evaluating the assignment equation so the value will be stored in V Prompts for variables on the right hand side of the equation The current value for Dis 2 5 Stores D prompts for L whose current value is 16 Stores L
64. in the following order Expression in parenthesis Factorial function requires inputting values before you press 1 Functions that require inputting values after pressing the function key for example COS SIN TAN ACOS ASIN ATAN LOG LN x2 1 x Vx TL 1x RND RAND IP FP INTG SGN nPr nCr CHG INT Rmdr ABS ex 10x unit conversion yy and yx ALG Summary C 1 Unary Minus oN Ow F l Doing Two argument Arithmetic in ALG This discussion of arithmetic using ALG replaces the following parts that are affected by ALG mode Two argument arithmetic operations are affected by ALG mode m Simple arithmetic m Power functions V9 W m Percentage calculations or Fea 4CHG m Permutations and Combinations EN LCJ fa oPr Quotient and Remainder of Division EW INTG 2 21HTG EA NTS BY Rnd Simple Arithmetic Here are some examples of simple arithmetic In ALG mode you enter the first number press the operator LE 29 E enter the second number and finally press the key To Calculate Press Display 12 3 01 2 44 3 ENTER lets 13 BEBE 12 3 01 2 E 3 ENTER 12 3 2 BEBE 12x3 1 2 3 ENTER Lexa 36 8666 12 3 1 2 CE 3 ENTER l2 3 4 6668 C 2 ALG Summary Power Functions In ALG mode to calculate a number y raised to a power x key in y x then press ENTER
65. is 1 just press R S 5 To calculate X given Q X skip to step 9 of these instructions 6 To calculate Q X given X KEQ D ENTER 7 After the prompt key in the value of X and press R S The result Q X is displayed 8 To calculate Q X for a new X with the same mean and standard deviation press and go to step 7 9 To calculate X given Q X press CL ENTER 10 After the prompt key in the value of Q X and press R S The result X is displayed 11 To calculate X for a new Q X with the same mean and standard deviation press and go to step 10 Variables Used D Dummy variable of integration M Population mean default value zero Q Probability corresponding to the upper tail area S Population standard deviation default value of 1 T Variable used temporarily to pass the value S x 27 to the inverse program X Input value that defines the left side of the upper tail area Example 1 Your good friend informs you that your blind date has 30 intelligence You interpret this to mean that this person is more intelligent than the local population except for people more than three standard deviations above the mean Suppose that you intuit that the local population contains 10 000 possible blind dates How many people fall into the 30 band Since this problem is stated in terms of standard deviations use the default value of zero for M and 1 for S Keys Display Description In RPN mode M Start
66. it is malfunctioning 1 Do the self test described in the next section If the calculator fails the self test it requires service 2 If the calculator passes the self test you may have made a mistake operating the calculator Reread portions of the manual and check Answers to Common Questions page A 1 3 Contact the Calculator Support Department listed on page A 8 The Self Test If the display can be turned on but the calculator does not seem to be operating properly do the following diagnostic self test 1 2 3 Hold down the key then press at the same time Press any key eight times and watch the various patterns displayed After you ve pressed the key eight times the calculator displays the copyright message 2867 HP DEW CO L P and then the message KED 1 Press the keys in the following sequence Support Batteries and Service A 5 k kK a E R S gt GTO KEQ MODE LJ gt ey gt Li gt o gt GIN cos gt N o gt A ude ENTER gt G2 LE gt LO Le EQN gt 4 gt 6 6 gt x a 1 2 gt gt H amp BH If you press the keys in the proper order and they are functioning properly the calculator displays EBD followed by two digit numbers The calculator is counting the keys using hexadecimal base If you press a key out of order or if a key isn t functioning properly the next keystroke displays a fail message see
67. mode The OCT annunciator is displayed when this mode is active Numbers are displayed in Octal format Binary mode The BIN annunciator is displayed when this mode is active Numbers are displayed in Binary format If a number has more than 12 digits the II and BIL keys allow to view the full number See Windows for Long Binary Numbers later in this chapter placed at the end of a number means that this number is a decimal number placed at the end of a number means that this number is an hexadecimal number To enter an hexadecimal number type the number followed by h Base Conversions and Arithmetic and Logic 11 1 a placed at the end of a number means that this number is an octal number To enter an octal number type the number followed by a b placed at the end of a number means that this number is a binary number To enter a binary number type the number followed by t Examples Converting the Base of a Number The following keystrokes do various base conversions Convert 125 9910 to hexadecimal octal and binary numbers Keys Display Description qoe BASE 70h Converts the decimal number to 2 2HEx base 16 Wea BASE 3 30CT i750 Base 8 Fes BASE 4 4B 1h 11111 1b Base 2 Wes BASE 1 10EC 125 9088 Note When non decimal bases are use only the integer part of numbers are used for display The fractional parts are kept unless operations are p
68. not produce meaningful results since the fractional parts of numbers are truncated Arithmetic in bases 2 8 and 16 is in 2 s complement form and uses integers only m Ifa number has a fractional part only the integer part is used for an arithmetic calculation 11 4 Base Conversions and Arithmetic and Logic m The result of an operation is always an integer any fractional portion is truncated Whereas conversions change only the display of the number but not the actual number in the X register arithmetic does alter the number in the X register If the result of an operation cannot be represented in valid bits the display shows OVERFLOW and then shows the largest positive or negative number possible Example Here are some examples of arithmetic in Hexadecimal Octal and Binary modes 12Fig6 E9A16 Keys Display Description Wea BASE 2 ZHEX Sets base 16 HEX annunciator on 7 2 CZ Fe BASE 6 FC9h Result 6h ENTER O 9 SIN ea BASE L6 6h 77608 43268 E BASE 3 30CT FFiio Sets base 8 OCT annunciator on Converts displayed number to octal 7 7 C6 0 FES BASE 34320 Result CIF ENTER WGA 6 Wea BASE 7 Foa 100g 5g 1 0 0 WE BASE 7 i4o Integer part of result 70 ENTER 5 f BASE W 79 5A016 10011002 Wed BASE 2 2HE 5 5ABh Sets base 16 HEX SIN 0 We
69. of times Tests of Comparison x y x 0 There are 12 comparisons available for programming Pressing or ea displays a menu for one of the two categories of tests m x for tests comparing x and y m x 0 for tests comparing x and 0 Remember that x refers to the number in the X register and y refers to the number in the Y register These do not compare the variables X and Y You can use x y and x 0 to compare two numbers if one of these isn t real number it will return an error message IHVALIO DAT Select the category of comparison then press the menu key for the conditional instruction you want The Test Menus x y x 0 forx y for x40 lt for x lt y lt for x lt 0 lt for x lt y lt for x lt 0 gt for x gt y gt for x gt 0 gt for xzy gt for x20 for x y for x 0 If you execute a conditional test from the keyboard the calculator will display TES or HO For example if x 2 and y 7 test x lt y Programming Techniques 14 7 Keys Display InRPN mode Z ENTER 2 EWG OID lt ENTER YES InALG mode WGI QE CIC lt ENTER YES Example The Normal and Inverse Normal Distributions program in chapter 16 uses the x lt y conditional in routine T Program Lines Description In RPN mode TeeS Calculates the correction for X guess T 16 STO amp Adds the correction to yield a new X guess Tii RBS T i2 6 6661 TELS cv Tests to see if th
70. or maximum see figure a below m The search halts because SOLVE is working on a horizontal asymptote an area where f x is essentially constant for a wide range of x see figure b below m The search is concentrated in a local flat region of the function see figure c below In these cases the values in the stack will be same as the values before executing SOLVE D 8 More about Solving f x f x f x c Case Where No Root Is Found Example A Relative Minimum Calculate the root of this parabolic equation x2 6x 13 0 It has a minimum at x 3 Enter the equation as an expression Keys Display Description EQN Selects Equation mode RCL DO EA FA Enters the equation J L6 J x RCL 3S ENTER HA2 6xX 13 More about Solving D 9 Lal CK EC7F4 LH i18 LC Now solve to find the root Keys Display LO Fea STO LX ENTER 1 0 ig EQN s 2 BxKtLS Fea SOLVE HO ROOT FHO Example An Asymptote Find the root of the equation 10 X Enter the equation as an expression Keys Display EQN ERICI EA RCL CO ENTER 1B IHYCHO Lal CK 6EAB LH 2 Cc 0 0 5 wea SOENEN GI 5 EQN 1B THWCxa Ta SOLVE s 8 1686 RY 6 1666 RY E SHOW a aeeeeeeeee D 10 More about Solving Checksum and length Cancels Equation mode Description Your initial guesses for the root Selects Equation mode displays the e
71. or values from the indirect registers in run or program modes In ALG mode begin entering the vector by pressing WBL RPN mode works similarly to ALG mode except that the key must be pressed first followed by pressing U To enter an element containing the value stored in a lettered variable press and the variable letter To enter an element from a stack register press the key and use the or keys to move the underline symbol so that it is under the stack register to be used and press ENTER To enter an element indirectly indicated by the value in the or J register press and either I or J For example to construct the vector C REGZ J in RPN mode press a LU then RCL O C RY OO ENTER RCL L ENTER 10 8 Vector Arithmetic 11 Base Conversions and Arithmetic and Logic The BASE menu za numbers in decimal b The LOGIC menu 0 BASE allows you to enter numbers and force the display of inary octal and hexadecimal base LOGIC provides access to logic functions BASE Menu Menu label Description DEC HEX OCT BIH Decimal mode This is the normal calculator mode Hexadecimal mode The HEX annunciator is displayed when this mode is active Numbers are displayed in hexadecimal format In RPN mode the keys SIN COS CAN 4 L and U4 act as shortcut to enter the digits A to F In ALG mode press A B C D E or F to enter the digits A to F Octal
72. program or routine m Execute a labeled program Press XEQ or while the label is displayed m Display a labeled program Press Wea while the label is displayed m Delete specific programs Press Ea while the label is displayed m See the checksum associated with a given program segment Press EE SHOW The catalog shows you how many bytes of memory each labeled program segment uses The programs are identified by program label 13 22 Simple Programming LEL C LH 67 where 67 is the number of bytes used by the program Clearing One or More Programs To clear a specific program from memory 1 Press EW MEM 2 2PM ENTER and display using and the label of the program 2 Press Wea CLEAR 3 Press LE to cancel the catalog or to back out To clear all programs from memory Press Wea to display program lines PRGM annunciator on Press Wea CLEAR 3 3FGM to clear program memory 3 The message CLE PGMS Y H prompts you for confirmation Press ENTER 4 Press 0 to cancel program entry Clearing all of memory fa 3RLL also clears all programs The Checksum The checksum is a unique hexadecimal value given to each program label and its associated lines until the next label This number is useful for comparison with a known checksum for an existing program that you have keyed into program memory If the known checksum and the one shown by your calculator are th
73. prompted for variable values you may enter complex numbers The values and format of the result are controlled by the display setting This is the same as calculating in ALG mode Equations that contain complex numbers can be solved and integrated Operations with Complex Numbers 9 7 Complex Number in Program In a program you can type a complex number For example 1i2 30 10 5 8 30 in program is Program lines ALG mode Description Feei LBL F Begins the program FeG2 i72 3916 5036 Faas RTH When you are running a program and are prompted for values by INPUT instructions you can enter complex numbers The values and format of the result are controlled by the display setting The program that contains the complex number can also be solved and integrated 9 8 Operations with Complex Numbers 10 Vector Arithmetic From a mathematical point of view a vector is an array of 2 or more elements arranged into a row or a column Physical vectors that have two or three components and can be used to represent physical quantities such as position velocity acceleration forces moments linear and angular momentum angular velocity and acceleration etc To enter a vector Press Wea 2 Enter the first number for the vector 3 Press L and enter a second number for a 2 D or 3 D vector 4 Pres L and enter a third number for a 3 D vector The HP 35s cannot handle vectors with more than 3 dimensions Vector operat
74. required to set a complex number format 1 Press KEW DISPLAY and then choose either 2 2 FY or CIQ 1484 in RPN mode in ALG mode you may also choose CICD 11x 4 2 Input your desired coordinate value x Li y x LE y Li or r Le a 3 press Example Polar to Rectangular Conversion In the following right triangles find sides x and y in the triangle on the left and hypotenuse r and angle in the triangle on the right x 3 Keys Display Description MODE 1 10E6 Sets Degrees and complex ESN DISPLAY 9 xir coordinate mode gomg 668315 ee08 Convert rOa polar to xiy ENTER rectangular Real Number Functions 4 11 Eu DISPLAY L JO 16 BEBE Bee i8r 8a 3 C_ 4 ENTER 5 666053 1361 Example Conversion with Vectors amp Sets complex coordinate mode Convert xiy rectangular to r0 a polar Engineer P C Bord has determined that in the RC circuit shown 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 and voltage lag equal to the angle in degrees equal to the polar magnitude r When the values are converted to rectangular coordinates the x value yields R in ohms the y value yields Xc in ohms R Xc G Keys Display MODE 1 10E6 Ea DISPLAY 9 Fri MALHA FP 89 36
75. see Entering Equations into the Equation List in chapter 6 and leave Equation mode 2 Enter the limits of integration key in the lower limit and press YJ then key in the upper limit 3 Display the equation Press and if necessary scroll through the equation list press or LY to display the desired equation 4 Select the variable of integration Press EN variable This starts the calculation Operations with Complex Numbers To enter a complex number Form xi 1 Type the real part 2 Press Li 3 Type the imaginary part Form 1 1 Type the real part 2 Press 3 Type the imaginary part 4 Press Li Form Fa 1 Type the value of r 2 Press Wea 8 3 Type the value of 0 C 8 ALG Summary To do an operation with one complex number Pe NS Select the function Enter the complex number z Press to calculate The calculated result will be displayed in Line 2 and the displayed form will be the one that you have set in MODE To do an arithmetic operation with two complex numbers eS Enter the first complex number z7 Select the arithmetic operation Enter the second complex number z2 Press to calculate The calculated result will be displayed in Line 2 and the displayed form will be the one that you have set in MODE Here are some examples with complex numbers Examples Evaluate sin 2 3i Keys Display Description ESN DISPLAY 9 Fr
76. the LL LE key followed by the desired exponent of ten 1 16 Getting Started Other Exponent Functions To calculate an exponent of ten the base 10 antilogarithm use Q07 To calculate the result of any number raised to a power exponentiation use see chapter 4 Understanding Entry Cursor As you key in a number the cursor _ appears and blinks in the display The cursor shows you where the next digit will go it therefore indicates that the number is not complete Keys Display Description waa 123 Entry not terminated the number is not complete If you execute a function to calculate a result the cursor disappears because the number is complete entry has been terminated 11 6285 Entry is terminated Pressing terminates entry To separate two numbers key in the first number press to terminate entry and then key in the second number 1 2 3 ENTER 123 0006 A completed number WA 127 Bees Another completed number If entry is not terminated if the cursor is present backspaces to erase the last digit If entry is terminated no cursor acts like and clears the entire number Try it Range of Numbers and OVERFLOW The smallest number available on the calculator is 9 99999999999 x 10499 while the largest number is 9 99999999999 x 10499 Ifa calculation produces a result that exceeds the largest possible number 9 99999999999 x 10499 or 9 99999999999 x 10499 is returned and the warni
77. the previous display content will be shown Pressing any other key clears the message but the function of the key will not be executed FH ACTIVE EFH JeSOLVE gt ALL VARS 6 BAD GUESS CALCULATING CLE ALL YH CLE EHH YH CLE PGMS YH DIVIDE BY amp DUPLICAT LEL A running program attempted to select a program label FH label while an integration calculation was running A running program attempted to integrate a program J FM d variable while another integration calculation was running A running program attempted to solve a program while an integration calculation was running The catalog of variables EW MEM 1 1 AR indicates no values stored You set a wrong guess number like a complex number or vector when SOLVING equation for a variable The calculator is executing a function that might take a while Allow you to verify clearing everything in memory Allows you to verily clearing the equation you are editing Occurs only in Equation entry mode Allows you to verify clearing all programs in memory Occurs only in Program entry mode Attempted to divide by zero Includes EW CHG if Y register contains zero Attempted to enter a program label that already exists for another program routine Messages F 1 EQH LIST TOP INTEGRATING INTERRUPTED INVALIO DATA INVALIO VAR INVALID x F 2 Messages Indicates the top of equation memory The memory sc
78. the program pointer to PRGM TOP the top of program memory Using RPN ALG and Equations in Programs You can calculate in programs the same ways you calculate on the keyboard 13 4 Simple Programming m Using RPN operations which work with the stack as explained in chapter 2 m Using ALG operations as explained in appendix C m Using equations as explained in chapter 6 The previous example used a series of RPN operations to calculate the area of the circle Instead you could have used an equation in the program An example follows later in this chapter Many programs are a combination of RPN and equations using the strengths of both Strengths of RPN Operations Strengths of Equations and ALG Operations Use less memory Easier to write and read Execute faster Can automatically prompt When a program executes a line containing an equation the equation is evaluated in the same way that evaluates an equation in the equation list For program evaluation in an equation is essentially treated as There s no programmable equivalent to for an assignment equation other than writing the equation as an expression then using STO to store the value in a variable For both types of calculations you can include RPN instructions to control input output and program flow Data Input and Output For programs that need more than one input or return more than one output you can decide how you want the program to
79. the same limits of integration You must re specify the limits of integration 0 1 since they were pushed off the stack by the subsequent division by n Keys Display Description LO ENTER EW Lz 3 1416 Enters the limits of integration lower limit first EQN COS kxSIMCT39 Displays the current equation LaljFA FH a Prompts for the variable of integration o AT Prompts for value of X 2 BEBE BIRS INTEGRATING x 3 Starts integrating and j calculates the result for 6 5176 kd f H t 6 amp 8 2681 The final result for Jo 3 Example Sine Integral Certain problems in communications theory for example pulse transmission through idealized networks require calculating an integral sometimes called the sine integral of the form S t f Fab x Find Si 2 8 4 Integrating Equations Enter the expression that defines the integrand s function sinx x If the calculator attempted to evaluate this function at x O the lower limit of integration an error DIVIDE BY amp would result However the integration algorithm normally does not evaluate functions at either limit of integration unless the endpoints of the interval of integration are extremely close together or the number of sample points is extremely large Keys Display Description EQN 3 3 lin salve Selects Equation mode EGH LIST TOP SIN RCL XQ SINCH Starts the equation DI SINC The closing right parenthesis i
80. the values in the X and Y registers bracket the root These bracketing numbers should be close together m The Z register press again contains D value of the equation at the root For an exact root this should be zero If it is not zero the root given was only an approximation this number should be close to zero If a calculation ends with the HO ROOT FHOD the calculator could not converge on a root You can see the value in the X register the final estimate of the root by pressing or to clear the message The values in the X and Y registers bracket the interval that was last searched to find the root The Z register contains the value of the equation at the final estimate of the root m If the X and Y register values aren t close together or the Z register value isn t close to zero the estimate from the X register probably isn t a root m If the X and Y register values are close together and the Z register value is close to zero the estimate from the X register may be an approximation to a root Interrupting a SOLVE Calculation To halt a calculation press or R S and the message INTERRUPTED will be shown The current best estimate of the root is in the unknown variable use EW to view it without disturbing the stack but solving cannot be resumed Choosing Initial Guesses for SOLVE The two initial guesses come from m The number currently stored in the unknown variable m The number in the X reg
81. to produce different values for the equation Remember that the value for this equation is the difference between the left and right sides of the equation The plot of the value of this equation looks like this 7500 40 H 20 H 4H For More Information This chapter gives you instructions for solving for unknowns or roots over a wide range of applications Appendix D contains more detailed information about how the algorithm for SOLVE works how to interpret results what happens when no solution is found and conditions that can cause incorrect results 7 12 Solving Equations 8 Integrating Equations Many problems in mathematics science and engineering require calculating the definite integral of a function If the function is denoted by f x and the interval of integration is a to b then the integral can be expressed mathematically as l f f x dx f x x a b The quantity can be interpreted geometrically as the area of a region bounded by the graph of the function f x the x axis and the limits x a and x b provided that f x is nonnegative throughout the interval of integration The operation J FN integrates the current equation with respect to a specified variable J FM d_ The function may have more than one variable Integrating Equations 8 1 Integrating Equations FN To integrate an equation 1 If the equation that defines the integrand s function isn t stored in the equatio
82. turns itself off after 10 minutes of inactivity If you see the low power indicator in the display replace the batteries as soon as possible See appendix A for instructions Adjusting Display Contrast Display contrast depends on lighting viewing angle and the contrast setting To increase or decrease the contrast hold down the key and press or B Getting Started 1 1 Highlights of the Keyboard and Display f D Scientific Calculator CA FE ALG RPN EQN GRAD 01234 A Z PRGM HEX OCT BIN HYPA lt 2 Sos ay se The AYG Sat at ht Se TA ye OAc MLO Re ELFIN oe FN ISG RTN xy R S cto xea MODE ee IPRGMAJ DsE_B BL C x20 D G N Yim Xs VIEW INPUT ARG lt a rc f ri fxev fi AN STO Rt Ej Ps F lle G HYP ui INTG xy LOG 10 sin cos tan se y pe ASNH acosi aman lx _K UN uJ lex M SHOW ENG ENG UNDO ENTER f E QO LASTX ABS NI RND O Ul P CLEAR Fd F HMS RAD CHG en
83. value 5613 VIEW Y Displays value S614 ETH Checksum and length 16B3 42 If you write lines S002 CFO and S003 CF1 as shown above the flags O and 1 are cleared so lines S006 and S010 do not take the natural logarithms of the X and Y inputs If you replace lines S002 and S003 by SF O and CF 1 then flag O is set so line S006 takes the natural log of the X input If you replace lines S002 and S003 by CF O and SF1 then flag 1 is set so line S010 takes the natural log of the Y input Programming Techniques 14 13 If you replace lines S002 and S003 by SFO and SF1 then flags O and 1 are set so lines S006 and S010 take the natural logarithms of the X and Y inputs Use above program to see how to use flags Keys Display Description In RPN mode XEQ SJ ENTER x Executes label S prompts for X value value 1 R S Y Stores 1 in X prompts Y value value ARs x Stores 1 in X displays X value 1 8868 after flag test R S Y Displays Y value after flag test i Bba You can try other three cases Remember to press I FLAGS 2 2CF LO and EW FLAGS 2 2CF 1 to clear flag 1 and O after you try them Example Controlling the Fraction Display The followi ng program lets you exercise the calculator s fraction display capability The program prompts for and uses your inputs for a fractional number and a denominat fraction di Messages or the c value The program also contains examples of ho
84. value and halts program execution Pressing to resume program execution or to execute the current program line stores your input in the variable Used only in programs UZ Reciprocal of argument e L6 N 1IF Integer part of x Lal variable Increment Skip if Greater For control number ccccccc fffii stored in variable adds ii increment value to ccccccc counter value and if the result gt fff final value skips the next program line Wea Converts pounds to kilograms Wea KM Converts miles to kilometers Wa Converts gallons to liters Wes LASTX Returns number stored in the LAST X register E 1b Converts kilograms to pounds 4 2 13 13 6 16 4 17 14 18 Operation Index Name Keys and Description Page LBL label LN LOG ey LR MILE Lal Ey ME 2PGM ey w 1MAR MODE NAND NOR NOT OCT a label Labels a program with a single letter for reference by the XEQ GTO or FN operations Used only in programs ra Natural logarithm Returns log e x Common logarithm Returns log 10 x Displays menu for linear regression EY 211 my Returns the slope of the regression line 2 x X yy 2 x x 2 ESN MILE Converts kilometers to miles Displays the amount of available memory and the catalog menu Begins catalog of programs Beg
85. value of data pair Enters y value of data pair Enters x value of data pair Enters y value of data pair Enters x value of data pair Enters y value of data pair Enters x value of data pair Enters y value of data pair Calculates the correlation coefficient R S B Calculates regression coefficient B 33 5271 R S M Calculates regression coefficient M 1 7661 R S x Prompts for hypothetical x value r BEEBE WARS YP Stores 37 in X and calculates y 25 6526 1 0 1 R S a Stores 101 in Y and calculates x 38 3336 Example 2 Repeat example 1 using the same data for logarithmic exponential and power curve fits The table below gives you the starting execution label and the results the correlation and regression coefficients and 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 CLJCENTER KEQ CE ENTER KEQ CP ENTER R 0 9965 0 9945 0 9959 B 139 0088 51 1312 8 9730 M 65 8446 0 0177 0 6640 Y y when X 37 98 7508 98 5870 98 6845 X x when Y 101 38 2857 38 3628 38 3151 Normal and Inverse Normal Distributions Normal distribution is frequently used to model the behavior of random variation about a mean This model assumes that the sample distribution is symmetric about the mean M with a standard deviation S a
86. with Complex Numbers 9 1 The Complex Stack A complex number occupies part 1 and part 2 of a stack level In RPN mode the complex number occupying part 1 and part 2 of the X register is displayed in line 2 while the complex number occupying part 1 and part 2 of the Y register is displayed in line 1 T Z Y Display in line 1 X Display in line 2 Complex Stack Complex Result Z Complex Operations Use the complex operations as you do real operations in ALG and RPN mode To do an operation with one complex number 1 Enter the complex number z as described before 2 Select the complex function 9 2 Operations with Complex Numbers Functions for One Complex Number z To Calculate Press Change sign z CZ Inverse 1 z ix Natural log In z We3 LN Natural antilog eZ Wea e Sin z SIN Cos z Cos Tan z TAN Absolute value ABS z Wes ABS Argument value ARG z ESN ARG To do an arithmetic operation with two complex numbers 1 Enter the first complex number z7 as described before 2 Enter the second complex number z2 as described before 3 Select the arithmetic operation Arithmetic With Two Complex Numbers z 7 and z2 To Calculate Press Addition z z2 Subtraction z z2 Multiplication z x z2 Division z z2 BHU Power function Z 72 Operations with Complex Numbers Examples Here are some examples of tr
87. x I x key in x 1 and press w LJ The x function calculates T x 1 The value for x cannot be a negative integer Probability Combinations To calculate the number of possible sets of n items taken r at a time enter n first E nCr then r nonnegative integers only No item occurs more than once in a set and different orders of the same r items are not counted separately Permutations To calculate the number of possible arrangements of n items taken r at a time enter n first E Pe then r nonnegative integers only No item occurs more than once in an arrangement and different orders of the same r items are counted separately Seed To store the number in x as a new seed for the random number generator press SEED Random number generator To generate a random number in the range O lt x lt 1 press Ea RAND The number is part of a uniformly distributed pseudo random number sequence It passes the spectral test of D Knuth The Art of Computer Programming vol 2 Seminumerical Algorithms London Addison Wesley 1981 Real Number Functions 4 15 The RANDOM function uses a seed to generate a random number Each random number generated becomes the seed for the next random number Therefore a sequence of random numbers can be repeated by starting with the same seed You can store a new seed with the SEED function If memory is cleared the seed is reset to zero A seed of zero will result in the
88. xv2 YW ZV i ZU XW j XV YU k where vy Xi Yj Zk and v2 Ui Vj Wk Program Lines Description In RPN mode Reei LBL R Defines the beginning of the rectangular input display routine R G2 INPUT amp Displays or accepts input of X REGS INPUT Y Displays or accepts input of Y R664 IMPUT Z Displays or accepts input of Z Rees GTO Reel Goes to ROO to input vectors Checksum and length D82E 15 E iLBLE Defines the beginning of the vector enter routine EBZ RCL Copies values in X Y and Z to U V and W respectively E e s STOU Ee e 4 RCL Y EGS STO WV Ee 6 RCL Z Eer STOW Fees GTO Reel Goes to ROO to input vectors Checksum and length B6AF 24 Miscellaneous Programs and Equations 17 11 Program Lines Description In RPN mode Ceei LEL C Defines the beginning of the cross product routine Cee2 REL Y CBE3 RCL H C664 REL Z CEES RCL W Cea Calculates YW ZV which is the X component Cher STOR C668 RCL Z C669 RCL U CBiB RCL 8 CB6ii RCL H Cale Calculates ZU WX which is the Y component CBis STOE CBi4d RCL 8 CEIS RCL W CBi RCL Y CBir RCL U CBeis C619 STO Z Stores XV YU which is the Z component CB2e RCL A C621 STO Stores X component CB2e2 RCL C623 STO Y Stores Y component C624 GTO Reel Goes to ROO1 to input vectors Checksum and length 838D 72 Example Calculate the cross product of two vectors v1 2i 5j 4k and v2 i 2j 3k 17 12 Miscellaneous Progr
89. you can separate the routine in various labels If you plan to have more than one program in the calculator memory it is better to have routines part of the main program label starting at a specific line number a A subroutine can itself call other subroutines The flow diagrams in this chapter use this notation REES GTO BEBEI O Program execution branches from this line to the line number marked from 1 Basi LBL E e Program execution branches from a line number marked gt to 1 to this line The example below show you to call a subroutine to change the sign of the number you input Subroutine E that is called from routine D by line D663 KEG EBBI changes sign of the number Subroutine E ends with a RTN instruction that sends program execution back to routine D to store and display the result at line DOO4 See the flow diagrams below DEBI LELO Starts here DBGZ INPUT x 0863 EQ EBBI gt 00 Calls subroutine E 0864 STOH Returns here DEBS VIEH DEBE RTH EI LELE 0 Starts subroutine E ge 7 Change sign of the number EGZ RTH Returns to routine D Nested Subroutines A subroutine can call another subroutine and that subroutine can call yet another subroutine This nesting of subroutines the calling of a subroutine within another subroutine is limited to a stack of subroutines 20 levels deep not counting the topmost program level The operation of nested subroutines is as s
90. 0000000000 4 i72 6 18 5 9 60000000000 9 365 34 12 2 83333333333 2 576 v 15 8192 0 00183105469 7 3823 A 12345678 12345 3 12349793 0000 12349793 16 3 16384 16 0001831055 16 174095 Accuracy Indicators The accuracy of a displayed fraction is indicated by the 4 and annunciators at the right of the display The calculator compares the value of the fractional part of the internal 12 digit number with the value of the displayed fraction If no indicator is lit the fractional part of the internal 12 digit value exactly matches the value of the displayed fraction If v is lit the fractional part of the internal 12 digit value is slightly less than the displayed fraction the exact numerator is no more than 0 5 below the displayed numerator If amp is lit the fractional part of the internal 12 digit value is slightly greater than the displayed fraction the exact numerator is no more than 0 5 above the displayed numerator This diagram shows how the displayed fraction relates to nearby values 4 means the exact numerator is a little above the displayed numerator and v means the exact numerator is a little below O77 16 07 16 407 16 a es 6 6 5 7 8 he 16 he 16 he 0 40625 0 43750 0 46875 5 3 Fractions This is especially important if you change the rules about how fractions are displayed See Changing the Fraction Display later For example if you force all fractions to have 5 as the denomina
91. 1 3 battery 1 1 A 3 flags 14 12 list of 1 13 low power 1 1 A 3 shift keys 1 2 answers to questions A 1 arithmetic binary 11 4 general procedure 1 18 hexadecimal 11 4 intermediate results 2 12 long calculations 2 12 octal 11 4 order of calculation 2 14 stack operation 2 5 9 2 assignment equations 6 9 6 11 6 12 7 1 backspace key canceling VIEW 3 4 clearing messages 1 4 clearing X register 2 3 2 7 deleting program lines 13 20 equation entry 1 4 leaving menus 1 4 1 8 operation 1 4 balance finance 17 1 base affects display 11 6 arithmetic 11 4 converting 11 2 default B 4 programs 11 8 13 25 setting 11 1 base mode default B 4 equations 6 5 6 11 13 25 programming 13 25 setting 13 25 batteries 1 1 A 3 Bessel function 8 3 best fit regression 12 7 16 1 C 13 BIN annunciator 11 1 Index 1 binary numbers See numbers arithmetic 11 4 converting to 11 2 range of 11 7 scrolling 11 8 typing 11 1 viewing all digits 11 8 borrower finance 17 1 branching 14 2 14 16 15 7 C CHG arguments 4 6 C 3 adjusting contrast 1 1 canceling prompts 1 4 canceling VIEW 3 4 clearing messages 1 4 clearing X register 2 3 2 7 leaving catalogs 1 4 leaving menus 1 4 1 8 on and off 1 1 operation 1 4 c value 5 4 leaving Equation mode 6 3 leaving Equation mode 6 4 canceling prompts 6 14 stopping SOLVE 7 8 stopping integration 8 2 leaving Program mode 13 7 leaving Program mode 13 7 canceling prompts 1
92. 10 Programming Techniques Flag 10 controls program execution of equations When flag 10 is clear the default state equations in running programs are evaluated and the result put on the stack When flag 10 is set equations in running programs are displayed as messages causing them to behave like a VIEW statement 1 Program execution halts 2 The program pointer moves to the next program line 3 The equation is displayed without affecting the stack You can clear the display by pressing or LC Pressing any other key executes that key s function 4 If the next program line is a PSE instruction execution continues after a 1 second pause The status of flag 10 is controlled only by execution of the SF and CF operations from the keyboard or by SF and CF statements in programs Flag 11 controls prompting when executing equations in a program it doesn t affect automatic prompting during keyboard execution When flag 11 is clear the default state evaluation SOLVE and f FN of equations in programs proceed without interruption The current value of each variable in the equation is automatically recalled each time the variable is encountered INPUT prompting is not affected When flag 11 is set each variable is prompted for when it is first encountered in the equation A prompt for a variable occurs only once regardless of the number of times the variable appears in the equation When solving no prompt occurs for the unk
93. 10 atm amp 8616 Example Program Using Equation Write a program that uses an equation to solve the Ideal Gas Law Keys Display Description In RPN mode w PROM Selects Program entry mode GTO CJL PEGM TOP Moves program pointer to top of the list of programs 3 80H Heei LEL H Labels the program FLAGS 01 Enables equation prompting sF 00 HGZ SF 11 EQN Evaluates the equation clearing RCL P x flag 11 Checksum and length RCO EM ag EDC8 9 RCN a Reo RI x Reo ENTER HEEF PxV HxRXT EN RIN HG4 ETH Ends the program Ka B BELG Cancels Program entry mode Checksum and length of program DF52 21 Now calculate the change in pressure of the carbon dioxide if its temperature drops by 10 C from the previous example 15 4 Solving and Integrating Programs Keys In RPN mode STO L SOLVE P of R S ui E re 5 N N ERD a R S RODA Display B BEIB B BEIB Wy 2 BEEBE H 8 6658 R B 6821 T 297 1866 T 257 1866 SOLVING P B 8589 B 8621 Description Stores previous pressure Selects program H Selects variable P prompts for V Retains 2 in V prompts for N Retains 005 in N prompts for R Retains 0821 in R prompts for T Calculates new T Stores 287 1 in T solves for new P Calculates pressure change of the gas when temperature drops from 297 1 K to 287 1 K neg
94. 17 7 range of 1 17 11 7 real 4 1 recalling 3 2 reusing 2 6 2 10 rounding 4 18 showing all digits 1 25 storing 3 2 truncating 11 6 typing 1 15 1 16 11 1 O 1 1 OCT annunciator 11 1 11 4 octal numbers See numbers arithmetic 11 4 converting to 11 2 range of 11 7 typing 11 1 one variable statistics 12 2 overflow flags 14 9 F 4 result of calculation 1 17 11 5 setting response 14 9 F 4 testing occurrence 14 9 P n A 2 parentheses in arithmetic 2 12 in equations 6 5 6 6 6 15 pause See PSE payment finance 17 1 percentage functions 4 6 periods in numbers 1 23 A 1 permutations 4 15 Physics constants 4 8 polar to rectangular coordinate conver sion 4 10 9 5 poles of functions D 6 polynomials 13 26 population standard deviations 12 7 power annunciator 1 1 A 3 power curve fitting 16 1 power functions 1 17 4 2 9 3 precedence equation operators 6 14 precision numbers 1 25 D 13 present value See financial calculations PRGM TOP 13 4 13 7 13 21 F 4 prime number generator 17 7 probability functions 4 15 normal distribution 16 11 program catalog 1 28 13 22 program labels branching to 14 2 14 4 14 16 checksums 13 23 clearing 13 6 duplicate 13 6 entering 13 4 13 6 executing 13 10 indirect addressing 14 20 14 21 14 23 moving to 13 22 purpose 13 4 typing name 1 3 viewing 13 22 program lines See programs program names See program labels program pointer 13 6 13 11 13 19 13 21 B 4 P
95. 2 13 Part 2 Programming 13 Simple Programming Part 1 of this manual introduced you to functions and operations that you can use manually that is by pressing a key for each individual operation And you saw how you can use equations to repeat calculations without doing all of the keystrokes each time In part 2 you ll learn how you can use programs for repetitive calculations calculations that may involve more input or output control or more intricate logic A program lets you repeat operations and calculations in the precise manner you want In this chapter you will learn how to program a series of operations In the next chapter Programming Techniques you will learn about subroutines and conditional instructions Example A Simple Program To find the area of a circle with a radius of 5 you would use the formula A z r2 and press RPN mode 5 x2 EN ALG mode 5 WW x EW Z ENTER to get the result for this circle 78 5398 But what if you wanted to find the area of many different circles Rather than repeat the given keystrokes each time varying only the 5 for the different radii you can put the repeatable keystrokes into a program Simple Programming 13 1 RPN mode ALG mode BEB1 x2 BEL SOCxIa xz BEES m BEES x This very simple program assumes that the value for the radius is in the X register the display when the program starts to run It computes the area and leaves it in the
96. 2 5 7 0 0 0 ENTER 4 1 886 8666 Four data pairs LG 4 68688 accumulated aAA xy x 4 ZH Calculates the mean price i4 W o 4 weighted for the quantity purchased Sample Standard Deviation Sample standard deviation is a measure of how dispersed the data values are about the mean sample standard deviation assumes the data is a sampling of a larger complete set of data and is calculated using n 1 as a divisor m Press P So for the standard deviation of x values m Press Wea S 0 gt for the standard deviation of y values The o and o items in this menu are described in the next section Population Standard Deviation Example Sample Standard Deviation Using the same process times as in the above mean example May Kitt now wants to determine the standard deviation time sx of the process 15 5 9 25 10 0 12 5 12 0 8 5 Calculate the standard deviation of the times Treat all the data as x values Keys Display Description Wes CLEAR 4 42 Clears the statistics registers LOL E GI 1 4866 Enters the first time MILI Enters the remaining data six wH data points entered amann 2000 5 SxS X Calculates the standard deviation oy time 2 0888 12 6 Statistical Operations Population Standard Deviation Population standard deviation is a measure of how dispersed the data values are about the mea
97. 3 15 interrupting programs 13 19 stopping SOLVE 15 1 stopping integration 15 8 c value B 4 c value B 6 calculator adjusting contrast 1 1 default settings B 4 environmental limits A 2 questions about A 1 resetting A 4 B 2 self test A 5 shorting contacts A 5 testing operation A 4 A 5 turning on and off 1 1 Index 2 cash flows 17 1 catalogs leaving 1 4 program 1 28 13 22 using 1 28 variable 1 28 3 4 chain calculations 2 12 change percentage functions 4 6 changing sign of numbers 1 15 9 3 checksums equations 6 19 13 7 13 24 programs 13 22 CLEAR menu 1 5 clearing equations 6 9 general information 1 4 memory 1 29 A 1 numbers 1 17 programs 1 29 13 23 statistics registers 12 2 variables 1 28 X register 2 3 2 7 clearing memory A 4 B 3 combinations 4 15 commas in numbers 1 23 A 1 comparison tests 14 7 complex numbers argument value 4 17 coordinate systems 9 5 entering 9 1 on stack 9 2 operations 9 2 viewing 9 2 conditional tests 14 6 14 7 14 9 14 12 14 17 constant filling stack 2 7 Continuous Memory 1 1 contrast adjustment 1 1 conversion functions 4 10 conversions angle format 4 13 angle units 4 13 coordinates 4 10 length units 4 14 mass units 4 14 number bases 10 1 11 1 temperature units 4 14 time format 4 13 volume units 4 14 coordinates converting 4 10 correlation coefficient 12 8 16 1 cosine trig 4 4 9 3 C 6 curve fitting 12 8 16 1 D Decimal mode See base mode deci
98. 33 GEEE Calculates denominator ES 33 6686 Puts 4 before 33 in preparation for division a 6 1212 Calculates 4 33 the answer Problems that have multiple parentheses can be solved in the same manner using the automatic storage of intermediate results For example to solve 3 4 x 5 6 on paper you would first calculate the quantity 3 4 Then you would calculate 5 6 Finally you would multiply the two intermediate results to get the answer Work through the problem the same way with the HP 35s except that you don t have to write down intermediate answers the calculator remembers them for you Keys Display Description 3 ENTER 4 4 7 BBE First adds 3 4 5 ENTER 6 4 11 6686 Then adds 5 6 RPN The Automatic Memory Stack 2 13 fr BEBE Then multiplies the intermediate answers together for the final answer Exercises Calculate 16 3805x5 181 005 81 0000 Solution WWW WMO WEEE WWIMWE Calculate J2 3 x 4 5 J 6 7 x 8 9 21 5743 Solution 2 ENTER 3 ES 4 ENTER BG EK A A ENTER 7 ES 08 ENTER MIKA Calculate 10 5 17 12 x 4 0 2500 Solution LOZ JEENTER O20 4 OI ENER SE Ey a or C1 LOJ ENTER 5 ZY ENTER HEA Order of Calculation We recommend solving chain calculations by working from the innermost parentheses outward However you can also ch
99. 5 WA A ENTER 62 54014 46 2772 4 12 Real Number Functions 77 8 ohms Description Sets Degrees and complex coordinate mode Enters 6 degrees of voltage lag Enters r ohms of total impedance Calculates x ohms resistance R Calculates y ohms reactance XC Time Conversions The HP 35s can convert between decimal and hexagesimal formats for numbers This is especially useful for time and angles measured in degrees For example in decimal format an angle measured in degrees is expressed as D ddd while in hexagesimal the same angle is represented as D MMSSss where D is the integer pat of the degree measure ddd is the fractional part of the degree measure MM is the integer number of minutes SS is the integer part of the number of seconds and ss is the fractional part of the number of seconds To convert between decimal format and hours minutes and seconds 1 Enter the number you wish to convert 2 Press EE EHMS to convert to hours degrees minutes and seconds or press Wes HMMS to convert back to decimal format Example Converting Time Formats How many minutes and seconds are there in 1 7 of an hour Use FIX 6 display format Keys Display Description ES DISPLAY 7 iF 1 Sets FIX 6 display format 6 EAEE EREA 8 668088 1 7 hour as a decimal fraction B irr a 8 BEEBE Equals 8 minutes and 34 29 B 683429 seconds Kav DISPLAY iF I 8 668088 Restores FIX 4
100. C Integer 1 Integer 2 Ey INTG 3 Rima Integer 1 Integer 2 ENTER Example To display the quotient and remainder produced by 58 9 Keys Display Description EUNT 2 2 INTE IDIVe 58 95 Displays the quotient WALLA ENTER 6 8688 ES UNTG 3 R mar RMOR 58 9 Displays the remainder 5 8 2 J 2 ENTER 4 88868 Parentheses Calculations Use parentheses when you want to postpone calculating an intermediate result until you entered more numbers For example suppose you want to calculate 30 85 12 C 4 ALG Summary If you were to key in L3JLOVEI SI SIE LZ LY the calculator would calculate the result 107 6471 However that s not what you want To delay the division until you ve subtracted 12 from 85 use parentheses Keys Display Description DOAMBEIE 2885 2 No calculation is done MCI 3B 85 12 _ Calculates 85 12 cI 3B 85 129xo Calculates 30 73 ENTER 3G 85 129 9 Calculates 30 85 12 3 6986 x9 You can omit the multiplication sign x before a left parenthesis Implied multiplication is not available in Equation mode For example the expression 2 x 5 4 can be entered as 2JLOJ SJE 4 without the key inserted between 2 and the left parenthesis Exponential and Logarithmic Functions To Calculate Press Display Natural logarithm base e Wea LNJLIJ ENTER JLHe do B
101. CL B Gee4 RCL M Calculates X Y B M GEES RTH Returns to the calling routine Checksum and length 9COF 15 B Gi LEL E This subroutine calculates y for the logarithmic model BEG2 RCL Bees LH Bee4 RCLx M BEES RCL B Calculates y MInX B BEGE RTH Returns to the calling routine Statistics Programs 16 5 Program Lines Description In RPN mode Checksum and length 889C 18 Hegi LEL H This subroutine calculates x for the logarithmic model Hee RCL Y HBBS RCL E Hee4 RCL M Hees es Calculates x e Y B M Hees RTH Returns to the calling routine Checksum and length ODBE 18 Ceei LEL C This subroutine calculates y for the exponential model Ceee RCL M CBGS REL Cee4 es Cee5 RCL B Calculates y BeMX C666 GTO MEGS Branches to M005 Checksum and length 9327 18 IGBI LBL I This subroutine calculates x for the exponential model 662 RCL Y I6 3 RCL B 6e 4 LH Tees RCL M Calculates x In Y B M 1 66 GTO HEES Goes to NO05 Checksum and length 7219 18 0661 LBL O This subroutine calculates y for the power model De62 RCL D663 RCL M D664 ye Dees RCL E Calculates Y B XM D666 GTO KEBS Goes to K005 Checksum and length 11B3 18 T6 1 LBL J This subroutine calculates x for the power model 16 6 Statistics Programs Program Lines Description In RPN mode Ieee RCL Y IG 63 RCL E Ie64 RCL M TEGS ix TEBE vs Calculates X Y B 1 M IG67GCTO OBBS Goes to O005 Che
102. CT gt L G6 RTH Checksum and length D45B 18 Feei LBL F Feie RTH Integrating a Program Description Setup for X Index for X Branches to main routine Setup for Y Index for Y Branches to main routine Main routine Stores index in I Defines program to solve Solves for appropriate variable Displays solution Ends program Calculates f x y Include INPUT or equation prompting as required In chapter 8 you saw how you can enter an equation or expression it s added to the list of equations and then integrate it with respect to any variable You can also enter a program that calculates a function and then integrate it with respect to any variable This is especially useful if the function you re integrating changes for certain conditions or if it requires repeated calculations To integrate a programmed function 1 Enter a program that defines the integrand s function See To write a program for FN below 15 7 Solving and Integrating Programs 2 Select the program that defines the function to integrate press EW label You can skip this step if you re reintegrating the same program 3 Enter the limits of integration key in the lower limit and press ENTER then key in the upper limit 4 Select the variable of integration and start the calculation press EW variable Notice that FN is required if you re integrating a programmed function but not if you re integrating an eq
103. DGS n If flag n n O through 11 is set executes the next program line if flag n is clear skips the next program line Converts liters to gallons MODE GRD Sets Grads angular mode Sets program pointer to line nnn of program label Sets program pointer to PRGM TOP a BASE B 6h Indicates a hexadecimal number A GASE Z 2HE Selects Hexadecimal base 16 mode Displays the HYP_ prefix for hyperbolic functions a Hours to hours minutes seconds Converts x from a decimal fraction to hours minutes seconds format HMs Hours minutes seconds to hours Converts x from hours minutes seconds format to a decimal fraction Used for entering complex numbers RCL LW ya STO W Value of variable whose letter corresponds to the numeric value stored in variable I J Lal Converts centimeters to inches EW INTG 2 21NT Produces the quotient of a division operation involving two integers 14 12 G 8 Operation Index Name Keys and Description Page INT INTG INPUT variable INV IP ISG variable gt KG gt KM gt L LASTx gt LB EINT 2 21NT Produces the quotient of a division operation involving two integers SW INTG 4 42 HTG Obtains the greatest integer equal to or less than given number e variable Recalls the variable to the X register displays the variable s name and
104. Description In RPN mode Wes PRGM Activates Program entry mode PRGM on FES CLEAR 3 Clears all of program ZF G 7 FRGM TOF memory ENTER Wes LBL AGGI LEL A Labels this program routine A for area Fes 2 Reee x2 Enters the three program EN z AGES 7 lines E3 AGES x E58 RIN REGS ETH Ends the program EN MEM 2 2PM LELA Displays label A and the LH 15 length of the program in bytes Ey SHOW CK DAF1 Checksum and length of LH 15 program 13 8 Simple Programming Cancels program entry PRGM annunciator off A different checksum means the program was not entered exactly as given here Example Entering a Program with an Equation The following program calculates the area of a circle using an equation rather than using RPN operations like the previous program Keys Display Description In RPN mode Wes PRGM GTO LJ PREM TOR Activates Program entry E mode sets pointer to top of memory Ws 82 EE EGI LEL E Labels this program routine E for equation Wes STO R Eee STOR Stores radius in variable R EQN EN Selects Equation entry mode enters the equation x RCL LR a E returns to Program entry aa pains be ER SHOW CK 7E5B LH 5 ESN RIN Eae4 RTH Ends the program EN EM 2 2PM LELE Displays label E and the LH 17 length of the program in bytes Est SHOW CK 2873 Checksum and length of LH i7 program KAKA
105. Display cccceceeseeeeeeeees 1 2 Shifed Keys ereenn e a E N AE 1 2 Alpha hays 2 cist oe A aaa es 1 3 Cursor KEYS savnacasnacsbnsnintnentcadnsethiananbaentiareseeesd ances esenandeebnseies 1 3 Backspacing and CleaninG wiissccsassecsvars eandvamtaasainensraanneuannnants 1 4 Using Men s semino alsa mancbauaseanani ayy 1 6 Exiting MONUS dscsavdedecee ded sanuscnaeenndewernteevineer igeeudesdydaagedengaase 1 8 RPN and ALG Modes tissiceiidcnipioes patie canatinp wien a e 1 9 Undo ey ca itive vse con censanaenr erm aes nantes 1 11 The Display and Annunciators cecceeseeeeeessreeeeeieeeeteeeeeees 1 12 Keying in Numbers 55 55 9p esanenaracencdoane aerumaieasam naan 1 15 Making Numbers Negative csessessseseerecnenntennnnnes 1 15 Exponents of Tes csicavsieentieanrsadnnadatneeaenmarecocenrepunierynts 1 15 Understanding Entry Cursor ccccceeeeeeceeeeeeeesteeeeeeeeeaes 1 17 Range of Numbers and OVERFLOW ccc cccceesteeeeeteeees 1 17 Performing Arithmetic Calculations cesssceeeseeeereeenreeeereees 1 18 Single Argument or Unary Operations cccceeseeeeenteeees 1 18 Two Argument or Binary Operations eeeeeeeeeeeeereeeeeee 1 19 Controlling the Display Formot 05 lt cadsureiaiacdenmasrarseanoraeaens 1 21 Periods and Commas in Numbers 2 ccccccccsesseeeseeeeees 1 23 Contents 1 Complex number display format F cece 1 24 SHOWing Full 1 2 Digit Prec
106. EAR 4 42 12 1 Clears statistics registers CLVARS Wea CLEAR 2 VARS 3 6 Clears all variables to zero Clx Fea CER 1 2 3 Clears x the X register to zero 2 7 13 7 Operation Index G 5 Name Keys and Description Page CLVARx B CLEAR 6 6CLVARx 1 4 Clears indirect variables whose address is greater than the x address fo zero CLSTK B CLEAR 5 5STK 2 7 Clears all stack levels to zero gt CM Wea gt m Converts inches to 4 14 centimeters nCr EW CC Combinations of n items 4 15 taken r at a time Returns n r n r COS COS Cosine 4 3 Returns cos x COSH EW HYP COS Hyperbolic 4 6 cosine Returns cosh x E CONST Accesses the 41 physics constants 4 8 d Wea BAE G 5 11 1 indicates a decimal number DEC Wea BASE 1 1 DEC 11 1 Selects Decimal mode DEG MODE 1 1DE6 4 4 Selects Degrees angular mode DEG Wea DEG Radians to degrees 4 13 Returns 360 2r x LDN Displays menu to set the display 1 21 format radix or thousand separator and display format of complex number DSE variable rs variable 14 18 Decrement Skip if Equal or less For control number ccccccc fffii stored in a variable subtracts ii increment value from cccecccc counter value and if the result lt fff final value skips the next program line Begins entry of exponents and adds 1 15 E to the number being entered Indicates
107. FOR NEXT loop with a negative increment After pressing a shifted key for ISG or DSE E amp R USG or W DSE you will be prompted for a variable that will contain the loop control number described below The Loop Control Number The specified variable should contain a loop control number ccccccc ffii where ccccccc is the current counter value 1 to 12 digits This value changes with loop execution m fffis the final counter value must be three digits This value does not change as the loop runs An unspecified value for fff is assumed to be 000 14 18 Programming Techniques jiis the interval for incrementing and decrementing must be two digits or unspecified This value does not change An unspecified value for ii is assumed to be 01 increment decrement by 1 Given the loop control number ccccccc fifii DSE decrements ccccccc to cccecce ii compares the new ccccccc with fff and makes program execution skip the next program line if this ccccccc lt fff Given the loop control number ccccccc fffii ISG increments ccccccc to ceccccc ii compares the new ccccccc with fff and makes program execution skip the next program line if this ccccccc gt fff Q gt Heel LBL WH If current value lt final value exit If current value gt final value continue loop Wee OSE A gt Q wWelecToweal i WG11xEQxee1 e0 CP O gt Weel LBL W If current value gt final value exit loop
108. G mode Wea x SAC Enter the square operation WAA SACS 4 Insert the number between the parentheses ENTER BOC3 4 Press the Enter key to see the result 11 56 In the example the square operator is shown on the key as but displays as SQ There are several single argument operators that display differently in ALG mode than they appear on the keyboard and differently than they appear in RPN mode as well These operations are listed in the table below Key In RPN RPN Program In ALG Equation ALG Program Ea x SQ w vx SQRT eg e EXP 107 10 ALOG Ux 1 x INV Two Argument or Binary Operations Two argument operations such as LE G LA and nr are also entered differently depending on the mode though the differences are similar to the case for single argument operators In RPN mode the first number is entered then the second number is placed in the x register and the two argument operation is invoked In ALG mode there are two cases one using traditional infix notation and another taking a more function oriented approach The following examples illustrate the differences Getting Started 1 19 Example Calculate 2 3 and 6Cy first in RPN mode and then in ALG mode Keys Display Description MODE 5 SRPH Switch to RPN mode if necessary 2 ENTER 2 Enter 2 then place 3 in the x register 3 Note the flashing cursor after the 3 7 don t press Enter a Pre
109. GN Eq SHOW SIN SINH E SOLVE variable E SPACE SQ SQRT STO variable STO variable STO variable STO x variable STO variable OAN ESCI n Selects Scientific display with n decimal places n O through 11 E SEED Restarts the random number sequence with the seed x ER FLAGS 1 1 SF n Sets flag n n O through 11 ES NTG 1 1 SGN Indicates the sign of x Shows the full mantissa all 12 digits of x or the number in the current program line displays hex checksum and decimal byte length for equations and programs SIN Sine Returns sin x Hyperbolic sine Returns sinh x WE3 SOLVE variable Solves the displayed equation or the program selected by FN using initial estimates in variable and x Inserts a blank space character during equation entry Wed x Square of argument WX Square root of x Wed STO variable tore Copies x into variable F STO variable tores variable x into variable Wed STO variable tores variable x into variable Wea STO Lx variable tores variable x x into variable Wed STO LE variable Stores variable x into variable 3 D n a n a n a n a 1 22 14 14 6 16 6 16 3 6 3 6 3 6 3 6 Operation Index G 13 Name Keys and Descript
110. HP 35s scientific calculator user s guide ra Edition 1 HP part number F2215AA 90001 Notice REGISTER YOUR PRODUCT AT www register hp com THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE PROVIDED AS IS AND ARE SUBJECT TO CHANGE WITHOUT NOTICE HEWLETT PACKARD COMPANY MAKES NO WARRANTY OF ANY KIND WITH REGARD TO THIS MANUAL INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF MERCHANTABILITY NON INFRINGEMENT AND FITNESS FOR A PARTICULAR PURPOSE HEWLETT PACKARD CO SHALL NOT BE LIABLE FOR ANY ERRORS OR FOR INCIDENTAL OR CONSEQUENTIAL DAMAGES IN CONNECTION WITH THE FURNISHING PERFORMANCE OR USE OF THIS MANUAL OR THE EXAMPLES CONTAINED HEREIN 1988 1990 1991 2003 2007 Hewlett Packard Development Company L P Reproduction adaptation or translation of this manual is prohibited without prior written permission of Hewlett Packard Company except as allowed under the copyright laws Hewlett Packard Company 16399 West Bernardo Drive MS 8 600 San Diego CA 92127 1899 USA Printing History Edition 1 February 2007 Contents Part 1 Basic Operation l Getting SIGHED sess saissseveriessexesswstesniesersenepetiaiaiensaiiviass 1 1 Important Preliminaries siehscsevenseseviavanianonivsvaiheileebuirdiemnneniacnenbbioanate 1 1 Turning the Calculator On and Off ccccceeeseeeeeeteeeeeeteeees 1 1 Adjusting Display Contrashiciisossaiiiisaninttesvsdasnecdialaageanieiass 1 1 Highlights of the Keyboard and
111. I vanoa Ci 2IsC3 4 Executes for dot product 4 and enters the second vector ENTER 11 6686 The dot product of two vectors is 11 Calculate the dot product of two vectors 9 5 and 2 2 Keys Display Description MODE 5 SRPH Switches to RPN mode FSVu ENC 6 C2 4666 5 88661 Enters the first vector 9 5 ENTER Co 4468 5 666 Fey 2G EF 8668 5 88661 and enters the second vector 2 2 2 2 10 4 Vector Arithmetic 28 6888 Presses X for dot product and the dot product of two vectors is 28 Angle between vectors The angle between two vectors A and B can be found as 0 ACOS A B A B Find the angle between two vectors A 1 0 B 0 1 Keys Display Description MODE 4 4ALG Switches to ALG mode MODE 1 iDEG Sets Degrees mode Fes ACOS ACOS lt s Arc cosine function fey jlo Acos lt ci ed Enters vector A 1 0 RI UNOL ACOS C1 BI CE 142 Enters vector B 0 1 for dot product of A and B ABS We3 C17 11 ABS 01 813m Finds the magnitude of LIMO vector A 1 0 ABS Fes C11 i 60 RBS CE 112m Finds the magnitude of CIC vector B 0 1 ACOS lt C1i I CB The angle between two 96 8866 vectors is 90 SWE HEE peewee m Z 4 m a Find the angle between two vectors A 3 4 B 0 5 Keys Display Description MODE 5 SRPH Switches to RPN mode MODE 1 1DEG Sets Degrees mo
112. IN Hyperbolic arc sine Returns sinh 1 x Wea ATAN Arc tangent Returns tan 1 x ESN HYP Wea ATAN Hyperbolic arc tangent Returns tanh 1 x BY 25151 t Returns the y intercept of the regression line y mX Page 6 4 4 6 1 9 6 16 4 4 4 6 4 4 4 6 12 11 G 4 Operation Index Name Keys and Description Page b T 8 n 2 41 Indicates a binary number re Displays the base conversion menu 11 1 BIN B HAEIN 11 1 Selects Binary base 2 mode Turns on calculator clears x clears 1 1 messages and prompts cancels 1 4 menus cancels catalogs cancels 1 8 equation entry cancels program 1 29 entry halts execution of an equation 6 3 halts a running program 13 7 13 19 c Lal Denominator 5 4 Sets denominator limit for displayed fractions to x If x 1 displays current c value PC Wea gt c Converts F to C 4 14 1 CF n ER FLAGS 2 EF n 14 12 Clears flag n n O through 11 3 Displays menu to clear numbers or 1 5 parts of memory clears indicated 1 28 variable or program from a MEM catalog clears displayed equation WES CLEAR 3 Clears all stored data equations 1 29 3ALL and programs Wes CLEAR 3 Clears all programs calculator in 13 23 ZPEM Program mode Wes CEAR Clears the displayed equation 13 7 ZEGH calculator in Equation mode Cle WES CL
113. INPUT F Stores data point frequency in F IG 4 i Enters increment for N 1663 STOB 1666 RCL F Recalls data point frequency fi Checksum and length 3387 19 Fae i LBL F Accumulate summations Fe 2 27 Fees STOI Stores index for register 27 Fe 4 RCL F Fees STOLL Updates X f in register 27 FEBE RELY X x Faeyr STO Z FBS 28 Fees STOI Stores index for register 28 F ie ECL Z F11 STO 1 Updates x in register 28 F 12 RLY xi Felis sToz Stores index for register 30 Fei4 36 Fis STO T F ie RCL Z Statistics Programs 16 19 Program Lines Description In ALG mode Feir STO CI Updates x f in register 30 FiS RCL B Fei STO H Increments or decrements N Fe2e RCL H Fe 2i RCL F Fe 22 ABS Fe 23 STO F Fe24 VIEW H Displays current number of data pairs Fees GTO 166i Goes to label line number for next data input Checksum and length F6CB 84 GEBI LBL G Calculates statistics for grouped data GEGZ x Grouped standard deviation GEBS STO Gee4 VIEH S Displays grouped standard deviation GBS x Weighted mean CEBE STO M Geer VIEH M Displays weighted mean Gees GTO 1881 Goes back for more points Checksum and length DAF2 24 Weed LBL U Undo data entry error Ueez i Enters decrement for N Uges STO Weed REL F Recalls last data frequency input UGES 7 Changes sign of fi UBe6 STOF Ugey GTO FGI Adjusts count and summations Checksum and length 03F4 23 16 20 Stat
114. If you didn t get the same results as the example you may have accidentally changed how fractions are displayed See Changing the Fraction Display later in this chapter The next topic includes more examples of valid and invalid input fractions Fractions in the Display In Fraction display mode numbers are evaluated internally as decimal numbers then they re displayed using the most precise fractions allowed In addition accuracy annunciators show the direction of any inaccuracy of the fraction compared to its 12 digit decimal value Most statistics registers are exceptions they re always shown as decimal numbers Display Rules The fraction you see may differ from the one you enter In its default condition the calculator displays a fractional number according to the following rules To change the rules see Changing the Fraction Display later in this chapter m The number has an integer part and if necessary a proper fraction the numerator is less than the denominator m The denominator is no greater than 4095 m The fraction is reduced as far as possible Examples These are examples of entered values and the displayed results For comparison the internal 12 digit values are also shown The 4 and annunciators in the last column are explained below 5 2 Fractions Entered Value Internal Value Displayed Fraction 2 3 8 2 37500000000 2 3 8 14 15 39 14 4687500000 i4 15732 54 12 4 5
115. One and two variable statistical data are entered or deleted in similar fashion using the or 1 2 key Data values are accumulated as summation statistics in six statistics registers 27 through 32 whose names are displayed in the SUMS menu Press M SUMS and see n Ex Ev Ex Eve Exy Note Always clear the statistics registers before entering a new set of i statistical data press WE3 CLEAR 4 42 Statistical Operations 12 1 Entering One Variable Data 1 Press CLEAR A 42 to clear existing statistical data 2 Key in each x value and press 2 3 The display shows n the number of statistical data values now accumulated Pressing actually enters two variables into the statistics registers because the value already in the Y register is accumulated as the y value For this reason the calculator will perform linear regression and show you values based on y even when you have entered only x data or even if you have entered an unequal number of xand y values No error occurs but the results are obviously not meaningtul To recall a value to the display immediately after it has been entered press Wea LAST x Entering Two Variable Data If the data is a pair of variables enter first the dependent variable the 2 variable of the pair and press ENTER and then enter the independent variable the first variable of the pair and press 2 1 Press Wea CLEAR 4 42 to clear existing stat
116. PUT instruction for each variable including the unknown INPUT instructions enable you to solve for any variable in a multi variable function INPUT for the unknown is ignored by the calculator so you need to write only one program that contains a separate INPUT instruction for every variable including the unknown If you include no INPUT instructions the program uses the values stored in the variables or entered at equation prompts 3 Enter the instructions to evaluate the function m A function programmed as a multi line RPN or ALG sequence must be in the form of an expression that goes to zero at the solution If your equation is f x g x your program should calculate f x g x O is implied m A function programmed as an equation can be any type of equation equality assignment or expression The equation is evaluated by the program and its value goes to zero at the solution If you want the equation to prompt for variable values instead of including INPUT instructions make sure flag 11 is set 4 End the program with a RTN Program execution should end with the value of the function in the X register Example Program Using ALG Write a program using ALG operations that solves for any unknown in the equation for the Ideal Gas Law The equation is Px V NxRxT where P Pressure atmospheres or N m2 V Volume liters N Number of moles of gas R The universal gas constant 0 0821 liter atm mole K or
117. QN IPX 1 5 Selects Equation mode displays the equation E SOLVE SOLVING Finds a root with guesses O and 5 2 BEBE ey 1 99999999999 Shows root to 11 decimal places Ry 2 G GG GEGE The previous estimate is slightly bigger RH 6 5006 f x is relatively large Note the difference between the last two estimates as well as the relatively large value for f x The problem is that there is no value of x for which f x equals zero However at x 1 99999999999 there is a neighboring value of x that yields an opposite sign for f x Example Find the root of the equation X 1 0 x As x approaches 6 f x becomes a very large positive or negative number Enter the equation as an expression Keys Display Description m 19 Z Selects Equation mode va Enters the equation MIE iE EA K353 CENTER 7 E WW B ae CR4 2 69 1 More about Solving D 7 EN SHOW CK 7 358 LH 1i LC Now solve to find the root Keys Display wW STO X ENTER 267 LIZ EQN ATOR 2 6I 1 Wea SOLVE HO ROOT FHO Checksum and length Cancels Equation mode Description Your initial guesses for the root Selects Equation mode displays the equation No root found for f x When SOLVE Cannot Find a Root Sometimes SOLVE fails to find a root The following conditions cause the message HO ROOT FHOD m The search terminates near a local minimum
118. S RCL RA6i4 RCL 0 RBIS RCL ABi 6 RCL E Rei RTH Checksum and length 9E5E 51 13 28 Simple Programming 14 Programming Techniques Chapter 13 covered the basics of programming This chapter explores more sophisticated but useful techniques m Using subroutines to simplify programs by separating and labeling portions of the program that are dedicated to particular tasks The use of subroutines also shortens a program that must perform a series of steps more than once m Using conditional instructions comparisons and flags to determine which instructions or subroutines should be used a Using loops with counters to execute a set of instructions a certain number of times m Using indirect addressing to access different variables using the same program instruction Routines in Programs A program is composed of one or more routines A routine is a functional unit that accomplishes something specific Complicated programs need routines to group and separate tasks This makes a program easier to write read understand and alter A routine typically starts at a label and ends with an instruction that stops program routing execution such as RTN or STOP Calling Subroutines KEQ RTN A subroutine is a routine that is called from executed by another routine and returns to that same routine when the subroutine is finished Programming Techniques 14 1 If you plan to have only one program in the calculator memory
119. Their purposes are as follows m Flag 7 toggles fraction display mode on or off clear off and set on m Flag 8 toggles between using any value less than or equal to the c value or using only factors of the c value clear use any value and set use only factors of the c value m Flag 9 operates only if Flag 8 is set and toggles between reducing or not reducing the fractions clear reduce and set do not reduce With Flags 8 and 9 appropriately cleared or set you can get the three fraction formats as shown in the table below 5 6 Fractions To Get This Fraction Format Change These Flags 8 9 Most precise Clear Factors of denominator Set Clear Fixed denominator Set Set You can change flags 8 and 9 to set the fraction format using the steps listed here Because flags are especially useful in programs their use is covered in detail in chapter 14 1 Press FLAGS to get the flag menu 2 To seta flag press 1 15F and type the flag number such as 8 To clear a flag press 2 2CF and type the flag number To see if a flag is set press 3 3F 7 and type the flag number Press or Lel to clear the YES or NO response Example This example illustrates the display of fractions in the three formats using the number nm This example assumes fraction display format is active and that Flag 8 is in its default state cleared Keys Display Description mmga Sets the m
120. a BASE 6 annunciator on Eh ENTER Base Conversions and Arithmetic and Logic 11 5 Wes BASE 4 41H 1401104 Changes to base 2 BIN mmo annunciator on This 3 8 2b terminates digit entry so no ENTER is needed between the numbers 141111611686 Result in binary base Wes BASE 2 2HEX SECh Result in hexadecimal base Wea BASE 7 1 0EC 1 516 6666 Restores decimal base The Representation of Numbers Although the display of a number is converted when the base is changed its stored form is not modified so decimal numbers are not truncated until they are used in arithmetic calculations When a number appears in hexadecimal octal or binary base it is shown 36 bits 12 octal digits or 9 hexadecimal digits Leading zeros are not displayed but they are important because they indicate a positive number For example the binary representation of 125 70 is displayed as 1111101b which is the same as these 36 digits 000000000000000000000000000001111101b Negative Numbers The leftmost most significant or highest bit of a number s binary representation is the sign bit it is set 1 for negative numbers If there are undisplayed leading zeros then the sign bit is O positive A negative number is the 2 s complement of its positive binary number Keys Display Description 5 4 C6 FES BASE 222h Enters a positive decimal 2 2HEX number then c
121. a negative power m Attempted to raise a negative number to a non integer power m Attempted to raise complex number 0 i 0 toa number with a negative real part Attempted an operation with an invalid indirect value I is not defined Attempted an operation with an invalid indirect value J is not defined Attempted to take a logarithm of zero or 0 i0 Attempted to take a logarithm of a negative number All of user memory has been erased see page The calculator has insufficient memory available to do the operation See appendix B The condition checked by a test instruction is not true Occurs only when executed from the keyboard Attempted to refer to a nonexistent program label or line number with LCTO KEQ or FH Note that the error HOHES I STENT can mean m you explicitly from the keyboard called a program label that does not exist or m the program that you called referred to another label which does not exist The result of integration does not exist The catalog of programs EW MEM 2 2P GM indicates no program labels stored No solution could be found for this system of linear equations Multiple solutions have been found for this system of linear equations Messages F 3 HO ROOT FHO OVERFLOW PRGM TOP RUHNING By SELECT FH SOLVE ACTIVE SOLVE C SOLVE gt SOLVE C FHJ SOLVING SQRTCHEG gt F 4 Messages SOLVE include EQN and PGM mode cannot
122. a list of messages and conditions in appendix F To see the line in the program containing the error causing instruction press 0 PRGM The program will have stopped at that point For instance it might be a instruction which caused an illegal division by zero Simple Programming 13 19 Editing a Program You can modity a program in program memory by inserting deleting and editing program lines If a program line contains an equation you can edit the equation To delete a program line 1 Select the relevant program or routine and press or to locate the program line that must be changed Hold the cursor key down to continue scrolling 2 Delete the line you want to change press directly Undo function is active The pointer then moves to the preceding line If you are deleting more than one consecutive program line start with the last line in the group 3 Key in the new instruction if any This replaces the one you deleted 4 Exit program entry LC or Fea PRGM To insert a program line 1 Locate and display the program line that is before the spot where you would like to insert a line 2 Key in the new instruction it is inserted after the currently displayed line For example if you wanted to insert a new line between lines A004 and A005 of a program you would first display line A004 then key in the instruction or instructions Subsequent program lines starting with the original line A005
123. a message will accompany the error annunciator as well To clear a message press or LJ in RPN mode you will return to the stack as it was before the error In ALG mode you will return to the last expression with the edit cursor at the position of the error so that you can correct it Getting Started 1 27 m Any other key also clears the message though the key function is not entered If no message is displayed but the annunciator appears then you have pressed an inactive or invalid key For example pressing LJ LJ will display A because the second decimal point has no meaning in this context All displayed messages are explained in appendix F Messages Calculator Memory The HP 35s has 30KB of memory in which you can store any combination of data variables equations or program lines Checking Available Memory Pressing EN displays the following menu iVAR 2 PGM nnn mim mam Where nnn is the amount of used indirect variables mim mmm is the number of bytes of memory available Pressing the L1 1 AR displays the catalog of direct variables see Reviewing Variables in the VAR Catalog in chapter 3 Pressing the 2 2FGM displays the catalog of programs 1 To enter the catalog of variables press LL 14AR to enter the catalog of programs press 2 2FGM To review the catalogs press or A To delete a variable or a program press Wea while viewing it in its catalog 4 To exit the catalog
124. address A through Z are direct addresses Both CJ and QN are used together to create an indirect address and this applies to both W and as well By itself I or J is either undefined no number in I or J or uncontrolled using whatever number happens to be left over in or J The Variables I and J You can store recall and manipulate the contents of or J just as you can the contents of other variables You can even solve for I J and integrate using or J The functions listed below can use variable i the variable J is the same 14 20 Programming Techniques STO INPUT DSE RCL VIEW ISG STO x I JFNd x lt gt RCL x SOLVE The Indirect Address I and J Many functions that use A through Z as variables or labels can use I or J to refer to A through Z variables or labels or statistics registers indirectly The function I or J uses the value in variable I to J to determine which variable label or register to address The following table shows how Programming Techniques 14 21 If 1 J contains Then I J will address variable A or label A 26 variable Z or label Z 27 n register 28 x register 29 Ly register 30 2x2 register 31 Ly2 register 32 xy register 0 Unnamed Indirect variables start 800 The Max Address is 800 lt 32 or I gt 800 or variables error INVALID tI undefined J lt 32 or l gt 800 or variables error INVALID J und
125. ag test is a conditional test that affects program execution just as the comparison tests do The FS n instruction tests whether the given flag is set If it is then the next line in the program is executed If it is not then the next line is skipped This is the Do if True rule illustrated under Conditional Instructions earlier in this chapter If you test a flag from the keyboard the calculator will display YES or HO 14 12 Programming Techniques It is good practice in a program to make sure that any conditions you will be testing start out in a known state Current flag settings depend on how they have been left by earlier programs that have been run You should not assume that any given flag is clear for instance and that it will be set only if something in the program sets it You should make sure of this by clearing the flag before the condition arises that might set it See the example below Example Using Flags Program Lines In RPN mode Description S 1 LBL S862 CFE Clears flag O the indicator for In X S 63 CF i Clears flag 1 the indicator for In Y s 4 INPUT X Prompts for and stores X S665 FS 6 It flag O is set S666 LH takes the natural log of the X input S667 STO Stores that value in X after flag test 663 INPUT Y Prompts for and stores Y Se 9 FS i If flag 1 is set 616 LH takes the natural log of the Y input S611 570 Stores that value in Y after flag test S612 VIEW x Displays
126. al accumulation Uges CTO Wee Loops for another X Y pair Checksum and length A79F 15 R i LBL R Defines the start of the output routine RBB F Calculates the correlation coefficient RBES STOR Stores it in R Ree4 VIEW R Displays the correlation coefficient REGS b Calculates the coefficient b RBE FS i If flag 1 is set takes the natural antilog of b REE es Rees STO B Stores b in B Ree VIEH E Displays value R18 m Calculates coefficient m Reii STOM Stores m in M Rei2 VIEW M Displays value Checksum and length 850C 36 YABI LBL Y Defines the beginning of the estimation projection loop 16 4 Statistics Programs Program Lines Description In RPN mode YEG INPUT Displays prompts for and if changed stores x value in X BRS FS If flag O isset YEE4 CTO KEGI Branches to KOO1 YES CTO MEGI Branches to M001 YEBE STO Y Stores y value in Y Yeer INPUT Y Displays prompts for and if changed stores y value in Y HRS FS If flag O is set Yee GTO OBBI Branches to O001 YIB CTO HEGI Branches to NO01 Ya1i STO X Stores X in X for next loop Yei2 GTO YEBI Loops for another estimate Checksum and length C3B7 36 RABBI LEL A This subroutine calculates y for the straight line model ABB RCL M AGES ECL A Reed RCL B Calculates y MX B FREES RTH Returns to the calling routine Checksum and length 9688 15 Geei LEL G This subroutine calculates x for the straight line model GGZ RCL Y GEES R
127. 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 Wea STO 4 Wea STO Wea STO X or Wea STO LE to do arithmetic in the variable itself and to store the result there It uses the value in the X register and does not affect the stack New value of variable Previous value of variable x x For example suppose you want to reduce the value in A 15 by the number in the X register 3 displayed Press Wa STO HA Now A 12 while 3 is still in the display 3 6 Storing Data into Variables A Result 15 3 that is A x a STO 1A Recall Arithmetic Recall arithmetic uses RCLJLE RCLJ LE ReH L or RCL LE to do arithmetic in the X register using a recalled number and to leave the result in the display Only the X register is affected The value in the variable remains the same and the result replaces the value in the x register New x Previous x x Variable For example suppose you want to divide the number in the X register 3 displayed by the value in A 12 Press LE A Now x 0 25 while 12 is still in A Recall arithmetic saves memory in programs using A one instruction uses half as much memory as A two instructions A T z Y Result 3
128. also leaves the value you just entered in the Xfiregister you don t have to recall the variable at a later time 6 you could INPUT it and use it when you need it You might be able to save some memory space this way However in a long program it is simpler to just input all your data up front and then recall individual variables as you need them Remember also that the user of the program can do calculations while the program is stopped waiting for input This can alter the contents of the stack which might affect the next calculation to be done by the program Thus the program should not assume that the X Y and Zfiregisters contents will be the same before and after the INPUT instruction If you collect all the data in the beginning and then recall them when needed for calculation then this prevents the stack s contents from being altered just before a calculation To respond to a prompt When you run the program it will stop at each INPUT and prompt you for that variable such as R76 B866 The value displayed and the contents of the X register will be the current contents of R To leave the number unchanged just press R S To change the number type the new number and press R S This new number writes over the old value in the X register You can enter a number as a fraction if you want If you need to calculate a number use normal keyboard calculations then press R S For example you can press 2 ENTER 5 OA R S
129. alue 3 is stored in A and 3 686868 returned to the stack MODE 4 4 ALG Switch to ALG mode if necessary 3 BEBE 3 Wes STO A SAL Again the Store command prompts for a letter and the A Z annunciator appears ENTER SIA The value 3 is stored in A and the 3 BBA result is placed in line 2 Storing Data into Variables 3 1 In ALG mode you can store an expression into a variable in this case the value of the expression is stored in the variable rather than the expression itself Example Keys Display Description mannan 1 374c Enter the expression then w STO G ENTER 1 75 proceed as in the previous example Each pink letter is associated with a key and a unique variable The A Z annunciator in the display confirms this Note that the variables X Y Z and T are different storage locations from the X register Y register Z register and T register in the stack Storing and Recalling Numbers Numbers and vectors are stored into and recalled from lettered variables by means of the Store F STO and Recall RELI commands Numbers may be real or complex decimal or fraction base 10 or other as supported by the HP 35s To store a copy of a displayed number X register to a direct variable Press W STO letter key ENTER To recall a copy of a number from a direct variable to the display Press letter key ENTER Example Storing Numbers Store Avogadro s number approximatel
130. alue of a variable without recalling that value to the x register The display takes the form Variable Value If the number has too many digits to fit into the display use FE3 2 gt _ or L to view the missing digits To cancel the VIEW display press or LE The VIEW command is most often used in programming but it is useful anytime you want to view a variable s value without affecting the stack Using the MEM Catalog The MEMORY catalog MEM provides information about the amount of available memory The catalog display has the following format 1 WAR 2 PGM nan fim mmm where mm mmm is the number of bytes of available memory and nnn is the amount of used indirect variables For more information on indirect variables see Chapter 14 The VAR catalog By default all direct variables from A to Z contain the value zero If you store a non zero value in any direct variable that variable s value can be viewed in the VAR Catalog MEM 1 1 AR 3 4 Storing Data into Variables Example In this example we store 3 in C 4 in D and 5 in E Then we view these variables via the VAR Catalog and clear them as well This example uses RPN mode Keys Display Description Wes CLEAR 2 2VAR Clear all direct variables 5 3 Fs STO C 4 Store 3 in C 4 in D and 5 in E 4 Wea STO D 5 CoH EN MEM iVAR ES Enter the VAR catalog 3 Note the and annunciators indic
131. ams ceeee 13 4 Data Input and Cutaut a ctsavenatiecuernesustanunasnratin asarnaeyrtes 13 5 Entering a Program ssseseeeeeeeeceeceeeeeeceeneeeeeaaeeaeeenteeeeeeeees 13 6 Clear functions and backspace key c ccccssssseeeseeeeeeeees 13 7 Function Names in Programs ssesseeeeeeeeeeeeeeeeeereeeees 13 8 RUNNING a Progra s sce2 nteiwreetawtuiettievbacaeheaseheaasvearetacessers 13 10 Executing a Program XEQ ccseeeeeeeteeeeeeeeeeeeeeeeeees 13 10 Testing Programe saa an iis a nn 13 11 Entering and Displaying Dota aici sven svensyenesuincibveraieeeniesgawses 13 12 Using INPUT for Entering Datetscicscesuessdkveesigsdasdsaerarseates 13 13 Using VIEW for Displaying Data ccccccessceeesseeeeteeees 13 15 Using Equations to Display Messages cccseeeseeeeeeees 13 16 Displaying Information without Stopping scceeereeeeees 13 18 Stopping or Interrupting a Program eeeceeeeseeeeteeerteeeees 13 19 Programming a Stop or Pause STOP PSE 0 0 0 eee 13 19 Interrupting a Running Program s ssseeeeeeeeeeeeeeeees 13 19 Error Stops micos asc aee eae e e EE E 13 19 Editing ea PEGG RCH senoms a e a E SeS 13 20 Program Memory sseeeeeeeeeeeeeeeeceeeeceeeeeeeeeeseneaeeeaaneaea 13 21 Viewing Program Memory ssssssssssssssssseesserrerrererereeeseeese 13 21 Memory Usages inenen a a h 13 22 The Catalog of Programs MEM ccssccceessee
132. ams and Equations Keys KEQ RJ ENTER LJ R S WARS WRS KEQ LE ENTER 2 R S 5 R S 4 R S KEQ LC ENTER R S R S z KTF a wv Display value value value Description Run R routine to input vector value Input v2 of x component Input v2 of y component Input v2 of z component Run E routine to exchange v2 in U V and W variables Input v1 of x component Input v1 of y component Input v1 of z component Run C routine to calculate x component of cross product Calculate y component of cross product Calculate z component of cross product Miscellaneous Programs and Equations 17 13 Part 3 Appendixes and Reference Support Batteries and Service Calculator Support You can obtain answers to questions about using your calculator from our Calculator Support Department Our experience shows that many customers have similar questions about our products so we have provided the following section Answers to Common Questions If you don t find an answer to your question contact the Calculator Support Department listed on page A 8 Answers to Common Questions Q How can determine if the calculator is operating properly A Refer to page A 5 which describes the diagnostic selfHtest Q My numbers contain commas instead of periods as decimal points How do restore the periods A Use the Et DISPLAY 5 5 function page 1 23 Q How do change the numb
133. and Messages in a Program Write an equation to find the surface area and volume of a cylinder given its radius and height Label the program C for cylinder and use the variables S surface area V volume R radius and H height Use these formulas V aR2H S 27 R2 27 RH 27R R H Keys Display Description In RPN mode Wes PROM Fes Program entry clears the CLEAR 3 SPGM PRGM TOP program memory yer rs GOK cee LELE Labels program Eu INPUT LR CBee IMPUT FE EW INPUT H CBZ INPUT H Instructions to prompt for radius and height 13 16 Simple Programming Keys In RPN mode EQN 2 x RaR LAA x kal RCL H ENTER STO EQN 2 x Gy 2 x RCL RIX ROR 4 BBE SHOW T uw Bis F JO FLAGS 1 KORIRA RCL B LO Re Wea SPACE Wea SPACE LR Reo E A ENTER OLE FLAGS 1 E g Bana T D D B I a Display CBE4 _7xR 2xH CK 74FE LH 7 CBGS STOW COGE 2x_qxRet R m CK 19B3 LH 11 Cher STOS CEES SF 16 Cee VOL ARE m CRIB CF 16 CBii VIEH V CBi2 VIEWS CBis RTH LEL C LH 67 CK 97 C3 LH 67 Description Calculates the volume Checksum and length of equation Store the volume in V Calculates the surface area Checksum and length of equation Stores the su
134. anty so the above limitation or exclusion might not apply to you This warranty gives you specific legal rights and you might also have other rights that vary from country to country state to state or province to province 7 TO THE EXTENT ALLOWED BY LOCAL LAW THE REMEDIES IN THIS WARRANTY STATEMENT ARE YOUR SOLE AND EXCLUSIVE REMEDIES EXCEPT AS INDICATED ABOVE IN NO EVENT WILL HP OR ITS SUPPLIERS BE LIABLE FOR LOSS OF DATA OR FOR DIRECT SPECIAL INCIDENTAL CONSEQUENTIAL INCLUDING LOST PROFIT OR DATA OR OTHER DAMAGE WHETHER BASED IN CONTRACT TORT OR OTHERWISE Some countries States or provinces do not allow the exclusion or limitation of incidental or consequential damages so the above limitation or exclusion may not apply to you 8 The only warranties for HP products and services are set forth in the express warranty statements accompanying such products and services HP shall not be liable for technical or editorial errors or omissions contained herein FOR CONSUMER TRANSACTIONS IN AUSTRALIA AND NEW ZEALAND THE WARRANTY TERMS CONTAINED IN THIS STATEMENT EXCEPT TO THE EXTENT LAWFULLY PERMITTED DO NOT EXCLUDE RESTRICT OR MODIFY AND ARE IN ADDITION TO THE MANDATORY STATUTORY RIGHTS APPLICABLE TO THE SALE OF THIS PRODUCT TO YOU Customer Support Australia 1300 55 1 664 or 03 9841 5211 A 8 Support Batteries and Service China Hong Kong Indonesia Japan Malaysia New Zealand Philippines Singapore South Korea Ta
135. apter 1 the section Fractions introduced the basics of entering displaying and calculating with fractions This chapter gives more information on these topics Here is a short review of entering and displaying fractions To enter a fraction press L twice once after the integer part of a mixed number and again between the numerator and denominator of the fractional part of the number To enter 2 3 8 press 2JLIJ 3 L J 8 To enter 5 8 press either JALIL or WLLL To toggle Fraction display mode on and off press Wea EDISP When Fraction display mode is turned off the display reverts to the previous display format set via the Display menu Choosing another format via this menu also turns off Fraction display mode if active Functions work the same with fractions as they do with decimal numbers except for RND which is discussed later in this chapter The examples in this chapter all utilize RPN mode unless otherwise noted Entering Fractions You can type almost any number as a fraction on the keyboard including an improper fraction where the numerator is larger than the denominator Example Keys Display Description FDISP Turns on Fraction display mode CL JG ENTER i i72 Enters 1 5 shown as a fraction FDISP 1 7588 Displays x as a decimal number play wea Li WABI ENTER i374 Enters 1 3 4 Wea wea FDISP 13 4 Displays x as a fraction Fractions 5 1
136. are moved down and renumbered accordingly To edit operand expression or equation in a program line 1 Locate or display the program line that you want to edit 2 Press or to start editing the program line These turn on the _ editing cursor but do not delete anything in the program line key actives the cursor to the left of the program line key actives the cursor to the end of the program line 13 20 Simple Programming 3 Moving the cursor _ and press repeatedly to delete the unwanted number or function then retype the rest of the program line After pressing Lel Undo function is active Notice 1 2 When the cursor is active in the program line or key will be disabled When you are editing a program line cursor active and the program line is empty using will have no effect If you want to erase the program line press and the program line will be erased You can use PAL and L key to review long program lines and without editing it In ALG mode can not be used as a function it is used to validate a program line An equation can be editing in any mode no matter which mode it was entered in Program Memory Viewing Program Memory Pressing Wea toggles the calculator into and out of program entry PRGM annunciator on program lines displayed When Program entry mode is active the contents of program memory are displayed Program memory starts at PRGM TOP The list of program line
137. ating that the and keys are active to help you scroll through the catalog however if Fraction Display mode is active the 4 and w annunciators will not be active to indicate accuracy unless there is only one variable in the catalog We return to our example illustrating how to navigate the VAR catalog D Scroll down to the next direct 4 variable with non zero value D 4 E Scroll down once more to see E 5 a While we are in the VAR catalog let s extend this example to show you how to clear the value of a variable to zero effectively deleting the current value We ll delete E E CLEAR C E is no longer in the VAR catalog 3 as its value is zero The next variable is C as shown Suppose now that you wish to copy the value of C to the stack 5 The value of C 3 is copied to the 3 xregister and 5 from defining E 5 previously moves to the y register Storing Data into Variables 3 5 To leave the VAR catalog at any time press either or LC An alternate method to clearing a variable is simply to store the value zero in it Finally you can clear all direct variables by pressing S CLEAR 2 2 ARS If all direct variables have the value zero then attempting to enter the VAR catalog will display the error message ALL VARS B If the value of a variable has too many digits to display completely you can use and to view the missing digits Arithmetic with Stored Variables Storage arithmetic and recall arithmetic
138. ation If you enter the equation incorrectly it will not have this checksum The length is the number of bytes of calculator memory used by the equation The checksum and length allow you to verify that equations you type are correct The checksum and length of the equation you type in an example should match the values shown in this manual Example Checksum and Length of an Equation Find the checksum and length for the pipe volume equation at the beginning of this chapter Entering and Evaluating Equations 6 19 Keys EQN as required EN SHOW hold release Ka 6 20 Entering and Evaluating Equations Display WEB 25xq_xO 2xL CK 49CR LH i4 VER 25x_7x0 2xL Description Displays the desired equation Display equation s checksum and length Redisplays the equation Leaves Equation mode 7 Solving Equations In chapter 6 you saw how you can use to find the value of the left hand variable in an assignmenttype equation Well you can use SOLVE to find the value of any variable in any type of equation For example consider the equation x2 3y 10 If you know the value of y in this equation then SOLVE can solve for the unknown x If you know the value of x then SOLVE can solve for the unknown y This works for word problems just as well Markup x Cost Price If you know any two of these variables then SOLVE can calculate the value of the third When the equation has only
139. ation as zero and 10499 than start the integration Keys Display Description miem g2 Specifies accuracy level ETRE icdss and limits of integration me i EQN MeEXP CM Selects Equation mode displays the equation EN THTEGRAT ING Approximation of the f integral B BBBEG The answer returned by the calculator is clearly incorrect since the actual integral of f x xe from zero to is exactly 1 But the problem is not that o was represented by 10499 since the actual integral of this function from zero to 10499 is very close to 1 The reason for the incorrect answer becomes apparent from the graph of f x over the interval of integration E 4 More about Integration f x x The graph is a spike very close to the origin Because no sample point happened to discover the spike the algorithm assumed that f x was identically equal to zero throughout the interval of integration Even if you increased the number of sample points by calculating the integral in SCI 11 or ALL format none of the additional sample points would discover the spike when this particular function is integrated over this particular interval For better approaches to problems such as this see the next topic Conditions That Prolong Calculation Time Fortunately functions exhibiting such aberrations a fluctuation that is uncharacteristic of the behavior of the function elsewhere are unusual enough that you are unlikely to have to int
140. ative result indicates drop in pressure Solving and Integrating Programs 15 5 Using SOLVE in a Program You can use the SOLVE operation as part of a program If appropriate include or prompt for initial guesses into the unknown variable and into the X register before executing the SOLVE variable instruction The two instructions for solving an equation for an unknown variable appear in programs as FH label SOLVE variable The programmed SOLVE instruction does not produce a labeled display variable value since this might not be the significant output for your program that is you might want to do further calculations with this number before displaying it If you do want this result displayed add a VIEW variable instruction after the SOLVE instruction If no solution is found for the unknown variable then the next program line is skipped in accordance with the Do if True rule explained in chapter 14 The program should then handle the case of not finding a root such as by choosing new initial estimates or changing an input value Example SOLVE in a Program The following excerpt is from a program that allows you to solve for x or y by pressing X or Y 15 6 Solving and Integrating Programs Program Lines In RPN mode S661 LBL HBB2 24 S663 GTO LEBI Checksum and length 62A0 11 YEBI LBL Y YBBe2 25 BGS GTO LEBI Checksum and length 221E 11 L 6i LEL L LeBe2 ST I L B3 FH F L 64 SOLVECT3 LOGS VIEW
141. ave questions about the product that are not related to this declaration write to Hewlett Packard Company P O Box 692000 Mail Stop 530113 Houston TX 77269 2000 For questions regarding this FCC declaration write to Hewlett Packard Company P O Box 692000 Mail Stop 510101 A 12 Support Batteries and Service Houston TX 77269 2000 or call HP at 281 514 3333 To identify your product refer to the part series or model number located on the product Canadian Notice This Class B digital apparatus meets all requirements of the Canadian Interference Causing Equipment Regulations Avis Canadien Cet appareil num rique de la classe B respecte toutes les exigences du R glement sur le mat riel brouilleur du Canada European Union Regulatory Notice This product complies with the following EU Directives e Low Voltage Directive 2006 95 EC e EMC Directive 2004 108 EC Compliance with these directives implies conformity to applicable harmonized European standards European Norms which are listed on the EU Declaration of Conformity issued by Hewlett Packard for this product or product family This compliance is indicated by the following conformity marking placed on the CE C Exxxx This marking is valid for non Telecom products product This marking is valid for EU non harmonized and EU harmonized Telecom products Telecom products e g Bluetooth Notified body number used only if applicabl
142. aximum c value back a to the default EN z a Most precise format 3167113 Flag 8 clear EEN FLAGS 7 iSF B Flag 8 set E 3116 819 Factors of denominator format 819 5 4095 EN FLAGS LT 1SF 66 4695 Flag 9 set 9 3 58074095 Fixed denominator format EN FLAGS 2 2CF Return to default format most 8 EN FLAGS 3167113 precise cr Fractions 5 7 Examples of Fraction Displays The following table shows how the number 2 77 is displayed in the three fraction formats for two c values Fraction How 2 77 Is Displayed Format c 4095 c 16 Most Precise 277 100 2 7700 2 10 134 27692 Factors of Denominator 21051 13654 27699 2 3 44 27500 Fixed Denominator 2 3153 40954 27699 2 12 164 2 7500 The following table shows how different numbers are displayed in the three fraction formats for a c value of 16 Fraction Number Entered and Fraction Displayed Format 2 2 5 2 2 3 2 9999 216 25 Most precise 2 21 2 22 34 3y 29 147 Factors of 2 21 2 211 16 3 25 8 denominator Fixed denominator 20 16 28 16 211 16 30 16 210 164 For a c value of 16 Rounding Fractions If Fraction display mode is active the RND function converts the number in the X register to the closest decimal representation of the fraction The rounding is done according to the current c value and the states of flags 8 and 9 The accura
143. c veusxcuurs toricensd tormomeavpesamienaes 5 6 Examples of Fraction Dis players tcmesersacvatsavorsoassearsganeeniiirtes 5 8 Rounding FROGIONS hd tesa uietnetate ctataaatabwsteraauasees soase a tase aaa ae 5 8 Fractions in EQuations cceeeeceeeeceeeeeeeecteeeeeeeeeeceeeeeeeeeeeeeeeees 5 9 Fractions in Programs cscccessseeeececeeeueneeeceeeeeueaeeceseeeueenes 5 10 6 Entering and Evaluating Equations sscssessesees 6 1 How You Can Use Equations ssseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeees 6 1 Summary of Equation Operations cccccceeseeeeesseeeeeeeeeeesseees 6 3 Entering Equations into the Equation List ccccceceesteeeeenreeees 6 4 Variables in Equations ics cis sasuiantnvenasaciya uetasaneaencantiautu reais 6 4 Numbers in Equations jctaciceniitaten oat etmntemase sss 6 5 Functions in Equations cceceeeeecceceenceceeeeeeeeeeeeeeenteeeeeeees 6 5 Parentheses InvEqualionsu ona ae a 6 6 Displaying and Selecting Equations cccccssessseeeeeeeetteeeeeeeees 6 6 Editing and Clearing Equatiansec s ids ciate caumlyaade Sanchssasuauetentctiaon 6 8 Types of Equations ieccustcrst ant Mack sh ehabtseteaeen vednmetancedyiastysantiias 6 9 Evaluating Equations ccc2risweiee wa rar Os 6 10 Using ENTER tor Evaluiationic ccivrsnencsieens measriaastanacatrocadend 6 11 Using XEQ for Evaluation asco asurcemdauenamnimarnaaenunesees 6 12 Responding to Equation Prompts ccce
144. calculation as the argument for the c function With the value in line 2 simply press W U The value in line 2 is displayed in Fraction format and the integer part is used to determine the maximum denominator 3 You may not use either a complex number or a vector as the argument for the c command The error message IHMALIO DATP will be displayed Choosing a Fraction Format The calculator has three fraction formats The displayed fractions are always the most accurate fractions within the rules for the selected format Most precise fractions Fractions have any denominator up to the c value and they re reduced as much as possible For example if you re studying math concepts with fractions you might want any denominator to be possible c value is 4095 This is the default fraction format Factors of denominator Fractions have only denominators that are factors of the c value and they re reduced as much as possible For example if you re calculating stock prices you might want to see 33 14 and 37 778 c value is 8 Or if the c value is 12 possible denominators are 2 3 4 6 and 12 m Fixed denominator Fractions always use the c value as the denominator they re not reduced For example if you re working with time measurements you might want to see 1 25 68 c value is 60 There are three flags that control the fraction format These flags are numbered 7 8 and 9 Each flag is either clear or set
145. can use I or J in an equation to specify a variable indirectly Notice that I or LJ means the variable specified by the number in variable I or J an indirect reference but that or J and I or where the user parenthesis are used instead of the I or J key means variable or J Unnamed indirect variables Placing a positive number into variable or J allows you to access up to 801 indirect variables The following example indicates how to use them Programming Techniques 14 23 Program Lines Description In RPN mode AGGI LBL AR AGZ 166 RABBS STO I RABB4 12345 RBS STO CT Defined the storage address range 0 100 and saved 12345 into address 100 AGGE 156 Ree STOI ABES 67326 Ree STO CTs Saves 67890 into address 150 The defined indirect storage range is now 0 150 AiB 166 RABii STOI ABi2 amp Reis STO T gt Stores O into indirect register 100 The defined range is still 0 150 ABi4d ie ABIS STOI RABie RCLCLS Display INVALID I because address 170 is undefined Rei RTH Note 1 If you want to recall the value from an undefined storage address the error message INVALID 12 will be shown See A014 2 The calculator allocates memory for variable O to the last non zero variable It is important to store O in variables after using them in order to release the memory Each allocated indirect register uses 37 bytes of program memory
146. ceeeeereeeeeeeeeteeeees 6 13 The Syntax of Equations x cruonnucu tent ieis 6 14 4 Contents Operator Precedence ysis cavdysessaciestonvnasaugrontyayruairaapeceauta 6 14 Equation Functions ceecceeeceeeeeeceeeeeeeeneeeeneeeeeseeeeeeeeeeers 6 16 Syntax ErrOrs sisisi ia iei ea eN R Eae 6 19 Verifying EGUCHI aisciucigansySenay tourer rensmeitbaunn eu vcheasuteeretavee 6 19 7 Solving Equations eseeee esee eseessesssessesssessesssessesssee 7 1 Solving am Equation o e ESTE 7 1 Solving built in Equation yisiwsudysaneedencstna tesa tnaceeysachaaaraeasyaess 7 6 Understanding and Controlling SOLVE cceeeeeceeeeeeeestteeees 7 7 Verifying the Result scat c 25 sacs di tectastiewaetaaee ture 7 7 Interrupting a SOLVE Calculation cs iosesiaiasocssasgascioalennese ves 7 8 Choosing Initial Guesses for SOLVE 0 ccceeeeeeesteeeetteeeees 7 8 For More Information eicca ene ued Gaeta Geet iyi ce 7 12 8 Integrating Equations csssccsssccssseecssscessseeees 8 1 Integrating Equations FN aii rcsucteies saan quttautiasaRasatoraaiiatuenemks 8 2 Accuracy of Integration s ssssesssnoeseneseoeeesotsesetersterssrtrsereeeeee 8 6 Specifying ACCUrAGY seis oy cesar chee leniramuwute 8 6 Interpreting ACCULOCY si i 8 6 For More Init QrninctiOMnsisaasaeor sate ty dantidens Yeensenkinestoue hu aicemateeeca este 8 8 9 Operations with Complex Numbers csscceseees 9 1 The Complex Stickien ni
147. ch Antilles 0 800 990 0114 800 71 1 2884 French Guiana 0 800 990 0114 800 71 1 2884 Grenada 1 800 7 1 1 2884 Guadelupe 0 800 990 0114 800 711 2884 Guatemala 1 800 999 5105 Guyana 159 e 800 71 1 2884 A 10 Support Batteries and Service NA Please logon to http www hp com for the latest service and support information Haiti Honduras Jamaica Martinica Mexico Montserrat Netherland Antilles Nicaragua Panama Paraguay Peru Puerto Rico St Lucia St Vincent St Kitts amp Nevis St Marteen Suriname Trinidad amp Tobago Turks amp Caicos US Virgin Islands Uruguay Venezuela 183 800 711 2884 800 0 123 800 7 1 1 2884 1 800 7 1 1 2884 0 800 990 011 e 877 219 8671 01 800 474 68368 800 HP INVENT 1 800 7 1 1 2884 00 1 800 872 2881 800 7 1 1 2884 1 800 0164 800 711 2884 00 1 800 7 1 1 2884 009 800 541 0006 0 800 10111 1 877 232 0589 1 800 478 4602 01 800 7 1 1 2884 1 800 7 1 1 2884 1 800 7 1 1 2884 156 800 7 11 2884 1 800 7 1 1 2884 01 800 71 1 2884 800 71 1 2884 0004 054 177 0 800 474 68368 0 800 HP INVENT Canada USA 800 HP INVENT 800 HP INVENT Support Batteries and Service A 11 Regulatory information Federal Communications Commission Notice This equipment has been tested and found to comply with the limits for a Class B digital device pursuant to Part 15 of the FCC Rules These limits are designed to provide reasonable protection against harmful
148. cksum and length 8524 21 Keei LBL K Determines if D001 or BOO1 should be run Kkee 2 FS i If flag q isset KEBS SEQ DEG Executes D001 Ke4 SEQ BEGI Executes BOO1 KBBS GTO YEBE Goes to YOO6 Checksum and length 4BFA 15 Maei LEL M Determines if C001 or A001 should be run Meee FS i If flag q isset MBBS sEQ CHEBI Executes C001 MEB4 SEO RABBI Executes A001 Hees GTO YEBE Goes to YOO6 Checksum and length 1C4D 15 0861 LEL 0 Determines if JOO1 or HOO1 should be run 0z FSF If flag q isset OB8BS XEQ JABI Executes JOO1 O864 XEQ HBI Executes HOO1 0865 GTO Yii Goes to YO11 Checksum and length OAA5 15 HEGI LBL H Determines if 1001 or GOO1 should be run HB2 FS i If flag 1 is set H s EQ Tee Executes 1001 HB4 SEG CHEI Executes G001 H 65 GTO Yell Goes to YO11 Checksum and length 666D 15 Statistics Programs 16 7 Flags Used Flag O is set if a natural log is required of the X input Flag 1 is set if a natural log is required of the Y input If flag 1 is set in routine N then 1001 is executed If flag 1 is clear GOO1 is executed Program instructions 1 2 6 7 8 9 Key in the program routines press when done Press and select the type of curve you wish to fit by pressing m SENTER for a straight line m LENITER for a logarithmic curve m EJ ENTER for an exponential curve or m PJ ENTER for a power curve Key in x value and press R S Key in y value and
149. ction is interesting it takes less time to reach this critical density To achieve the same density of sample points the total number of sample points required over the larger interval is much greater than the number required over the smaller interval Consequently several more iterations are required over the larger interval to achieve an approximation with the same accuracy and therefore calculating the integral requires considerably more time E 8 More about Integration Because the calculation time depends on how soon a certain density of sample points is achieved in the region where the function is interesting the calculation of the integral of any function will be prolonged if the interval of integration includes mostly regions where the function is not interesting Fortunately if you must calculate such an integral you can modify the problem so that the calculation time is considerably reduced Two such techniques are subdividing the interval of integration and transformation of variables These methods enable you to change the function or the limits of integration so that the integrand is better behaved over the interval s of integration More about Integration E 9 Messages The calculator responds to certain conditions or keystrokes by displaying a message The symbol comes on to call your attention to the message For significant conditions the message remains until you clear it Pressing or clears the message and
150. cy indicatior turns off if the fraction matches the decimal representation exactly Otherwise the accuracy indicatior stays on See Accuracy Indicators earlier in this chapter In an equation or program the RND function does fractional rounding if Fraction display mode is active 5 8 Fractions Example Suppose you have a 56 3 4 inch space that you want to divide into six equal sections How wide is each section assuming you can conveniently measure 1 16 inch increments What s the cumulative roundoff error Keys Display EN FLAGS ENTER L8 1 6 EW lt WABA 56 374 LEO D wa SYlbAsA 5 97 16 6 x 36 578 RCL LD 8 i78 ER ageer eirg E FDISP 6 1250 Fractions in Equations Description Sets Flag 8 Sets up fraction format for 1 16 inch increments Flags 8 and 9 should be the same as for the previous example Stores the distance in D The sections are a bit wider than 9 7 16 inches Rounds the width to this value Width of six sections The cumulative round off error Clears flag 8 Turns off Fraction display mode You can use a fraction in an equation When an equation is displayed all numerical values in the equation are shown in their entered form Also fraction display mode is available for operations involving equations When you re evaluating an equation and you re prompted for variable values you may enter fractions values are d
151. d with an arrow In this text we will use the graphics RJ LC LA and 1 to refer to these keys Getting Started 1 3 Backspacing and Clearing Among the first things you need to know are how to clear an entry correct a number and clear the entire display to start over Keys for Clearing Key Description Backspace If an expression is in the process of being entered erases the character to the left of the entry cursor _ Otherwise with a completed expression or the result of a calculation in line 2 Ce replaces that result with a zero also clears error messages and exits menus behaves similarly when the calculator is in program entry and equation entry modes as discussed below m Equation entry mode If an equation is in the process of being entered or edited erases the character immediately to the left of the insert cursor otherwise it the equation has been entered no insert cursor present deletes the entire equation Program entry mode If a program line is in the process of being entered or edited erases the character to the left of the insert cursor otherwise if the program line has been entered deletes the entire line Clear or Cancel Clears the displayed number to zero or cancels the current situation such as a menu a message a prompt a catalog or Equation entry or Program entry mode 1 4 Getting Started Keys for Clearing continued Key
152. de XEQ S J ENTER M Starts the initialization routine 8 86668 5 5 R s 57 Stores 55 for the mean 1 6666 QHR 15 3886 Stores 15 3 for the standard deviation XEQ D ENTER K Starts the distribution program and value prompts for X 9 LO R S Q Enters 90 for X and calculates Q X 6B 6iii Thus we would expect that only about 1 percent of the students would do better than score 90 Keys Display Description In RPN mode XEQ J ENTER a Starts the inverse routine B 61ii OIC IGIR x Stores 0 1 10 percent in Q X and 4 6877 calculates X R S a Resumes the inverse routine B 1686 0 8 R S HE Stores 0 8 100 percent minus 20 42 1232 percent in Q X and calculates X Grouped Standard Deviation The standard deviation of grouped data Sxy is the standard deviation of data points x X2 Xn occurring at positive integer frequencies fi f2 0 fre 2 gt xf x poe ee an s E 16 18 Statistics Programs This program allows you to input data correct entries and calculate the standard deviation and weighted mean of the grouped data Program Listing Program Lines Description In ALG mode S861 LBL Start grouped standard deviation program S862 CLE Clears statistics registers 27 through 32 SBBS B S664 STOW Clears the count N Checksum and length E5BC 13 Te e i LBL I Input statistical data points IGZ INPUT Stores data point in X 1663
153. de Ey sey ji4 2 Finds the dot product of ENTER Wed O N 2e epee two vectors SIX BML 28 600 Finds the magnitude of Wea ABS T BEBE vector 3 4 Vector Arithmetic 10 5 Fey IG 5 6686 Wed ABS 5 4808 Ea 20 OPGE 25 000G E 36 G 9808 Wea ACOS 26 36 9699 Vectors in Equations Finds the magnitude of vector 0 5 Multiplies two vectors Divides two values The angle between two vectors is 36 8699 Vectors can be used in equations and in equation variables exactly like real numbers A vector can be entered when prompted for a variable Equations containing vectors can be solved however the solver has limited ability if the unknown is a vector Equations containing vectors can be integrated however the result of the equation must be a real or a 1 D vector or a vector with O as the 2 4 and 3 elements 10 6 Vector Arithmetic Vectors in Programs Vectors can be used in program in the same way as real and complex numbers For example 5 6 2 x 7 8 x 9 10 in a program is Program lines Description GEBI LEL G Begins the program GBBB2 C3 6J 2x C7 88 xC 9 16 5 6 GBEES RTH A vector can be entered when prompted for a value for a variable Programs that contain vectors can be used for solving and integrating Vector Arithmetic 10 7 Creating Vectors from Variables or Registers It is possible to create vectors containing the contents of memory variables stack registers
154. diately follow the delete operation any intervening operations will keep Undo from retrieving the deleted object In addition to retrieving an entire entry atter its deletion Undo can also be used while editing an entry Press UNDO while editing to recover a digit in an expression that you just deleted using an expression you were editing but cleared using a character in an equation or program that you just deleted using while in equation or program mode Please note also that the Undo operation is limited by the amount of available memory Getting Started 1 11 The Display and Annunciators HItS TN 68 First Line 3662340370 Second Line The display comprises two lines and annunciators Entries with more than 14 characters will scroll to the left During input the entry is displayed in the first line in ALG mode and the second line in RPN mode Every calculation is displayed in up to 14 digits including an E sign exponent and exponent value up to three digits C0 CE ALG RPN EQN GRAD 01234 A Z PROM HEX OCT BIN HYPA E t 4 a x Annunciators The symbols on the display shown in the above figure are called annunciators Each one has a special significance when it appears in the display 1 12 Getting Started HP 35s Annunciators Annunciator Meaning Chapter E ALG PRGM EQN 01234 RAD or GRAD HEX OCT BIN HYP The E Busy annunciator appears while
155. displayed R Roll Up The Wea RH roll up key has a similar function to except that it rolls the stack contents upward one register at a time The contents of the X register rotate into the Y register what was in the T register rotates into the X register and so on Exchanging the X and Y Registers in the Stack Another key that manipulates the stack contents is x exchange y This key swaps the contents of the X and Y registers without affecting the rest of the stack Pressing twice restores the original order of the X and Y register contents The function is used primarily to swap the order of numbers in a calculation For example one way to calculate 9 13 x 8 Press MJ ENTER LSJ 9 AY A The keystrokes to calculate this expression from left to right are 9 ENTER 1 3 ENTER 8G E Note Understand that there are no more than four numbers in the stack at any given time the contents of the T register the top register iS will be lost whenever a fifth number is entered 2 4 RPN The Automatic Memory Stack Arithmetic How the Stack Does It The contents of the stack move up and down automatically as new numbers enter the X register lifting the stack and as operators combine two numbers in the X and Y registers to produce one new number in the X register dropping the stack Suppose the stack is filled with the numbers 1 2 3 and 4 See how the stack drops and lifts its conte
156. dius 2 817940285x10 15 m Zo Characteristic impendence of 376 7303 13461 Q vacuum aE Compton wavelength 2 426310215x10 12 m xen Neutron Compton wavelength 1 319590898x10 15 m acp Proton Compton wavelength 1 321409847x10 15 m a Fine structure constant 7 297352533x10 3 o Stefan Boltzmann constant 5 6704x10 8 W m K4 t Celsius temperature 273 15 atm Standard atmosphere 101325 Pa y P Proton gyromagnetic ratio 267522212 st Ci First radiation constant 374177 107x10 16 W m2 C2 Second radiation constant 0 014387752 m K Go Conductance quantum 7 74809 1696x10 5 S E The base number of natural 2 71828 182846 logarithm natural constant Reference Peter J Mohr and Barry N Taylor CODATA Recommended Values of the Fundamental Physical Constants 1998 Journal of Physical and Chemical Reference Data Vol 28 No 6 1999 and Reviews of Modern Physics Vol 72 No 2 2000 To insert a constant 1 Position your cursor where you want the constant inserted 2 Press EW CONST to display the physics constants menu 3 Press or you can press ES CONST to access the next page one page at a time to scroll through the menu until the constant you want is underlined then press to insert the constant Note that constants should be referred to by their names rather than their values when used in expressions equations and programs Real Number Functions 4 9 Conversion Functions The HP 35s supports four types of conversion
157. e refer to the product label Hewlett Packard GmbH H TRE Herrenberger Strasse 140 71034 Boeblingen Germany Support Batteries and Service A 13 Japanese Notice COREL FRUBSES ERS AEM MBS VCCI DREE FD DAB RRR E CT COREIA KERR CRATS CCS RWELTLY ETM TOREDIG OTLEY a YEREL TRASNA E VB MEAs SHOT CEMBVET WRAAE oft gt TILLY RY RUALTC ESL Disposal of Waste Equipment by Users in Private Household in the European Union This symbol on the product or on its packaging indicates that this product must not be disposed of with your other household waste Instead it is your responsibility to dispose of your waste equipment by handing it over to a designated collection point for the recycling of waste electrical and electronic equipment The separate collection Hand recycling of your waste equipment at the time of disposal will help to conserve natural resources and ensure that it is recycled in a manner that protects human health and the environment For more information about where you can drop off your waste equipment for recycling please contact your local city office your household waste disposal service or the shop where you purchased the product Perchlorate Material special handling may apply This calculator s Memory Backup battery may contain perchlorate and may require special handling when recycled or disposed in California A 14 Support Batteries and Service User Memory and the Stack This appendix c
158. e same then you have correctly entered all the lines of the program To see your checksum 1 Press EN MEM 2 2 FGM for the catalog of program labels 2 Display the appropriate label by using the cursor keys if necessary 3 Press and hold i to display CE checksum and LH length Simple Programming 13 23 For example to see the checksum for the current program the cylinder program Keys Display Description In RPN mode EN MEM 2 LBL C Displays label C which takes 2PGM ENTER LH 67 67 bytes EN SHOW hold 9 PRES FCS Checksum and length LH 67 If your checksum does not match this number then you have not entered this program correctly You will see that all of the application programs provided in chapters 16 and 17 include checksum values with each labeled routine so that you can verify the accuracy of your program entry In addition each equation in a program has a checksum See To enter an equation in a program line earlier in this chapter Nonprogrammable Functions The following functions of the HP 35s are not programmable Wea CLEAR 3 3PM STO LIL Wed CLEAR 3 ALL GTO LJ label line number Ey MEM lv 4 Cd 2 Ey SHOW Wea PRGM EQN An 6B A Wea EDISP E UNDO Wed CLEAR 6 amp CLVARx Programming with BASE You can program instructions to change the base mode using M BASE These settings w
159. e 1 and line 2 and the sign b o h will be added following the number to represent base 2 8 16 To view the next screen s content in line 2 press ESIL or EL to change the screen Base Conversions and Arithmetic and Logic 11 3 LOGIC Menu Menu label Description AHD Logical bit by bit AND of two arguments For example AND 1 100b 1010b 1000b 0R Logical bit by bit XOR of two arguments For example XOR 1101b 1011b 110b or Logical bit by bit OR of two arguments For example OR 1100b 1010b 1110b HOT Returns the one s complement of the argument Each bit in the result is the complement of the corresponding bit in the argument For example NOT 1011b 111111111111111111111111111111110100b MAHD Logical bit by bit NAND of two arguments For example NAND 1100b 1010b 11111111111111111111111 1111111110111b HOR Logical bit by bit NOR of two arguments For example NOR 1 100b 1010b 111111111111111111111111111111110001b The AND OR XOR NOT NAND NOR can be used as logic functions Fraction complex vector arguments will be seen as an IHYALID DATA in logic function Arithmetic in Bases 2 8 and 16 You can perform arithmetic operations using 4 LE and L in any base The only function keys that are actually deactivated in HEX mode are VJ Le UN LA LZ and However you should realize that most operations other than arithmetic will
160. e REGX REGY REGZ and REGT commands To use these instructions press first Then pressing produces a menu in the display showing the X Y Z T registers Pressing or will move the underline symbol indicating which register is presently selected Pressing will place an instruction into a program or equation that recalls the value of the chosen stack register for further use These are displayed as REGX REGY REGZ and REGT For example a program line entered by first pressing and then entering the instructions REGX x REGY x REGZ x REGT will compute the product of the values in the 4 stack registers and place the result into the X register It will leave the previous values of X Y and Z in the stack registers Y Z and T Many such efficient uses of values in the stack are possible in this manner that would not otherwise be available on the HP35s User Memory and the Stack B 7 ALG Summary About ALG This appendix summarizes some features unique to ALG mode including Two argument arithmetic Exponential and Logarithmic functions W 07 i 0G Wea e re LN Trigonometric functions Parts of numbers Reviewing the stack Operations with complex numbers Integrating an equation Arithmetic in bases 2 8 and 16 Entering statistical two variable data Press 4 4RLG to set the calculator to ALG mode When the calculator is in ALG mode the ALG annunciator is on In ALG mode operations are performed
161. e correction is significant T614 GTO Tesi Goes back to start of loop if correction is significant Continues if correction is not significant THIS RCL Tei VIEW amp Displays the calculated value of X Line T009 calculates the correction for Xguess Line T013 compares the absolute value of the calculated correction with 0 0001 If the value is less than 0 0001 Do If True the program executes line T014 if the value is equal to or greater than 0 0001 the program skips to line T015 14 8 Programming Techniques Flags A flag is an indicator of status It is either set true or clear false Testing a flag is another conditional test that follows the Do if true rule program execution proceeds directly if the tested flag is set and skips one line if the flag is clear Meanings of Flags The HP 35s has 12 flags numbered O through 11 All flags can be set cleared and tested from the keyboard or by a program instruction The default state of all 12 flags is clear The three key memory clearing operation described in appendix B clears all flags Flags are not affected by WEa CLEAR 3 SALL t ENTER Flags 0 1 2 3 and 4 have no pre assigned meanings That is their states will mean whatever you define them to mean in a given program See the example below Flag 5 when set will interrupt a program when an overflow occurs within the program displaying OVERFLOW and An overflow occurs when a result exce
162. e equation Checksum and length A 2 liter bottle contains 0 005 moles of carbon dioxide gas at 24 C Assuming that the gas behaves as an ideal gas calculate its pressure Since Equation mode is turned on and the desired equation is already in the display you can start solving for P Keys Display Description W 3 SOLVE e We Solves for P prompts for V value 2 R S H Stores 2 in V prompts for value N L JO LO S R S R Stores 005 in N prompts value for R L JLO 8 2 1 R S T Stores 0821 in R prompts value for T WAHAB T Calculates T Kelvins 1 ENTER 297 1606 R S SOLV IHG Stores 297 1 in T solves for P P in atmospheres B BEIG A 5 iter flask contains nitrogen gas The pressure is 0 05 atmospheres when the temperature is 18 C Calculate the density of the gas N x 28 V where 28 is the molecular weight of nitrogen Keys Display Description EQN Px HxRxT Displays the equation Wea SOLVE P Solves for N prompts for P B BEIB L LO S R S We Stores 05 in P prompts for 2 8008 V BRs R Stores 5 in V prompts for CREER R R S T Retains previous R prompts 297 1886 for T MAENE BAAB T Calculates T Kelvins goa 291 1600 Solving Equations 7 5 R S SOLVING Stores 291 1 in T solves for H N 8 6165 FAJE ES 0 2929 Calculates mass in grams Nx 28 RAMA B B586 Calculates density in grams per liter Solving built in Equation
163. e is current value of L Stores L calculates V in cubic inches and stores the result in V 6 2 Entering and Evaluating Equations Summary of Equation Operations All equations you create are saved in the equation list This list is visible whenever you activate Equation mode You use certain keys to perform operations involving equations They re described in more detail later When displaying equations in the equation list two equations are displayed at a time The currently active equation is shown on line 2 Key Operation Enters and leaves Equation mode Evaluates the displayed equation If the equation is an assignment evaluates the right hand side and stores the result in the variable on the left hand side If the equation is an equality or expression calculates its value like XEQ See Types of Equations later in this chapter XEQ Evaluates the displayed equation Calculates its value replacing with if an is present SOLVE Solves the displayed equation for the unknown variable you specify See chapter 7 w Integrates the displayed equation with respect to the variable you specify See chapter 8 EJ Deletes the current equation or deletes the element to the left of the cursor C or Begins editing the displayed equation only moving the cursor and not deleting any content A or FE Scroll the current equation display screen LA or Steps up or down through
164. e number of digits displayed the faster the calculation but the calculator will presume that the function is accurate to the only number of digits specified To specify the accuracy of the integration set the display format so that the display shows no more than the number of digits that you consider accurate in the integrand s values This same level of accuracy and precision will be reflected in the result of integration If Fraction display mode is on flag 7 set the accuracy is specified by the previous display format Interpreting Accuracy After calculating the integral the calculator places the estimated uncertainty of that integral s result in the Y register Press to view the value of the uncertainty For example if the integral Si 2 is 1 6054 0 0002 then 0 0002 is its uncertainty 8 6 Integrating Equations Example Specifying Accuracy With the display format set to SCI 2 calculate the integral in the expression for Si 2 from the previous example Keys Display Description Ey DIsPLAy 2 1 6168 Sets scientific notation with two 28C1 2 decimal places specifying that the function is accurate to two decimal places RY RY B ABEG Rolls down the limits of integration 2 BBE from the Z and T registers into the X and Y registers EQN SIHCHI H Displays the current Equation Ey x INTEGRATING The integral approximated to two j decimal places 1 61668 EZDI 1 61E 2 The uncertainty of the a
165. e the replicating effect of to clear the stack quickly press O ENTER ENTER ENTER All stack 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 feature of to other advantages To add a number to itself press 2 6 RPN The Automatic Memory Stack Filling the stack with a constant The replicating effect of together with the replicating effect of stack drop from T into Z allows you to fill the stack with a numeric constant for calculations Example Given bacterial culture with a constant growth rate of 50 per day how large would a population of 100 be at the end of 3 days Replicates T register B mim H m Z 4 m 7 1 Fills the stack with the growth rate Keys in the initial population Calculates the population after 1 day Calculates the population after 2 days AOR UON Calculates the population after 3 days How to Clear the Stack Clearing the X register puts a zero in the X register The next number you key in or recall writes over this zero There are four ways to clear the contents of the X register that is to clear x 1 Press LC 2 Press Le 3 Press Wa CLEAR 1 1 Mainly used during program entry 4 Press Wea CLEAR 5 S5TE to clear the X Y Z and T registers to zero For example if you intended to enter 1 and 3 but mistakenly entered
166. eds the largest number that the calculator can handle The largest possible number is substituted for the overflow result If flag 5 is clear a program with an overflow is not interrupted though OWERFLOM is displayed briefly when the program eventually stops Flag 6 is automatically set by the calculator any time an overflow TOO BIG occurs although you can also set flag 6 yourself It has no effect but can be tested Besides when using non decimal bases in programs flag 6 also gets set for TOO BIG in programs Flags 5 and 6 allow you to control overflow conditions that occur during a program Setting flag 5 stops a program at the line just after the line that caused the overflow By testing flag 6 in a program you can alter the program s flow or change a result anytime an overflow occurs Flags 7 8 and 9 control the display of fractions Flag 7 can also be controlled from the keyboard When Fraction display mode is toggled on or off by pressing Wea EDISP flag 7 is set or cleared as well Programming Techniques 14 9 Flag Fraction Control Flags Status 7 8 9 Clear Fraction display Fraction Reduce fractions to Default off display real denominators not smallest form numbers in the greater than the c current display value format Set Fraction display Fraction No reduction of on display real denominators are fractions Used numbers as factors of the c only if flag 8 is fractions Value set 14
167. eeetteeeeeaes 13 22 Contents 7 Clearing One or More Programs ssccceeesseeeeetteeeenneeees 13 23 The Checksum oa ss ds tate tatesstatatnasaten auasees aaantauan ta an tana 13 23 Nonprogrammable Functions cccsseeeseeeeeeeetetteeeeeeeneees 13 24 Programming with BASE 2 hcansata havea tgoumbarctetwetgembureiiottees 13 24 Selecting a Base Mode in a Program cccccccesesseeeeeeeteees 13 25 Numbers Entered in Program Lines cccssccceeeeeeetteeees 13 25 Polynomial Expressions and Horner s Method cceceeeeeees 13 26 14 Programming Techniques scsscsssssreeseeeseeees 14 1 Routines in Programs cccccessseeecceceeeeeneeececeeeaeaeeeeeeeeeueenes 14 1 Calling Subroutines XEQ RTN ceeccceeeeeeeetteeeeeeeeseeeees 14 1 Nested Subroutines ccccesessseceeeeseceeeeeeeeereeeeeeneenaeeeeee 14 2 BrehehiigtG lO tthe Ran ea as 14 4 A Programmed GTO Instruction syswsscicvven veenevevestkver ive vane 14 5 Using GTO from the Key board asad ced wadvugdeeteavgiasieniuaadtves 14 5 Conditional msttuchOnSss cicalsssncedtesduien tans arama anaes 14 6 Tests of Comparison x y 20 anita ucatncscntentoicrs 14 7 FAOS a e E E AP adnuuceinelt 14 9 LOOPS EE AANE EEE E A A 14 16 Conditional Loops GTO sssssnnsssessoissssseesssssseerrssseetersee 14 17 Loops with Counters DSE ISG ssosnseosoeooseeesoeeesereeeeee 14 18 Indirectly Addressing Variables and Labe
168. een their LLI LLI arguments such as and For such infix operators enter them in an equation in the same order Other functions normally have one or more arguments after the function name such as COS and LN For such prefix functions enter them in an equation where the function occurs the key you press puts a left parenthesis after the function name so you can enter its arguments m Ifthe function has two or more arguments press LO to separate them Entering and Evaluating Equations 6 5 Parentheses in Equations You can include parentheses in equations to control the order in which operations are performed Press to insert parentheses For more information see Operator Precedence later in this chapter Example Entering an Equation Enter the equation r 2 x c x t a 25 Keys EQN RCL R W a ESEON E o RCL T RCL WIC IGIZIS ENTER EN SHOW K Display V B 25x7_7ex0 2xL R 20 Ree2xCx_ R 2xCxto S2xCxCT Rat 25 _ R 2xCx T Aates CK SE5F LH 14 Description Shows the last equation used in the equation list Starts a new equation with variable R Enters a number Enters infix operators Enters a prefix function with a left parenthesis Enters the argument and right parenthesis Terminates the equation and displays it Shows its checksum and length Leaves Equation mode Displaying and Selecting Equations The equation
169. efined The INPUT I INPUT J and VIEW I VIEW J operations label the display with the name of the indirectly addressed variable or register The SUMS menu enables you to recall values from the statistics registers However you must use indirect addressing to do other operations such as STO VIEW and INPUT The functions listed below can use I or J as an address For FN I or J refers to a label for all other functions I or J refers to a variable or register 14 22 Programming Techniques STO I J INPUT I J RCL I J VIEW I J STO x 1 3 DSE I J RCL x 1 3 ISG I J X lt gt I J SOLVE I J FN I J FN d I J You can not solve or integrate for unnamed variables or statistic registers Program Control with I J Since the contents of can change each time a program runs or even in different parts of the same program a program instruction such as STO I or J can store value to a different variable at different times For example STO 1 indicates storing the value in Variable A This maintains flexibility by leaving open until the program runs exactly which variable or program label will be needed Indirect addressing is very useful for counting and controlling loops The variable I or J serves as an index holding the address of the variable that contains the loop control number for the functions DSE and ISG Equations with I J You
170. egrate one unknowingly A function that could lead to incorrect results can be identified in simple terms by how rapidly it and its low order derivatives vary across the interval of integration Basically the more rapid the variation in the function or its derivatives and the lower the order of such rapidly varying derivatives the less quickly will the calculation finish and the less reliable will be the resulting approximation More about Integration E 5 Note that the rapidity of variation in the function or its low order derivatives must be determined with respect to the width of the interval of integration With a given number of sample points a function f x that has three fluctuations can be better characterized by its samples when these variations are spread out over most of the interval of integration than if they are confined to only a small fraction of the interval These two situations are shown in the following two illustrations Considering the variations or fluctuation as a type of oscillation in the function the criterion of interest is the ratio of the period of the oscillations to the width of the interval of integration the larger this ratio the more quickly the calculation will finish and the more reliable will be the resulting approximation f x 1 I Calculated integral ofthis function will be accurate I I I I I I I Calculated integral Of this function may be inaccurate 1
171. egration instructions appear in the program as FH label JFH 4 variable The programmed FN instruction does not produce a labeled display J value since this might not be the significant output for your program that is you might want to do further calculations with this number before displaying it If you do want this result displayed add a PSE Wza or STOP R S instruction to display the result in the X register after the J FN instruction If the PSE instruction immediately follows an equation that is displayed Flag 10 set during each iteration of integrating or solving the equation will be displayed for 1 second and execution will continue until the end of each iteration During the display of the equation no scrolling or keyboard input is allowed Example FN in a Program The Normal and Inverse Normal Distributions program in chapter 16 includes an integration of the equation of the normal density function D M 2 I 2 D dD 5 Jin M e The e 2 S 2 function is calculated by the routine labeled F Other routines prompt for the known values and do the other calculations to find Q D the upper tail area of a normal curve The integration itself is set up and executed from routine Q 15 10 Solving and Integrating Programs GEG1 LBL aee2 RCL M Recalls lower limit of integration Hees RCL Recalls upper limit of integration X D e e 4 FH F Specifies the function 8685 FH
172. el for example A001 GTO A ENTER press and hold the display will show GTO ABB1 Conditional Instructions Another way to alter the sequence of program execution is by a conditional test a true false test that compares two numbers and skips the next program instruction if the proposition is false For instance if a conditional instruction on line A005 is that is is x equal to zero then the program compares the contents of the X register with zero If the X register does contain zero then the program goes on to the next line If the X register does not contain zero then the program skips the next line thereby branching to line A007 This rule is commonly known as Do if true ABBI LELA Do next if true ARBES x 67 gt 00 Skip next if false ABBE CTO BeBi Aber LH 0 RAGES STOR BGGi LBL B The above example points out a common technique used with conditional tests the line immediately after the test which is only executed in the true case is a branch to another label So the net effect of the test is to branch to a different routine under certain circumstances There are three categories of conditional instructions 14 6 Programming Techniques Comparison tests These compare the X and Y registers or the X register and zero Flag tests These check the status of flags which can be either set or clear m Loop counters These are usually used to loop a specified number
173. en press CP For y lt O x must be an integer To Calculate Press Result J96 WAKA 14 8886 3 125 LO 2I S CAIENTER 3 ay 5 BEGG pr 4625 L6 ZI SJENTER 4 EZ 5 GREG 14 37893 QOLAT 2 e006 l OMIM Trigonometry Entering 7 Press Et to place the first 12 digits of m into the X register The number displayed depends on the display format Because EW Z is a function that returns an approximation of 7 to the stack it is not necessary to press Note that the calculator cannot exactly represent n since is a transcendental number Real Number Functions 4 3 Setting the Angular Mode The angular mode specifies which unit of measure to assume for angles used in trigonometric functions The mode does not convert numbers already present see Conversion Functions later in this chapter 360 degrees 2r radians 400 grads To set an angular mode press MODE A menu will be displayed from which you can select an option Option Description Annunciator DEG Sets degree mode which uses decimal degrees rather than hexagesimal degrees degrees minutes seconds RAD Sets radian mode RAD none GRAD Sets gradient mode GRAD Trigonometric Functions With x in the display To Calculate Press Sine of x SIN Cosine of x COS Tangent of x TAN Arc sine of x E ASIN Arc cosine of x
174. enter and return information For input you can prompt for a variable with the INPUT instruction you can get an equation to prompt for its variables or you can take values entered in advance onto the stack Simple Programming 13 5 For output you can display a variable with the VIEW instruction you can display a message derived from an equation you can display process in line 1 you can display the program result in line 2 or you can leave unmarked values on the stack These are covered later in this chapter under Entering and Displaying Data Entering a Program Pressing Wea toggles the calculator into and out of Program entry mode turns the PRGM annunciator on and off Keystrokes in Program entry mode are stored as program lines in memory Each instruction command or expression occupies one program line In ALG mode you can enter an expression directly in a program To enter a program into memory 1 Press Wea to activate Program entry mode 2 Press GTO LIL to display FREM TOP This sets the program pointer to a known spot before any other programs As you enter program lines they are inserted before all other program lines If you don t need any other programs that might be in memory clear program memory by pressing WB CLEAR L3 3F G To confirm that you want all programs deleted press after the message CLR PGMS YH 3 Give the program a label a single letter A through Z Press Wa
175. ep 3 in the above list If you want to use different limits begin at step 2 To work another problem using a different equation start over from step 1 with an equation that defines the integrand 8 2 Integrating Equations Example Bessel Function The Bessel function of the first kind of order O can be expressed as lez J x A cos x sin f dt Find the Bessel function for x values of 2 and 3 Enter the expression that defines the integrand s function cos x sin f Keys Display Wea CLEAR 3 3ALL lt ENTER EQN SES lin salve EQH LIST TOP COS cosex3 x SIN COS kxSINGD RCL COSCXxSINCTI3 DIR COSCKxSINETI 9 ENTER COS CekxSIHCT 33 Est SHOW CK E1EC LH 13 Cc Description Clears memory Selects Equation mode Types the equation Terminates the expression and displays its left end Checksum and length Leaves Equation mode Now integrate this function with respect to t from zero to 1 x 2 Keys Display MODE 2 2R AD CO ENTER EN 7 F idia EQN COS HxSINGT I ey FM a Description Selects Radians mode Enters the limits of integration lower limit first Displays the function Prompts for the variable of integration Integrating Equations 8 3 o H7 Prompts for value of X value 2 R s INTEGRATING x 2 Starts integrating j calculates result for B r34 z Jf amp B 2239 The final result for J 2 Now calculate Jo 3 with
176. er 3A6h 16611666b 6348h TAGh b16611666b 1 592 6666 Sets base 8 OCT annunciator on Converts displayed number to octal Integer part of result Set base 16 HEX annunciator on Result in hexadecimal base Restores decimal base Entering Statistical Two Variable Data In ALG mode remember to enter an x y pair in reverse order y xory x so that y ends up in the Y register and X in the X register 1 Press Wea CLEAR 4 4 to clear existing statistical data 2 Key in the y value first and press 3 Key in the corresponding x value and press 2 ALG Summary C 11 4 The display shows n the number of statistical data pairs you have accumulated 5 Continue entering x y pairs n is updated with each entry If you wish to delete the incorrect values that were just entered press 2 After deleting the incorrect statistical data the calculator will display the last statistical data entered in line 1 top line of the display and value of n in line 2 If there are no statistical data the calculator will display n 0 in line 2 Example After keying in the x y values on the left make the corrections shown on the right Initial x y Corrected x y 20 4 20 5 400 6 40 6 Keys Display Description FES CLEAR 4 45 Clears existing statistical data 4 Y 2 0 E 26 y Enters the first new data pair 1 6666 6
177. er the beginning balance is positive while money paid out is negative Miscellaneous Programs and Equations 17 5 Part 2 What interest rate would reduce the monthly payment by 10 Keys Display Description In RPN mode EQN Pi x 1 1 1 m Displays the leftmost hart of the TVM equation Fes SOLVE 1 P Selects prompts for P 156 59 Lel P Rounds the payment to two decimal 156 59 places ERLI G P Calculates new payment 176 59 R S H Stores 176 89 in P prompts for N 36 86 R S F Retains 36 in N prompts for F B 86 R S B7 Retains O in F prompts for B Jro B R S SOLVING Retains 5750 in B calculates I monthly interest rate 8 56 mae 6 75 Calculates annual interest rate Part 3 Using the calculated interest rate 6 75 assume that you sell the car after 2 years What balance will you still owe In other words what is the future balance in 2 years Note that the interest rate from part 2 is not zero so you won t get a DIVIDE BY error when you calculate the new I Keys Display Description In RPN mode EQN Pxi xti 1 I m Displays leftmost part of the TVM equation LIRNA P Selects F prompts for P ir6 59 R S I Retains P prompts for l B 6 17 6 Miscellaneous Programs and Equations R S H Retains 0 56 in J prompts for N 36 68 aW Rs B Stores 24 in N prompts for B 3 708 B R S SOLVING Retains 5750 in B calculates F the F future balance Again
178. er of decimal places in the display A Use the DISPLAY menu page 1 21 Q How do I clear all or portions of memory A TEX CLEAR displays the CLEAR menu which allows you to clear x the number in the X register all direct variables all of memory all statistical data all stack levels and all indirect variables Q What does an E in a number for example 2 1E 14 mean Support Batteries and Service A 1 A Exponent of ten that is 2 51 x 10 13 Q The calculator has displayed the message MEMORY FULL What should do A You must clear a portion of memory before proceeding See appendix B Q Why does calculating the sine or tangent of radians display a very small number instead of 0 A n cannot be represented exactly with the 12 digit precision of the calculator Q Why do get incorrect answers when use the trigonometric functions A You must make sure the calculator is using the correct angular mode MODE 1DEG 2RAD or ZGRD Q What does an annunciator in the display mean A It indicates something about the status of the calculator See Annunciators in chapter 1 Q Numbers show up as fractions How do get decimal numbers A Press fea FDISP Environmental Limits To maintain product reliability observe the following temperature and humidity limits Operating temperature O to 45 C 32 to 113 F a Storage temperature 20 to 65 C 4 to 149 F m Operating
179. erformed that erase them and will be displayed if the decimal base is selected Convert 24FF16 to binary base The binary number will be more than 14 digits the maximum display long Keys Display Description TA BASE 2 ZHEX 24FFh Use the key to type F WA a EAEE 6h 11 2 Base Conversions and Arithmetic and Logic WE BASE 4 4B 1N The entire binary number does 16616811111111m not fit The annunciator indicates that the number continues to the right LISS 4 Displays the rest of the number The full number is 10010011111111 LEE 10610611111111 Displays the first 14 digits again Wea BASE 1 DEC 2 471 888 Restores base 10 you can use menu to enter base n sign b o d h following the operand to represent 2 8 10 16 base number in any base mode A number without a base sign is a decimal number Note In ALG mode 1 The result s base mode is determined by the current base mode setting 2 If there is no active command line there is no blinking cursor on line 1 changing the base will update line 2 to be in the new base 3 After pressing or changing the base mode calculator will automatically add a current base sign b o h following the result to represent base 2 8 16 number in line 2 4 To edit expression again press or In RPN mode When you enter a number in line 2 press ENTER and then change the base mode the calculator will convert the base of the numbers in lin
180. es are about the same so the approximation will be fairly accurate if f x is one of these functions However the actual integral of the function shown with a dashed line is quite different from those of the others so the current approximation will be rather inaccurate if f x is this function The algorithm comes to know the general behavior of the function by sampling the function at more and more points If a fluctuation of the function in one region is not unlike the behavior over the rest of the interval of integration at some iteration the algorithm will likely detect the fluctuation When this happens the number of sample points is increased until successive iterations yield approximations that take into account the presence of the most rapid but characteristic fluctuations For example consider the approximation of f xe dx 0 Since you re evaluating this integral numerically you might think that you should represent the upper limit of integration as 10499 which is virtually the largest number you can key into the calculator More about Integration E 3 Try it and see what happens Enter the function f x xe Keys Display Description EQN Select equation mode RCL OQ es 27 Me EMP Enter the equation 12 RCL CX ENTER WE MPM End of the equation EN SHOW CK 2FE6 Checksum and length LH 9 K Cancels Equation mode Set the display format to SCI 3 specify the lower and upper limits of integr
181. etH 6 Redisplays the equation F 3 SOLVE XX SOLVING Calculates negative root using a guesses O and 10 3 BEBE RD REN SHOW amp 88eeeeReeeR fx 0 Certain cases require special consideration m If the function s graph has a discontinuity that crosses the x axis then the SOLVE operation returns a value adjacent to the discontinuity see figure a below In this case f x may be relatively large More about Solving D 5 m Values of f x may be approaching infinity at the location where the graph changes sign see figure b below This situation is called a pole Since the SOLVE operation determines that there is a sign change between two neighboring values of x it returns the possible root However the value for f x will be relatively large If the pole occurs at a value of x that is exactly represented with 12 digits then that value would cause the calculation to halt with an error message f x f x a Special Case A Discontinuity and a Pole Example A Discontinuous Function Find the root of the equation IP x 1 5 Enter the equation Keys Display Description EQN Selects Equation mode EN INTC 6 1F Enter the equation Red dA EWE LL IS ENTER IPCHI 1 5 Kav SHOW Ck 02C1 Checksum and length LH 9 Cancels Equation mode D 6 More about Solving Now solve to find the root Keys Display Description 0 FES STO 5 Your initial guesses for the root ENTER 5 j E
182. eteeees 11 8 Using base in program and equations cceceeeeeeeeeeeeees 11 8 12 Statistical Operations sscsscssscesseecsseeesseeeeees 12 1 Entering Statistical Data a s1s20sacseeunsaontectu venue ten cena enusoanatenyes 12 1 Entering One Variable Data ecececcceeeeescreeeeeeeeeneeeeeees 12 2 Entering Two Variable Data ececeseceeeeeeteeeeeeeeeneeeeeene 12 2 Correcting Errors in Data Entry eseeeeeeeeeeeeeeeeeeeeeeees 12 2 Statistical Calculations cscs csecuy cetvan tenet tanec eee eters 12 4 M an rice rie cin ie halen etn enadeta naan nab Meee i e ad eaeaes 12 4 Sample Standard Deviation ccccceeceeceeeeeeesteeeeeentteeees 12 6 Population Standard Deviation ccccccceeeesseeeeeeeeeeneeeeeeees 12 7 Linear Regressions einen nenna aE Ee 12 7 Limitations on Precision of Data ccccccceesseeeeeseeeeeeteeeneaes 12 10 Summation Values and the Statistics Registers ceeeeeee 12 11 Summation Statistics a a i as 12 11 Access to the Statistics Registers ccsssssseeeeeeesteeeeeeeees 12 12 6 Contents Part2 Programming 13 Simple Programming sscssssssscsseesecesesseeseeees 13 1 Designing iG Programi sams aneneen aTe e ETE 13 3 Selecting a Mode so iivcaisvaieataasssninsiotstveswwoosaoevanetucsntiaeds 13 3 Program Boundaries LBL and RTN ceeeeeeerreeeeeeeeeees 13 4 Using RPN ALG and Equations in Progr
183. etic inside 3 6 catalog of 1 28 3 4 clearing 1 28 clearing all 1 5 clearing while viewing 13 15 exchanging with X 3 8 in equations 6 3 7 1 in programs 13 12 15 1 15 7 indirect addressing 14 20 14 21 names 3 1 number storage 3 1 of integration 8 2 15 7 C 8 polynomials 13 26 program input 13 14 program output 13 15 13 18 recalling 3 2 3 4 separate from stack 3 2 showing all digits 13 15 solving for 7 1 15 1 15 6 D 1 testing 14 7 storing 3 2 unaffected by VIEW 13 15 storing from equation 6 12 typing name 1 3 viewing 3 4 13 15 13 18 vectors absolute value 10 3 addition subtraction 10 1 angle between two vectors 10 5 coordinate conversions 4 12 9 5 creating vectors from variables or registers 10 8 cross product 17 11 dot product 10 4 in equation 10 6 in program 10 7 VIEW displaying program data 13 15 13 18 15 6 displaying variables 3 4 no stack effect 13 15 stopping programs 13 15 volume conversions 4 14 W weight conversions 4 14 weighted means 12 4 windows binary numbers 11 8 X XEQ evaluating equations 6 10 6 12 running programs 13 10 13 22 X ROOT arguments 6 17 X register affected by prompts 6 14 arithmetic with variables 3 6 clearing 1 5 2 3 2 7 clearing in programs 13 7 displayed 2 3 during programs pause 13 19 exchanging with variables 3 8 exchanging with Y 2 4 not clearing 2 5 part of stack 2 1 Index 11 Index 12
184. eviously just press G4 If the number has an exponent affects only the mantissa the non exponent part of the number Exponents of Ten Exponents in the Display Numbers with explicit powers of ten such as 4 2x10 are displayed with an E preceding the exponent of 10 Thus 4 2x10 is entered and displayed as 4 2E 5 A number whose magnitude is too large or too small for the display format will automatically be displayed in exponential form For example in FIX 4 format for four decimal places observe the effect of the following keystrokes Getting Started 1 15 Keys Display Description 0016100 00 a BAGGEZ Shows number being entered 0 0 6 2 ENTER B 8681 Rounds number to fit the display format wama 4 28 E 5 Automatically uses scientific notation waang because otherwise no significant digits ENTER would appear Keying in Powers of Ten The LE key is used to enter powers of ten quickly For example instead of entering one million as 1000000 you can simply enter MJ EILE The following example illustrates the process as well as how the calculator displays the result Example Suppose you want to enter Planck s constant 6 6261x1034 Keys Display Description WAA 4 Enter the mantissa m 6 6261_ a 2 Equivalent to x10 6 621E_ S L4IGA ENTER 6 6e1E 34 Enter the exponent 6 621E 34 For a power of ten without a multiplier as in the example of one million above press
185. fer execution to a part of the program other than the next line This is called branching Unconditional branching uses the GTO go fo instruction to branch to a specific program line label and line number 14 4 Programming Techniques A Programmed GTO Instruction The GTO label instruction press label line number transfers the execution of a running program to the specified program line The program continues running from the new location and never automatically returns to its point of origination so GTO is not used for subroutines For example consider the Curve Fitting program in chapter 16 The GTO Z 1 instruction branches execution from any one of three independent initializing routines to LBL Z the routine that is the common entry point into the heart of the program S 1 LBL Can start here S664 GTO 2661 4 Branches to Z001 Le i LBLL Can start here L 64GTO 2661 gt 00 Branches to Z001 Ee iLBLE Can start here ES 64 GTO 2661 4 Branches to Z001 61LBL2 0 Branch to here Using GTO from the Keyboard You can use to move the program pointer to a specified label line number without starting program execution Programming Techniques 14 5 m To PRGM TOP og m Toa specific line number label line number line number lt 1000 For example CTO LJAMO L For example press CTO AJ LO 5 The display will show GTO ARBES If you want to go to the first line of a lab
186. format E B 6834 Angle Conversions When converting to radians the number in the x register is assumed to be degrees when converting to degrees the number in the x register is assumed to be radians Real Number Functions 4 13 To convert an angle between degrees and radians Example In this example we convert an angle measure of 30 to 7 6 radians Keys Display Description Io 8 8888 Enter the angle in degrees 36 Eat CRAD B BABA Convert to radians Read the result 8 5236 as 0 5236 a decimal approximation of 1 6 Unit Conversions The HP 35s has ten unit conversion functions on the keyboard kg gt lb C gt F gt cm gt in gt l gt gal gt MILE gt KM To Convert To Press Displayed Results 1 lb kg ERILE 6 4336 kilograms 1 kg lb MM 2 2846 pounds 32 F C ERFA Le Ee 6 BBBG C 100 C F 1 CO LO Ea 212 8886 F l in cm 1 Wea cm 2 5488 centimeters 100 cm in 1 LO LO EE in 32 3781 inches 1 gal 1 Wea 1 3 7854 liters 11 gal 1 at 0 B 2642 gallons 1 MILE KM momen 1 6893 KMS 1KM MILE GG GME amp 6214 MilES 4 14 Real Number Functions Probability Functions Factorial To calculate the factorial of a displayed non negative integer x O lt x lt 253 press FX C the right shifted key Gamma To calculate the gamma function of a noninteger
187. fraction display Keys In RPN mode Ea MARS R S R S WABE 22 F CIW Loops R S O FLAGS Display We value Oo value DECIMAL 16 8868 2 93868 MOST PRECISE 28 liw 26415 FACTOR DEHOM 2ivea 212 FIsED DEHOM 28 164 Description Executes label F prompts for a fractional number V Stores 2 53 in V prompts for denominator D Stores 16 as the c value Displays message then the decimal number Message indicates the fraction format denominator is no greater than 16 then shows the fraction w indicates that the numerator is a little below 8 Message indicates the fraction format denominator is factor of 16 then shows the fraction Message indicates the fraction format denominator is 16 then shows the fraction Stops the program and clears flag 10 Branching backwards that is to a label in a previous line makes it possible to execute part of a program more than once This is called looping D661 LBL O Dee2 INPUT M DB63 INPUT H D664 INPUT T D665 GTO DEGI 14 16 Programming Techniques This routine is an example of an infinite loop lt can be used to collect the initial data After entering the three values it is up to you to manually interrupt this loop by pressing label line number to execute other routines Conditional Loops GTO When you want to perform an operation until a certain condition is met but you don t
188. g sure that the positive sign is facing outward 6 Remove and insert the other battery as in steps 4 through 5 Make sure that the positive sign on each battery is facing outward 7 Replace the battery compartment cover 8 Press C Testing Calculator Operation Use the following guidelines to determine if the calculator is working properly Test the calculator after every step to see if its operation has been restored If your calculator requires service refer to page A 8 The calculator won t turn on steps 1 4 or doesn t respond when you press the keys steps 1 3 1 Reset the calculator Hold down the key and press GTO It may be necessary to repeat these reset keystrokes several times 2 Erase memory Press and hold down CJ then press and hold down both and Li Memory is cleared and the MEMORY CLEAR message is displayed when you release all three keys A 4 Support Batteries and Service 3 Remove the batteries see Changing the Batteries and lightly press a coin against both battery contacts in the calculator Replace the batteries and turn on the calculator It should display MEMORY CLEAR 4 If the calculator still does not respond to keystrokes use a thin pointed object to press the RESET hole Stored data usually remain intact Reset Hole RESET CL If these steps fail to restore calculator operation it requires service If the calculator responds to keystrokes but you suspect that
189. gram entry executes the 13 20 current program line not during program entry orl Moves the cursor and does not 1 14 delete any content BJ o FED Scrolls the display to show more 1 11 digits to the left and right displays 6 4 the rest of an equation or binary 11 8 number goes the next menu page in the CONST and SUMS menus a Goes to the top line of the equation 6 3 or the first line of the last label in program mode a Goes to the last line of the equation 6 3 or the first line of the next label in program mode L Separates the two or three 6 5 arguments of a function 1 x UZ Reciprocal 1 18 10x ra Common exponential 4 2 Returns 10 raised to the x power WE3 Percent 4 6 Returns y x x 100 CHG E 4CHG Percent change 4 6 Returns x y 100 y T E Z Returns the approximation 4 3 3 14159265359 12 digits X Accumulates y x into statistics 12 2 registers as EV Removes y x from 12 2 statistics registers x Wes SUMS L 12 11 Returns the sum of x values G 2 Operation Index Name Keys and Description Page x2 xy Ly xy Ox oy J FN d variable a mmaa Returns the sum of squares of x values Aasum ANAA 2x Returns the sum of products of x and y values Wea SUMS gt 2 Returns the sum of y values Wea SUMS DID IDI 23 Returns the sum of squares of y values Wea SO IL 0 Returns p
190. he maximum denominator value enter the value and then press EW Uc Fraction display mode will be automatically enabled The value you enter cannot exceed 4095 m To recall the c value to the X register press LL EW lt m To restore the default value to 4095 press LO EW La or enter any value greater than 4095 as the maximum denominator Again Fraction display mode will be automatically enabled The c function uses the absolute value of the integer part of the number in the X register It doesn t change the value in the LAST X register If the displayed fraction is too long to fit in the display the I gt annunciator will appear you can then use PIL and Fa J to scroll page by page to see the rest of the fraction To see the number s decimal representation press EW and then hold SHOW Example This example illustrates the steps required to set the maximum denominator to 3125 and then show a fraction that is too long for the display Keys Display Description BOWE Set the maximum denominator to A 3125 1 4 fe e 6 Note the missing digits in the 1282664 888731 denominator LD 6 Scroll right to see the rest of the 25 denominator Notes 1 In ALG mode you can enter an expression in line 1 and then press EW Uc In this case the expression is evaluated and the result is used to determine the maximum denominator Fractions 5 5 2 In ALG mode you can use the result of a
191. he operand for a noncommutative two argument operation in the wrong order in RPN mode simply press the key to exchange the contents in the x and y registers This is explained in detail in Chapter 2 see the section entitled Exchanging the X and Y Registers in the Stack Controlling the Display Format All numbers are stored with 12 digit precision however you may control the number of digits used in the display of numbers via the options in the Display menu Press Kai to access this menu The first four options FIX SCI ENG and ALL control the number of digits in the display of numbers During some complicated internal calculations the calculator uses 15 digit precision for intermediate results The displayed number is rounded according to the display format Fixed Decimal Format F 1 FIX format displays a number with up to 11 decimal places 11 digits to the right of the or radix mark if they fit After the prompt F 1 _ type in the number of decimal places to be displayed For 10 or 11 places press CIO or LJUN For example in the number 123 456 7682 the 7 0 8 and 9 are the decimal digits you see when the calculator is set to FIX 4 display mode Any number that is too large 10 or too small 10 to display in the current decimal place setting will automatically be displayed in scientific format Getting Started 1 21 Scientific Format SC 1 SCI format displays a number in scientific nota
192. hecksums 6 19 B 2 equation lengths 6 19 B 2 number digits 1 25 13 7 program checksums 13 22 B 2 program lengths 13 22 B 2 prompt digits 6 14 14 14 sample standard deviations 12 6 SCI format See display format in programs 13 7 setting 1 22 scrolling binary numbers 11 8 equations 6 7 13 7 13 16 seed random number 4 15 self test calculator A 5 shift keys 1 3 sign of numbers 1 15 9 3 11 6 sign conventions finance 17 1 Sign value 4 17 sine trig 4 4 9 3 A 2 C 6 single step execution 13 11 slope curve fit 12 8 16 1 SOLVE checking results 7 7 D 3 discontinuity D 5 evaluating equations 7 1 7 7 evaluating programs 15 2 flat regions D 8 how it works 7 7 D 1 in programs 15 6 initial guesses 7 2 7 7 7 8 7 12 15 6 minimum or maximum D 8 multiple roots 7 9 no restrictions 15 11 no root found 7 8 15 6 D 8 pole D 6 purpose 7 1 results on stack 7 2 7 7 D 3 resuming 15 1 round off D 13 stopping 7 2 7 8 using 7 1 stack See stack lift affected by prompts 6 14 13 14 complex numbers 9 2 effect of 2 6 equation usage 6 1 exchanging with variables 3 8 exchanging X and Y 2 4 filling with constant 2 7 long calculations 2 12 operation 2 1 2 5 9 2 program calculations 13 14 program input 13 12 program output 13 12 purpose 2 1 2 2 registers 2 1 reviewing 2 3 C 7 rolling 2 3 C 7 separate from variables 3 2 Index 9 size limit 2 4 9 2 unaffected by VIEW 13 15 stack lift See stack default sta
193. heme is circular so E H LIST TOP is also the equation after the last equation in equation memory The calculator is calculating the integral of an equation or program This might take a while A running CALCULATE SOLVE or FN operation was interrupted by pressing or in ALG RPN EQN or PGM mode Data error m Attempted to save or calculate error data m Attempted to calculate combinations or permutations with r gt n with non integer ror n or with n 1016 m Attempted to save a complex number or vector in the statistical data m Attempted to save a base n number that contains digits greater than the largest base n number digit allowed m Attempted to save an invalid data in the statistical register using operation m Attempt to compare complex numbers or vectors m Attempted to use a trigonometric or hyperbolic function with an illegal argument m TAN with x an odd multiple of 90 u FE ACOS or FES ASIN with x lt 1 or x gt 1 m Ee HYP Wed ATAN with x lt 1 or x gt 1 m ES HYP A ACOS with x lt 1 Attempted to enter an invalid variable name when solving an equation Attempted a factorial or gamma operation with x as a negative integer INVALIO vx INVALIO T gt IHVALID J LOG Bs LOG CHEG2 MEMORY CLEAR MEMORY FULL HO HOHES ISTENT HO LABELS HO SOLUTIOHW MULT SOLUTIOW Exponentiation error m Attempted to raise O to the Oth power or to
194. hown below 14 2 Programming Techniques MAIN program Top level LBLAOOT LBLBOOT LBLCOOT 4 LBL DOOI Z Y v XEQ B001 XEQ C001 XEQ D001 SN w 3 1416 x RMDR CRN en en T Torn End of program Attempting to execute a subroutine nested more than 20 levels deep causes an E OVERFLOW error Example A Nested Subroutine The following subroutine labeled S calculates the value of the expression va b c d as part of a larger calculation in a larger program The subroutine calls upon another subroutine a nested subroutine labeled Q to do the repetitive squaring and addition This saves memory by keeping the program shorter than it would be without the subroutine Programming Techniques 14 3 In RPN mode S661 LBL S862 INPUT A S663 IHPUT E S664 IHPUT C S665 IHPUT O Starts subroutine here Enters A Enters B Enters C Enters D SBE RCL D Recalls the data SEF REL C S665 REL S669 RCL A 818 x2 A2 S611 SEG Geel gt D A2 B2 gt 812 xEA A881 gt O A2 B2 C2 gt 5013 EG ROBIL gt O A2 B2 C2 D2 gt 5814 fx VA B C D S615 RTH Returns to main routine 661 LEL Q 000 Nested subroutine QB 2 xiy QEZ x2 QBG4 Adds x2 e 8485 RTH Returns to subroutine S Branching GTO As we have seen with subroutines it is often desirable to trans
195. i Sets display form SINJ 2 JL3ILi_ SINC2 3L2 ENTER SIMNC2 3i 9 Result is 9 15454 4 1689 9 1545 i 4 1689 Examples Evaluate the expression z1 z2 z3 where z 23 13 i z2 2 i z3 4 3i ALG Summary C 9 Keys Display Description EW DISPLAY CO Sets display form 18x41 Kar in 6 241 4 342 WAMA WHA AWA TRESE EE ENTER C2Et1 Fast 2 05 Result is 2 5006 92 68664 2 5000 9 0000 i Examples Evaluate 4 2 5 i x 3 2 3 i Keys Display Description wwa 5i3x03 8 273540 wW ENTER C4 8 2 54 9K03 Result is 11 7333 4 3 8667 11 7333 i 3 8667 Arithmetic in Bases 2 8 and 16 Here are some examples of arithmetic in Hexadecimal Octal and Binary modes Example 12F 16 E9A 6 Keys Display Description Fed BASE 2 2HE Sets base 16 HEX annunciator on C 10 ALG Summary 1 2 RCL LE ea BASE 6 Eh I RCL CEJ RCL A Wea BASE L6 6h ENTER 3 BASE 3307 77 es BASE 772 SMDoawe BASE 7 70 ENTER 1 LO 0 fea BASE 7 Fo H0 BASE LZ 7 2 ENTER Fes BASE 2 2HEX 5 RCL AJ LO re BASE 6 amp h 1 0 0 0 FES BASE ENTER E6 AAA 12Fh E9 Ah 77608 4326 8 12Fh ESAh rriia YreBo 43260 24320 100g 5g 1660750 ido 5A076 100110002 SRBH COO agh igaiiaa
196. icates that the result might be correct to only three decimal places In reality this result is accurate to seven decimal places when compared with the actual value of this integral Since the uncertainty of a result is calculated conservatively the calculator s approximation in most cases is more accurate than its uncertainty indicates For More Information This chapter gives you instructions for using integration in the HP 35s over a wide range of applications Appendix E contains more detailed information about how the algorithm for integration works conditions that could cause incorrect results and conditions that prolong calculation time and obtaining the current approximation to an integral 8 8 Integrating Equations 9 Operations with Complex Numbers The HP 35s can use complex numbers in the form LY ete raa It has operations for complex arithmetic x complex trigonometry sin cos tan and the mathematics functions z 1 z Z 72 In z and ez where z 7 and z2 are complex numbers The form x yi is only available in ALG mode To enter a complex number Form 1 1 Type the real part 2 Press Li 3 Type the imaginary part Form 1 1 Type the real part 2 Pres 3 Type the imaginary part 4 Press Li Form r a 1 Type the value of r 2 Press Wea 8 3 Type the value of 6 The examples in this chapter all utilize RPN mode unless otherwise noted Operations
197. igonometry and arithmetic with complex numbers Evaluate sin 2i3 Keys Display Description ERY DISPLAY 9 2 1 Sets display format 2 Li 3 SIN 9 15454 4 1689 Result is 9 1545 i 4 1689 Evaluate the expression z 1 z2 23 where z7 23 i 13 z2 2i1 z3 4i 3 Perform the calculation as Keys Display ES DISPLAY 9 2x LY 2U 3ILJ US JENTER 23 0000113 6088 23 GG884 13 8808 WEL ENTER 2 8086 1 BAGG 2 BGGG LI BBGG 43 23 GE0G 13 8888 2 BG88 2 8888 E 2 50664 9008 Evaluate 4 i 2 5 x 3 i 2 3 Keys Display ESN DISPLAY 9 2 1 MQOQOIWWIGE 4 68697 4 4806 ENTER 4 0000 0 4008 9 4 Operations with Complex Numbers Description Sets display format ENTER z1 ENTER z2 z2 z3 Result is 2 i 2 z 1 z2 z3 Result is 2 5 i9 Description Sets display format Enters 4i 2 5 BMDDIMLIBIE 4 68607 e 4eee Enters 3i 2 3 31 6 273 E3 11 73334 3 8667 Resultis 11 7333i 3 8667 Evaluate z where z 1i 1 Keys Display Description CLH ENTER 1 BGBG L1 BBG ENTER 1illntermediate 1 pagaii paaa result of wW G888 5 8888 7 2 result is Oi 5 me 87764 8 4794 Final result is 0 8776 i 0 4794 Using Complex Numbers in Polar Notation Many applications use real numbers in polar form or polar notation These forms use pairs of numbers as do complex numbers so you can do arithmetic with these numbers by using the co
198. imation In other words the uncertainty estimate in the Y register is an almost certain upper bound on the difference between the approximation and the actual integral Conditions That Could Cause Incorrect Results Although the integration algorithm in the HP 35s is one of the best available in certain situations it like all other algorithms for numerical integration might give you an incorrect answer The possibility of this occurring is extremely remote The algorithm has been designed to give accurate results with almost any smooth function Only for functions that exhibit extremely erratic behavior is there any substantial risk of obtaining an inaccurate answer Such functions rarely occur in problems related to actual physical situations when they do they usually can be recognized and dealt with in a straightforward manner Unfortunately since all that the algorithm knows about f x are its values at the sample points it cannot distinguish between f x and any other function that agrees with f x at all the sample points This situation is depicted below showing over a portion of the interval of integration three functions whose graphs include the many sample points in common E 2 More about Integration f x With this number of sample points the algorithm will calculate the same approximation for the integral of any of the functions shown The actual integrals of the functions shown with solid blue and black lin
199. in RPN mode or press 2 LA 5 ENTER RZS in ALG mode Before you press ENTER the expression will be displayed in line 2 After you press ENTER the result of expression will replace the expression to display in line 2 and be saved in X register 13 14 Simple Programming m To cancel the INPUT prompt press LE The current value for the variable remains in the X register If you press to resume the program the canceled INPUT prompt is repeated If you press during digit entry it clears the number to zero Press again to cancel the INPUT prompt Using VIEW for Displaying Data The programmed VIEW instruction amp variable stops a running program and displays and identities the contents of the given variable such as A r9 J398 This is a display only and does not copy the number to the X register If Fraction display mode is active the value is displayed as a fraction m Pressing copies this number to the X register E If the number is wider than 14 characters such as binary complex vector numbers pressing L and 0 L2 displays the rest m Pressing LC or Le erases the VIEW display and shows the X register m Pressing Wea clears the contents of the displayed variable Press to continue the program If you don t want the program to stop see Displaying Information without Stopping below For example see the program for Normal and Inverse Normal Distributions in chapter 16 Lines T015 and
200. in an equation you will not be prompted to for its value as the current value stored in the unnamed indirect variable will be used automatically See chapter 14 m To leave the number unchanged just press R S Entering and Evaluating Equations 6 13 m To change the number type the new number and press R S This new number writes over the old value in the X register You can enter a number as a fraction if you want If you need to calculate a number use normal keyboard calculations then press R S For example you can press 2 ENTER 5 2 R S in RPN mode or press 2 5 ENTER R S in ALG mode Before pressing ENTER the expression will display in line 2 and after pressing ENTER the result of the expression will display in line 2 m To cancel the prompt press LE The current value for the variable remains in the X register and displays in right side of the line two If you press during digit entry it clears the number to zero Press again to cancel the prompt m To display digits hidden by the prompt press SHOW In RPN mode each prompt puts the variable value in the X register and disables stack lift If you type a number at the prompt it replaces the value in the X register When you press R S stack lift is enabled so the value is saved on the stack The Syntax of Equations Equations follow certain conventions that determine how they re evaluated a How operators interact m What
201. ins catalog of variables Displays menu to set ALG or RPN mode or angular modes Fe SUMS n Returns the number of sets of data points EN COGIC G SHAND Logic operator EN LOGIC 6 0R Logic operator EN LOGIC A 40T Logic operator B BASE 70 Indicates an octal number 3 BASE 307 Selects Octal base 8 mode 13 3 12 4 12 7 G 10 Operation Index Name OR Wea OFF nPr Wa PRM PSE rOa RAD RAD RADIX RADIX RANDOM RCL variable Keys and Description 3 aR Logic operator Turns the calculator off Wea Permutations of n items taken rata time Returns n n Activates or cancels toggles Program entry mode Pause Halts program execution briefly to display x variable or equation then resumes Used only in programs Lal Returns the correlation coefficient between the x and y values Dlx xy Y V XP xy 7 EN OSA 0 irao Changes the display of complex numbers MODE 1 i FAD Selects Radians angular mode E LRAD Degrees to radians Returns 22 360 x Ca DISPLAY L6 6 Selects the comma as the radix mark decimal point awm Selects the period as the radix mark decimal point a Executes the RANDOM function Returns a random number in the range O through 1 RCL variable Recall Copies variable into the X register
202. interference in a residential installation This equipment generates uses and can radiate radio frequency energy and if not installed and used in accordance with the instructions may cause harmful interference to radio communications However there is no guarantee that interference will not occur in a particular installation If this equipment does cause harmful interference to radio or television reception which can be determined by turning the equipment off and on the user is encouraged to try to correct the interference by one or more of the following measures Reorient or relocate the receiving antenna e Increase the separation between the equipment and the receiver e Connect the equipment into an outlet on a circuit different from that to which the receiver is connected e Consult the dealer or an experienced radio or television technician for help Modifications The FCC requires the user to be notified that any changes or modifications made to this device that are not expressly approved by Hewlett Packard Company may void the user s authority to operate the equipment Declaration of Conformity for Products Marked with FCC Logo United States Only This device complies with Part 15 of the FCC Rules Operation is subject to the following two conditions 1 this device may not cause harmful interference and 2 this device must accept any interference received including interference that may cause undesired operation If you h
203. ion Page STOP Run stop 13 19 Begins program execution at the current program line stops a running program and displays the X register Fe SUMS Displays the summation menu 12 4 sx a 12 6 Returns sample standard deviation of x values Db x n 1 sy 12 6 Returns sample standard deviation of y values V yP n TAN TAN Tangent Returns tan x 4 3 TANH E HYP WAN Hyperbolic 4 6 tangent Returns tanh x VIEW variable EN VIEW variable 3 4 Displays the labeled contents of 13 15 variable without recalling the value to the stack XEQ Evaluates the displayed equation 6 12 XEQ label XEQ label 14 1 Executes the program identified by label x2 EA Square of x 4 2 Tx Square root of x 4 2 yy EN CZ The xth root of y 4 2 X 12 4 E Returns the mean of x values xj n G 14 Operation Index Name Keys and Description Page gt cy y x lt gt variable x lt gt y a a x y x lt y x lt y x gt y xz2y m A G Given a y value in the X register returns the x estimate based on the regression line x y b m E L Factorial or gamma Returns x x 1 2 1 or T x 1 EEZ The argument root of argument2 ELLO w Returns weighted mean of x values Zy x j Lyj Displays the mean arithmetic average menu Lal x exchange Exchanges x with a variable EX x exchange y Move
204. ion mode AJF JES Enters the equation RULA WALI ROD LILA TES RCL 8 ENTER 2xK3 4ek 2 6m gt w SHOW CK B9A0 Checksum and length LH 18 Cancels Equation mode Now solve the equation to find the root Keys Display Description maco i6_ Initial guesses for the root ENTER 1 0 EQN 2xK 3 4xk 2 Gmp Selects Equation mode displays the left end of the equation rs SOLVING Solves for X displays the result x 1 6566 RH 1 6566 Final two estimates are the same to four decimal places RY 4 BBBBE 11 f x is very small so the approximation is a good root Example An Equation with Two Roots Find the two roots of the parabolic equation x2 x 6 0 Enter the equation as an expression D 4 More about Solving Keys Display Description EQN Selects Equation mode RO DIDI Enters the equation RCL LJL Reet 6 ENTER Eat SHOW CK 3971 Checksum and length LH K Cancels Equation mode Now solve the equation to find its positive and negative roots Keys Display Description 0 Wes STO 16 Your initial guesses for the positive ENTER UJ 0 root EQN HeZtk 6 Selects Equation mode displays the equation rs SOLVING Calculates the positive root using Ke guesses O and 10 2 BEBE RH 2 6808 Final two estimates are the same RE SHOW eeeeeeeeeee ffx 0 0 Wes STO KX 16 Your initial guesses for the ENTER DAMEA negative root EQN HO
205. ions Addition and subtraction The addition and subtraction of vectors require that two vector operands have the same length Attempting to add or subtract vectors of different length produces the error message INVALID DATA 1 Enter the first vector 2 Enter the second vector 3 Press or E Vector Arithmetic 10 1 Calculate 1 5 2 2 1 5 2 2 Keys Display Description MODE 5 SRPH Switches to RPN mode if necessary AMAM ci 5ee8 2 26881 Enters 1 5 2 2 MMwmow Ci 5ee8 2 28087 ENTER EVI WOIG 3 61 5ee68 2 2668 Enters 1 5 2 2 maoa 1 5 2 2 E3 8 8668 Adds two vectors CE BEGG G GBE Calculate 3 4 4 5 2 3 1 4 oo Keys Display Description MODE 4 4ALG Switches to ALG mode HMB 3 4 4 51_ Enters 3 4 4 5 BO YOIGII QADAB 3 4 4 51 C2 3 1 4 Enters 2 3 1 4 Loen EE ES ENTER L 3 44 5 C2 32 1 Subtracts two vectors C 5 7606 3 1606 Multiplication and divisions by a scalar 1 Enter a vector 2 Enter a scalar 3 Press for multiplication or LE for division 10 2 Vector Arithmetic Calculate 3 4 x5 Keys Display Description MODE 5 SRPH Switches to RPN mode BDA 62 8808 4 0880 Enters 3 4 ENTER C3 6666 4 6866 5 C3 6666 4 6666 Enters 5 as a scalar a E3 6 BEBE Performs multiplication C15 660G 26 6666 Calculate 2 4 2 Keys Display Description
206. ions Put the number in the display then execute the function there is no need to press ENTER Real Number Functions 4 1 To Calculate Press Natural logarithm base e Wes LN Common logarithm base 10 Est LOG Natural exponential ale Common exponential antilogarithm U Quotient and Remainder of Division You can use EN UNTG 2 21NT and UNTO 3 4R mar to produce the integer quotient and integer remainder respectively from the division of two integers 1 Key in the first integer Press to separate the first number from the second 3 Key in the second number Do not press ENTER 4 Press the function key Example To display the quotient and remainder produced by 58 9 Keys Display Description CS 8 ENTER N E peee Displays the quotient NTG 2 2 INT SCENER 9 EE 4 oppe Displays the remainder NTG 3 2R mdr Z Power Functions In RPN mode to calculate a number y raised to a power x key in y x then press 2 For y gt 0 x can be any number for y lt 0 x must be positive 4 2 Real Number Functions To Calculate Press Result 152 1 5 fe amp 225 8888 106 6 EW 10 i GGG GOB 6686 54 CEER AA 625 888 WENER WLA 24 6 3799 1 4 3 LC 4 CAI ENTER 3 2 2 7446 In RPN mode to calculate a root x of a number y the xth root of y key in y ENTER x th
207. ions 17 3 Variables Used N The number of compounding periods l The periodic interest rate as a percentage For example if the annual interest rate is 15 and there are 12 payments per year the periodic interest rate i is 15 12 1 25 B The initial balance of loan or savings account P The periodic payment F The future value of a savings account or balance of a loan Example Part 1 You are financing the purchase of a car with a 3 year 36 month loan at 10 5 annual interest compounded monthly The purchase price of the car is 7 250 Your down payment is 1 500 B 7 250 1 500 1 10 5 per year N 36 months P Keys Display Description In RPN mode m iF 1x Selects FIX 2 display format EAN O as needed Px1 x 1 1 1 m Displays the leftmost part of the TVM equation Fes SOLVE EA I Selects P prompts for I value COCICIGIENTER i Converts your annual interest mao a 6 88 rate input to the equivalent monthly rate R S H Stores 0 88 in l prompts for N value BILIRS F Stores 36 in N prompts for F value 17 4 Miscellaneous Programs and Equations 0 R S B Stores O in F prompts for B value C26 COJ ENTER E Calculates B the beginning MAME 3 758 6 loan balance R S SOLVING Stores 5750 in B calculates P monthly payment P 156 89 The answer is negative since the loan has been viewed from the borrower s perspective Money received by the borrow
208. is a quick reference for all functions and operations and their formulas where appropriate The listing is in alphabetical order by the function s name This name is the one used in program lines For example the function named FIX n is executed as EW DISPLAY 1 1F 1 n Nonprogrammable functions have their names in key boxes For example Le Non letter and Greek characters are alphabetized before all the letters function names preceded by arrows for example gt DEG are alphabetized as if the arrow were not there The last column marked gt refers to notes at the end of the table Name Keys and Description Page CZ Changes the sign of a number 1 15 1 LE Addition Returns y x 1 19 1 Subtraction Returns y x 1 19 1 x x Multiplication Returns y x x 1 19 1 LE Division Returns y x 1 19 1 Power Indicates an exponent 6 16 1 t Deletes the last digit keyed in clears 1 4 x clears a menu erases last function 1 8 keyed in an equation deletes an 6 3 equation deletes a program step 13 7 Displays previous entry in catalog 1 28 moves to previous equation in 6 3 equation list moves program pointer 13 11 to previous step 13 20 Operation Index G 1 Name Keys and Description Page Displays next entry in catalog moves 1 28 to next equation in equation list 6 3 moves program pointer to next line 13 11 during pro
209. ision ccccceseeesseeeeeeeenteeees 1 25 Fractions oren n e a at eel iota nde ated a teed ees 1 26 EnteritigiFracthOns i ot siushis vice ronaweenstecaesaeanndeawed Een 1 26 MeSSAGES i ioien i ni e i a se tannceledobd ede ETE 1 27 Calculator Memos s ccniadengkeacinccmcecasere me cameens Meeks 1 28 Checking Available Memory ccccceessereeeeeeesteeeeeeeeaes 1 28 Clearing All of Memory sscrscssssn svete team yauseddoedugrstustewuaiwees 1 29 RPN The Automatic Memory Stack cccsscceeeeees 2 1 Whatthe Stack lsiera a oes a ae 2 1 The X and Y Registers are in the Display cccceeeeeeeeeees 2 3 Clearing the X Register waco a 2 3 Reviewing the Stack cessis cctuseideasgeiy cendueeuen Seve hes eer aaa antes 2 3 Exchanging the X and Y Registers in the Stack ceeeee 2 4 Arithmetic How the Stack Does It cceceeeeeseeeeeeeetttteeeeeeeaees 2 5 How ENTER Works idictcr tt cin innnan Shaw eter aren ares 2 6 How to Clear the Stack iuscaiasaurouveissnmmicarantantnacis sdenctiangia 2 7 Thre LAST X REGISIEE aa nanami nengone aE a enaa 2 8 Correcting Mistakes with LAST X o eceessececeeeeeeteeeeeeeeetteeeees 2 9 Reusing Numbers with LAST X ccceesseceeeeeeeereeeeeeeeetneeeees 2 10 Chain Calculations in RPN Mode ssssceeeeeeeeesteeeeeeeseees 2 12 Work from the Parentheses Out cccccccesseeeeesteeeneneeees 2 12 Ce N E EE TEN E E E me sie eena aaah 2 14 Order of Cale
210. isplayed using the current display format See chapter 6 for information about working with equations Fractions 5 9 Fractions in Programs You can use a fraction in a program just as you can in an equation numerical values are shown in their entered form When you re running a program displayed values are shown using Fraction display mode if it s active If you re prompted for values by INPUT instructions you may enter fractions The program s result is displayed using the current display format A program can control the fraction display using the c function and by setting and clearing flags 7 8 and 9 See Flags in chapter 14 See chapters 13 and 14 for information about working with programs 5 10 Fractions Entering and Evaluating Equations How You Can Use Equations You can use equations on the HP 35s in several ways m For specifying an equation to evaluate this chapter m For specifying an equation to solve for unknown values chapter 7 m For specifying a function to integrate chapter 8 Example Calculating with an Equation Suppose you frequently need to determine the volume of a straight section of pipe The equation is V 25 rd2 where d is the inside diameter of the pipe and l is its length You could key in the calculation over and over for example Ce JLZJCSJ ENTER GWAK ee I KOLO EX calculates the volume of 16 inches of 2 1 2 inch diameter pipe 78 5398 cubic inches However
211. ister Ls ExY t views xy register 14 8686 Statistical Operations 12 11 Ee B b bJ b Eyes 26 BEGE Ex 16 6686 zy 6 BEGG Ex 4 BEBBE n 2 66668 4 8666 2 8666 t Views Xy register t Views x register tt Views Ly register tt Views x register tt Views n register Leaves VAR catalog Access to the Statistics Registers The statistics register assignments in the HP 35s are shown in the following table Summation registers should be referred to by names and not by numbers in expression equations and programs Statistics Registers Register Number Description n 27 Number of accumulated data pairs x 28 Sum of accumulated x values Ly 29 Sum of accumulated y values Ex2 30 Sum of squares of accumulated x values Ly2 31 Sum of squares of accumulated y values Exy 32 Sum of products of accumulated x and y values 12 12 Statistical Operations You can load a statistics register with a summation by storing the number 27 through 32 of the register you want in I or J and then storing the summation value ETON or N Similarly you can press EW VIEW U or LU or REL or to view or recall a register value the display is labeled with the register name The SUMS menu contains functions for recalling the register values See Indirectly Addressing Variables and Labels in chapter 14 for more information Statistical Operations 1
212. ister the display 7 8 Solving Equations These sources are used for guesses whether you enter guesses or not If you enter only one guess and store it in the variable the second guess will be the same value since the display also holds the number you just stored in the variable If such is the case the calculator changes one guess slightly so that it has two different guesses Entering your own guesses has the following advantages m By narrowing the range of search guesses can reduce the time to find a solution m If there is more than one mathematical solution guesses can direct the SOLVE procedure to the desired answer or range of answers For example the equation of linear motion d vot l 2gt2 can have two solutions for t You can direct the answer to the required solution by entering appropriate guesses The example using this equation earlier in this chapter didn t require you to enter guesses before solving for T because in the first part of that example you stored a value for T and solved for D The value that was left in T was a good realistic one so it was used as a guess when solving for T If an equation does not allow certain values for the unknown guesses can prevent these values from occurring For example y t logx results in an error if x lt O message HO ROOT FHD In the following example the equation has more than one root but guesses help find the desired root Solving Equations 7 9
213. istical data 2 Key in the y value first and press ENTER 3 Key in the corresponding x value and press 2 4 The display shows n the number of statistical data pairs you have accumulated 5 Continue entering x y pairs n is updated with each entry To recall an x value to the display immediately after it has been entered press Wea LAST x Correcting Errors in Data Entry If you make a mistake when entering statistical data delete the incorrect data and add the correct data Even if only one value of an x y pair is incorrect you must delete and reenter both values 12 2 Statistical Operations To correct statistical data 1 Reenter the incorrect data but instead of pressing 2 press EW 2 This deletes the value s and decrements n 2 Enter the correct value s using If the incorrect values were the ones just entered press EN to retrieve them then press EN to delete them The incorrect y value was still in the Y register and its x value was saved in the LAST X register After deleting the incorrect statistical data calculator will display the value of Y register in line 1 and value of n in line 2 Example Key in the x y values on the left then make the corrections shown on the right Initial x y Corrected x y 20 4 20 5 400 6 40 6 Keys Display Description CEAR 42 Clears existing statistical data 4 ENTER 2 0 4 6888 E
214. istics Programs Flags Used None Program Instructions of R SP 2 Key in the program routines press when done Press to start entering new data Key in xj value data point and press R S Key in fi value frequency and press R S Press after VIEWing the number of points entered Repeat steps 3 through 5 for each data point If you discover that you have made a data entry error xj or fi after you have pressed in step 4 press ENTER and then press again Then go back to step 3 to enter the correct data 7 When the last data pair has been input press to calculate and display the grouped standard deviation 8 Press to display the weighted mean of the grouped data 9 To add additional data points press and continue at step 3 To start a new problem start at step 2 Variables Used X Data point F Data point frequency N Data pair counter 5 Grouped standard deviation M Weighted mean i Index variable used to indirectly address the correct statistics register Register 27 Summation Xf Register 28 Summation Exif Register 30 Summation Ex 2fi Example Enter the following data and calculate the grouped standard deviation Statistics Programs 16 21 Group Xi fi Keys In ALG mode KEQ IRS E R5 l EG R S L6 J R S ly E ARs R5 b N Display a value F value H 1 66686 a T BEBB F ir BeBe H 2 BREE a
215. itive or negative number possible for the too big number Windows for Long Binary Numbers The longest binary number can have 36 digits Each 14 digit display of a long number is called a window 36 bit number LEBER EER BEER RE EGER REE GEER EERE Geeeob Highest Window Lowest Window Displayed When a binary number is larger than the 14 digits the or annunciator or both appears indicating in which direction the additional digits lie Press the indicated key EIL or L to view the obscured window Press to display left WEx lt EL Press to display right window window IBBBEEERREEGE6 FERRER REESR556 FEEE8506b Using base in program and equations Equations and program are affected by the base setting and binary octal and hexadecimal numbers can be entered in equation and in program as well as when the calculator prompts for a variable Results will be displayed according to the current base 11 8 Base Conversions and Arithmetic and Logic 12 Statistical Operations The statistics menus in the HP 35s provide functions to statistically analyze a set of one or two variable data real numbers Mean sample and population standard deviations a Linear regression and linear estimation x and y m Weighted mean x weighted by y a Summation statistics n x Ly 2x2 ae and xy x y SUMS fan Entering Statistical Data n EX vy EX Ly EXY
216. its the data m Slope of the calculated line y intercept of the calculated line m To find an estimated value for x or y key in a given hypothetical value for y or x then press D ERJ or EWLRIL 4 m To find the values that define the line that best fits your data press EW followed by F m or E Example Curve Fitting The yield of a new variety of rice depends on its rate of fertilization with nitrogen For the following data determine the linear relationship the correlation coefficient the slope and the y intercept X Nitrogen Applied kg per hectare Y Grain Yield 0 00 20 00 40 00 60 00 80 00 4 63 5 78 6 61 7 21 7 78 metric tons per hectare Keys AAA 3 Display Description p ay P Clears all previous statistical data 12 8 Statistical Operations 4 JLEJLSICENTER LO Enters data displays n a HOMME 0 Y 2166 BOMMeam d 788 0 WUWU ENER 6 We QQOGCQGENER 8 7 7506 Five data pairs entered OE 5 6000 e F amp OEmMb Displays linear regression B A 9558 menu Correlation coefficient data closely approximate a straight line x OF mB Slope of the line 8 8387 or mb y intercept 4 5568 y 8 50 7 xK we 7 50 g a r 0 9880 7 7 Pa k 6 50 p Z m 0 0387 5190 4 50 0 20 40 60 80 Statistical Operations 12 9 What if 70 kg of nitrogen fertilizer were applied to the rice
217. iwan Thailand Vietnam 010 68002397 2805 2563 65 6100 6682 852 2805 2563 65 6100 6682 09 574 2700 65 6100 6682 6100 6682 2 56 1 2700 852 2805 2563 65 6100 6682 65 6100 6682 EMEA Telephone numbers Austria Belgium Belgium Czech Republic Denmark Finland France Germany Greece Netherlands Ireland Italy Luxembourg Norway Portugal Russia South Africa Spain Sweden Switzerland French 01 360 277 1203 02 620 00 86 02 620 00 85 296 335 612 82 33 28 44 09 8171 0281 01 4993 9006 069 9530 7103 210 969 6421 020 654 5301 01 605 0356 02 754 19 782 2730 2146 23500027 021 318 0093 495 228 3050 0800980410 913753382 08 5199 2065 022 827 8780 Support Batteries and Service A 9 Switzerland German 01 439 5358 Switzerland Italian 022 567 5308 United Kingdom 0207 458 0161 Anguila 1 800 711 2884 Antigua 1 800 7 1 1 2884 Argentina 0 800 555 5000 Aruba 800 8000 800 711 2884 Bahamas 1 800 711 2884 Barbados 1 800 711 2884 Bermuda 1 800 711 2884 Bolivia 800 100 193 Brazil 0 800 709 7751 British Virgin Islands 1 800 711 2884 Cayman Island 1 800 711 2884 Curacao 001 800 872 288 1 800 7 1 1 2884 Chile 800 360 999 Colombia 01 8000 5 1 4746 8368 01 8000 51 HP INVENT Costa Rica 0 800 01 1 0524 Dominica 1 800 7 1 1 2884 Dominican Republic 1 800 7 1 1 2884 Ecuador 1 999 119 800 711 2884 Andinatel 800 225 528 e 800 711 2884 Pacifitel El Salvador 800 6160 Fren
218. j 7 8 lilo SOLVE Q c R l HMs si pec T _ lb MILE gt in nCr EK 4 5 6 x zk Uj Erm v em w Cnr LOGIC gal SEED LR ra 1 2 3 ms x C y ew CO OFF G ie zZ xy ON SPACE 1 Foise _ LJ LI ab Shifted Keys Each key has three functions one printed on its face a left shifted function yellow and a right shifted function blue The shifted function names are printed in yellow above and in blue on the bottom of each key Press the appropriate shift key EW or M before pressing the key for the desired function For example to turn the calculator off press and release the EN shift key then press LC 1 2 Getting Started Pressing or Fed turns on the corresponding Kal or Fd annunciator symbol at the top of the display The annunciator remains on until you press the next key To cancel a shift key and turn off its annunciator press the same shift key again Alpha Keys Left shifted function gt INIG TAN Right shifted gt ATAN Jj lt Letter for alphabetic function key Most keys display a letter in their bottom right corner as shown above Whenever you need to type a letter for example a variable or a program label the A Z annunciator appears in the display indicating that the alpha keys are active Variables are covered in chapter 3 labels are covered in chapter 13 Cursor Keys Each of the four cursor direction keys is marke
219. 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 a constant amount B until the resulting A is less than or equal to B Program lines Description In RPN mode S661 LBL S662 IMPUT A S663 IMPUT B S664 RCL A It is easier to recall A than to remember where it is in the stack 685 RCL E Calculates A B S866 STOR Replaces old A with new result Seer RCL B Recalls constant for comparison SEBS xiv Is B lt new A 5669 GT S864 Yes loops to repeat subtraction S616 VIEW A No displays new A S611 ETH Checksum and length 2737 33 Programming Techniques 14 17 Loops with Counters DSE ISG When you want to execute a loop a specific number of times use the increment skip if greater than or decrement skip if less than or equal to conditional function keys Each time a loop function is executed in a program it automatically decrements or increments a counter value stored in a variable It compares the current counter value to a final counter value then continues or exits the loop depending on the result For a count down loop use Wea variable For a count up loop use EW variable These functions accomplish the same thing as a FOR NEXT loop in BASIC FOR variable initial value T9 final value STEF increment HE T variable A DSE instruction is like a
220. laces affects what you see but it does not affect the internal representation of numbers Any number stored internally always has 12 digits For example in the number 14 8745632019 you see only 14 8746 when the display mode is set to FIX 4 but the last six digits 632019 are present internally in the calculator To temporarily display a number in full precision press EW SHOW This shows you the mantissa but no exponent of the number for as long as you hold down SHOW Keys Display Description 4 5JENTERJLL 58 5006 Four decimal places displayed wW EEN DISPLAY 2 2SC1 5 85e1 Scientific format two decimal 2 places and an exponent EEN DISPAY SJ SENG 58 5E6 Engineering format 2 Getting Started 1 25 KEW DISPLAY 4 4ALL 58 5 All significant digits trailing zeros dropped EN DISPLAY AJ IF IX 58 5006 Four decimal places no exponent 4 Ux 8 81r1 Reciprocal of 58 5 hold 178348178248 Shows full precision until you release SHOW Fractions The HP 35s allows you to enter and operate on fractions displaying them as either decimals or fractions The HP 35s displays fractions in the form a b c where a is an integer and both b and c are counting numbers In addition b is such that O lt b lt c and c is such that 1 lt c lt 4095 Entering Fractions Fractions can be entered onto the stack at any time 1 Key in the integer part of the number and press LJ
221. lay for the number being displayed to change in multiples of 3 with the mantissa adjusted accordingly 1 22 Getting Started Example This example illustrates the behavior of the Engineering format using the number 12 346E4 It also shows the use of the EN LENG and R ENG gt functions This example uses RPN mode Keys Display Description EN DISPLAY C3J SEN EHG Choose Engineering format G 4 B EGGEe Enter 4 for 4 significant digits after the 6 BBGGEG 1 DAWA 145 46E3 Enter 12 346E4 EILA ENTER 123 46E3 EN LENG or 123 46E3 ENG 123 46E3 Ea ENG 123 46E3 Increases the exponent by 3 B 12346E6 EN ENG 123 46E3 Decreases the exponent by 3 123 46E3 ALL Format ALL The All format is the default format displaying numbers with up to 12 digit precision If all the digits don t fit in the display the number is automatically displayed in scientific format Periods and Commas in Numbers The HP 35s uses both periods and commas to make numbers easier to read You can select either the period or the comma as the decimal point radix In addition you can choose whether or not to separate digits into groups of three using thousand separators The following example illustrates the options Getting Started 1 23 Example Enter the number 12 345 678 90 and change the decimal point to the comma Then choose to have no thousand separator Finally retu
222. line or a program line is being displayed You might have noticed that several function names include an x or y This is no coincidence these letters refer to the X and Y registers For example raises ten to the power of the number in the X register Clearing the X Register Pressing Wea CLEAR 1 always clears the X register to zero it is also used to program this instruction The key in contrast is context sensitive It either clears or cancels the current display depending on the situation it acts like Wea CLEAR 1 only when the X register is displayed also acts like Wea CLEAR 1 when the X register is displayed and digit entry is terminated no cursor present Reviewing the Stack Rv Roll Down The roll down key lets you review the entire contents of the stack by rolling the contents downward one register at a time You can see the numbers as they roll through the x and y registers Suppose the stack is filled with 1 2 3 4 press 1 ENTER 2 ENTER 3 ENTER 4 Pressing four times rolls the numbers all the way around and back to where they started RPN The Automatic Memory Stack 2 3 What was in the X register rotates into the T register the contents of the T register rotate into the Z register etc Notice that only the contents of the registers are rolled the registers themselves maintain their positions and only the X and Y register s contents are
223. list Cleared Cleared FN lakel Null Null Program pointer PRGM TOP PRGM TOP Program memory Cleared Cleared Stack lift Enabled Enabled Cleared to zero Cleared to zero Not defined RPN 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 disabled regarding its behavior when the next number is placed in the X register Refer to chapter 2 The Automatic Memory Stack All functions except those in the following two lists will enable stack lift B 4 User Memory and the Stack Disabling Operations The five operations ENTER 2 Q3 CEAR 1 and Fea CLEAR STK disable stack lift A number keyed in after one of these disabling operations writes over the number currently in the X register The Y Z and T registers remain unchanged In addition when and act like CLx they also disable stack lift The INPUT function disables stack lift as it halts a program for prompting so any number then entered writes over the X register but it enables stack lift when the program resumes Neutral Operations The following operations do not affect the status of stack lift DEG RAD FIX SCI DEC HEX CLVARS GRAD ENG ALL OCT BIN PSE SHOW RADIX RADIX CLZ CFRE R amp S andSTOP Cand i
224. list contains two built in equations 2 2 lin solve and 3 3 lin Solve and the equations you ve entered You can display the equations and select one to work with 6 6 Entering and Evaluating Equations To display equations 1 Press EQN This activates Equation mode and turns on the EQN annunciator The display shows an entry from the equation list m EG LIST TOP jf the equation pointer is at the top of the list m The current equation the last equation you viewed Press or to step through the equation list and view each equation The list wraps around at the top and bottom EN LIST TOP marks the top of the list To view a long equation 1 3 Display the equation in the equation list as described above If it s more than 14 characters long only 14 characters are shown The annunciator indicates more characters to the right Press to begin editing the equation at the beginning or press to begin editing the equation at the end Then press or repeatedly to move the cursor through the equation one character at a time and gt display when there are more characters to the left or right Press WES L lt or L to scroll the long equations in line 2 by a screen To select an equation Display the equation in the equation list as described above The displayed equation in line 2 is the one that s used for all equation operations Example Viewing an Equation View the last equation you entered
225. ls eeceeeeeee 14 20 The Variables I and J sccsscsssscssscsssscsssccssscsscesseenes 14 20 The Indirect Address I and J ccccececeeeeeeeeececeeeceeeeeees 14 21 Program Control with 1 J esesesessssssesssesessessesesesesseseseseesese 14 23 Equations with 1 J eseeesessssesesesossesesesessesessesesesseseseseseese 14 23 Unnamed indirect variables 0 iiississisaswesaovanracedensacineeuss 14 23 8 Contents 15 Solving and Integrating Programs sssessssees 15 1 Solving a PrGGrait tcca hs hoas caclsaay seasaaterhineee aed tea tion 15 1 Using SOLVE in a Program cceeeeeeeeeeceeeceeeeeeeeeeeeenteeeneeeees 15 6 Integrating a Program ccseeeeecceeeeneeeeeceeeeeaeeneecceeaeaueeeeeeees 15 7 Using Integration in a Program ceeeeeeceeeceeeeeeeeeeeeeeaeeeees 15 10 Restrictions on Solving and Integrating sccceeceesseeeeeeeeees 15 11 16 Statistics Programs 0 c0ciccscssuccsecsasensoesesanecnessooacens 16 1 Curve FIHING ecin eveds cacse ca coeds cedaceetn E ais 16 1 Normal and Inverse Normal Distributions c cseeceeeeeeees 16 11 Grouped Standard Devintion lt sac eaieiawisars cous auacanonimaanvantacee 16 18 17 Miscellaneous Programs and Equations 06 17 1 Time Value of MONG Wiis sas tients cctatachontedeedbieda erteiegnathaieiaiae 17 1 Prime Number Generator cccccsessceeeeeeeesneeeeeeeeeeeeeeseeeas 17 7
226. lues in the display For a long equation the and annunciators show that scrolling is active for this program line You can use PK and EL to scroll the display Clear functions and backspace key Note these special conditions during program entry m always cancels program entry It never clears a number to zero E In program line view status deletes the current program line and L lt gt begins the edit status In program line edit status deletes a character before the cursor m To program a function to clear the X register use Wa CLEAR 1 1 When you insert or erase a line in a program GTO and XEQ statements are automatically updated if needed For example Simple Programming 13 7 ABBI LEL A AGES 2 3 ABES ite AbB4 GTO ABES Now erase line A002 and line A004 changes to A003 GTO A002 Function Names in Programs The name of a function that is used in a program line is not necessarily the same as the function s name on its key in its menu or in an equation The name that is used in a program is usually a fuller abbreviation than that which can fit on a key or ina menu Example Entering a Labeled Program The following keystrokes delete the previous program for the area of a circle and enter a new one that includes a label and a return instruction If you make a mistake during entry press to delete the current program line then reenter the line correctly Keys Display
227. mal point A 1 degrees angle units 4 4 A 2 converting to radians 4 14 denominators controlling 5 4 14 10 14 14 range of 1 26 5 2 setting maximum 5 4 discontinuities of functions D 5 display adjusting contrast 1 1 X register shown 2 3 display format affects integration 8 2 8 6 8 7 affects rounding 4 18 default B 4 periods and commas in 1 23 A 1 setting 1 21 A 1 do if true 14 6 15 6 DSE 14 18 clearing stack 2 6 copying viewed variable 13 15 duplicating numbers 2 6 ending equations 6 4 6 8 13 7 evaluating equations 6 10 6 11 separating numbers 1 17 2 6 stack operation 2 6 exponent 1 16 E in numbers 1 15 1 22 A 1 ENG format 1 22 See also display format entry cursor backspacing 1 4 meaning 1 17 EQN annunciator in equation list 6 4 6 7 in Program mode 13 7 EQN LIST TOP 6 7 F 2 equality equations 6 9 6 11 7 1 equation list adding to 6 4 displaying 6 6 editing 6 8 EQN annunciator 6 4 in Equation mode 6 3 operation summary 6 3 Equation mode backspacing 1 4 6 8 during program entry 13 7 leaving 1 4 6 3 shows equation list 6 3 starting 6 3 6 7 equations and fractions 5 9 as applications 17 1 base mode 6 5 6 11 13 25 checksums 6 19 13 7 13 24 compared to ALG 13 4 compared to RPN 13 4 controlling evaluation 14 11 deleting 1 5 6 9 deleting in programs 13 20 displaying 6 6 displaying in programs 13 16 13 18 14 11 editing 1 4 6 8 editing in programs 13 7 13 20 entering 6 4 6 8 en
228. mous compared with the correct data in such a case it would be wise to clear and reenter all the data 12 10 Statistical Operations Summation Values and the Statistics Registers The statistics registers are six unique locations in memory that store the accumulation of the six summation values Summation Statistics Pressing Wea gives you access to the contents of the statistics registers m FA to recall the number of accumulated data sets m Press 2 to recall the sum of the x values m Press OIO 2 to recall the sum of the y values m Press OO 2 4 2 and DILILILIL Zx to recall the sums of the squares and the sum of the products of the x and y values that are of interest when performing other statistical calculations in addition to those provided by the calculator If you ve entered statistical data you can see the contents of the statistics registers Press EW MEM 7 1 AR ENTER then use and to view the statistics registers Example Viewing the Statistics Registers Use to store data pairs 1 2 and 3 4 in the statistics registers Then view the stored statistical values Keys Display Description FES CLEAR 4 42 Clears the statistics registers 2 ENTER 11 E 2 6888 Stores the first data pair 1 2 4 ENTER 3 G A face Stores the second data pair 3 4 2 BEEBE n t Displays VAR catalog and views n MEM 7 1 VAR 2 8E88 reg
229. mplex operations imaginary Example Vector Addition Add the following three loads Operations with Complex Numbers 9 5 L2 185 Ib 5 62 170 Ib 5 143 Ly L3 100 Ib 261 Keys Display Description MODEJO 1DEG Sets Degrees mode LoDE JERR Sets complex mode 18r8a 1 8 5 fea Le 155 6066062 BREE Enters L L6 ILZ ENTER 155 GBBB962 HBBE pomm 170 00000143 00 Enters Lo DAENT 170 00600143 660m Wwe 155 BB6EQ952 BEEE Enters L3 and adds L2 L3 IW 151 45290178 666m E3 178 93720111 148m Adds L L2 L3 AL ee Scrolls the screen to see the rest of the answer You can do a complex operation with numbers whose complex forms are different however the result form is dependent on the setting in LDISPLAY menu 9 6 Operations with Complex Numbers Evaluate 111 34 10 56 30 Keys Display Description MODE 1 10EG Sets Degrees mode EEN DISPLAY E 0 Sets complex mode 18r8a COC CENTER 1 4142045 060A Enters 1i 1 4142945 6688 DAAE F see89ie ce00 Enters 30 10 ENTER 3 080918 e008 SIOZ 1 4142945 ee00 Enters 5430 and adds 30 LE Y 8661922 5241 10 E3 9 2688025 53595 Adds 1i1 result is 9 20880 25 8898 Complex Numbers in Equations You can type complex numbers in equations When an equation is displayed all numeric forms are shown as they were entered like xiy or r a When you evaluate an equation and are
230. n Population standard deviation assumes the data constitutes the complete set of data and is calculated using n as a divisor m Press Wea o for the population standard deviation of the x values m Press Wea SALLALI c for the population standard deviation of the y values Example Population Standard Deviation Grandma Hinkle has four grown sons with heights of 170 173 174 and 180 cm Find the population standard deviation of their heights Keys Display Description Wea CLEAR 4 42 Clears the statistics registers mgoa Enters data Four data points DAEN EAEI ee 2 accumulated OE 4 0088 a o Sa OE Calculates the population oy standard deviation 3 6315 Linear Regression Linear regression L R also called linear estimation is a statistical method for finding a straight line that best fits a set of x y data Note To avoid a STAT ERROR message enter your data before i executing any of the functions in the L R menu Statistical Operations 12 7 L R Linear Regression Menu Menu Key Description fes Estimates predicts x for a given hypothetical value of y based on the line calculated to fit the data e Estimates predicts y for a given hypothetical value of x based on the line calculated to fit the data K Correlation coefficient for the x y data The correlation coefficient is a number in the range 1 through 1 that measures how closely the calculated line f
231. n list key it in see Entering Equations into the Equation List in chapter 6 and leave Equation mode The equation usually contains just an expression 2 Enter the limits of integration key in the lower limit and press ENTER then key in the upper limit 3 Display the equation Press and if necessary scroll through the equation list press or LY to display the desired equation 4 Select the variable of integration Press EN variable This starts the calculation LZ uses far more memory than any other operation in the calculator If executing LZ causes a MEMORY FULL message refer to appendix B You can halt a running integration calculation by pressing or R S and the message INTERRUPTED will be shown in line 2 but the integration cannot be resumed However no information about the integration is available until the calculation finishes normally The display format setting affects the level of accuracy assumed for your function and used for the result The integration is more precise but takes much longer in the ALL and higher F 1 SCI and ENG settings The uncertainty of the result ends up in the Y register pushing the limits of integration up into the T and Z registers For more information see Accuracy of Integration later in this chapter To integrate the same equation with different information If you use the same limits of integration press move them into the X and Y registers Then start at st
232. n you can edit the equation just like you would when entering a new equation 3 Press or to save the edited equation in the equation list replacing the previous version Using menus while editing an equation 1 When editing an equation selecting a setting menu such as MODE E50 DISPLAY or WER CLEAR will end the equation edit status 2 When editing an equation selecting an insert or view menu such as LR azn So Bw BES od MN AEM and EN CONST the equation will still be in edit mode after inserting the item 3 The menus X22 FLAGS P 20 are disabled in equation mode 6 8 Entering and Evaluating Equations To clear a saved equation Scroll the equation list up or down until the desired equation is in line 2 of the display and then press Le To clear all saved equations In EQN mode press Wea CLEAR Select 3 FE N The CLE EGN Y H menu is displayed Select Y ENTER Example Editing an Equation Remove 25 in the equation from the previous example Keys Display Description EQN R 2xCx T A2 25 Shows the current equation in the equation list Ea 2xeCx T A 25 Activates cursor at the end of the 7 equation caaea 2xeCxCOS T Aa Deletes the number 25 ENTER R 2xCx T A2 Shows the end of edited equation in the equation list Ke Leaves Equation mode Types of Equations The HP 35s works with three types of equations Equalities The equa
233. n is wide enough to require excessive calculation time but not so wide that it would be calculated incorrectly Note that because f x xe x approaches zero very quickly as x approaches the contribution to the integral of the function at large values of x is negligible Therefore you can evaluate the integral by replacing the upper limit of integration by a number not so large as 10499 say 103 Rerun the previous integration problem with this new limit of integration Keys Display Description CO ENTER 7 ES New upper limit 3 EQN SKERP E Selects Equation mode displays the equation More about Integration E 7 EN INTEGRATING Integral The calculation takes a minute or two 1 666E6 x 1 866E 3 Uncertainty of approximation This is the correct answer but it took a very long time To understand why compare the graph of the function between x O and x 103 which looks about the same as that shown in the previous example with the graph of the function between x 0 and x 10 f x 0 10 You can see that this function is interesting only at small values of x At greater values of x the function is not interesting since it decreases smoothly and gradually in a predictable manner The algorithm samples the function with higher densities of sample points until the disparity between successive approximations becomes sufficiently small For a narrow interval in an area where the fun
234. n terms of the unknown variable x SOLVE starts with an estimate for the unknown variable x and refines that estimate with each successive execution of the function ffx If any two successive estimates of the function f x have opposite signs then SOLVE presumes that the function f x crosses the x axis in at least one place between the two estimates This interval is systematically narrowed until a root is found For SOLVE to find a root the root has to exist within the range of numbers of the calculator and the function must be mathematically defined where the iterative search occurs SOLVE always finds a root provided one exists within the overflow bounds if one or more of these conditions are met Two estimates yield f x values with opposite signs and the function s graph crosses the x axis in at least one place between those estimates figure a below f x always increases or always decreases as x increases figure b below The graph of f x is either concave everywhere or convex everywhere figure c below More about Solving D 1 m f f x has one or more local minima or minima each occurs singly between adjacent roots of f x figure d below f x f x L x a b f x f x to Function Whose Roots Can Be Found In most situations the calculated root is an accurate estimate of the theoretical infinitely precise root of the equation An ideal solution is one for which f x O However a
235. nator but a negative numerator causing a negative square root Keys Display Description LO Wea STO ENTER CAMO iB_ EQN SQRTCH H 8 313m Selects Equation mode displays the left end of the equation E SOLVE HO ROOT FHD No root found for f x Example A Local Flat Region Find the root of the function f x x 2ifx lt l f x 1 for 1 lt x lt 1 a local flat region f x x 2 ifx gt 1 In RPN mode enter the function as the program 3661 LBL J Je62 i JBBS 2 J664 RCL s IBB5 xiv JEBE RTH JeG7 4 JEBES TEGI 7 TBIG x y Ie1i Fy Iei2 RTH Checksum and length 9412 39 D 12 More about Solving Solve for X using initial guesses of 10 8 and 10 8 Keys Display Description In RPN mode ERIE Enters guesses 2AM i s Mw En aman 1 6 8 Selects program J as the function Wes SOLVE X Solves for X displays the result 2 BEEBE Round Off Error The limited 12 digit precision of the calculator can cause errors due to rounding off which adversely affect the iterative solutions of SOLVE and integration For example x 1 10 10 0 has no roots because f x is always greater than zero However given initial guesses of 1 and 2 SOLVE returns the answer 1 0000 due to round off error Round off error can also cause SOLVE to fail to find a root The equation x 7 0 has a root at 7 However no 12 digit number exactly equals
236. nd approximates the shape of the bell shaped curve shown below Given a value x this program calculates the probability that a random selection from the sample data will have a higher value This is known as the upper tail area Q x This program also provides the inverse given a value Q x the program calculates the corresponding value x Statistics Programs 16 11 Upper tail area X xX x o T z x x 0 2 Jy Q x 0 5 This program uses the built in integration feature of the HP 35s 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 probability Q x 16 12 Statistics Programs Program Listing Program Lines In RPN mode S661 LBL S862 B S663 STOM S664 IMPUT M S665 1 S666 STO S S667 IHFPUT S668 RTH Description This routine initializes the normal distribution program Stores default value for mean Prompts for and stores mean M Stores default value for standard deviation Prompts for and stores standard deviation S Stops displaying value of standard deviation Checksum and length 7OBF 26 Degi LEL OD D662 IHPUT DEBS KEH QBBI D664 STO 4 D665 VIEW Q D666 GTO DEGI This routine calculates Q X given X Prompts for and stores X Calculates upper tail area Stores value in Q so VIEW function can display it Displays Q X Loops to calculate another Q X
237. nd length in bytes of the equation For example CR 382E LH 41 To see the total memory requirements of specific programs 1 Press EN MEM 2 2PM to display the first label in the program list 2 Scroll through the program list press or until you see the desired program label and size For example LEL F LH 57 3 Optional Press EW to see the checksum hexadecimal and length in bytes of the program For example CE 2CC3 LH 37 To see the memory requirements of an equation in a program 1 Display the program line containing the equation 2 Press EN to see the checksum and length For example CE ABF1 LH 15 Resetting the Calculator If the calculator doesn t respond to keystrokes or if it is otherwise behaving unusually attempt to reset it Resetting the calculator halts the current calculation and cancels program entry digit entry a running program a SOLVE calculation an J FN calculation a VIEW display or an INPUT display Stored data usually remain intact To reset the calculator hold down the key and press GTO If you are unable to reset the calculator try installing fresh batteries If the calculator cannot be reset or if it still fails to operate properly you should attempt to clear memory using the special procedure described in the next section If the calculator still does not respond to keystrokes use a thin pointed object to press the RESET hole The calculator can reset itself if it is dro
238. ng message OVERFLOW appears Getting Started 1 17 Performing Arithmetic Calculations The HP 35s can operate in either RPN mode or in Algebraic mode ALG These modes affect how expressions are entered The following sections illustrate the entry differences for single argument or unary and two argument or binary operations Single Argument or Unary Operations Some of the numerical operations of the HP 35s require a single number for input such as U4 LA LN and SIN These single argument operations are entered differently depending on whether the calculator is in RPN or ALG mode In RPN mode the number is entered first and then the operation is applied If the key is pressed after the number is entered then the number appears in line 1 and the result is shown in line 2 Otherwise just the result is displayed in line 2 and line 1 is unchanged In ALG mode the operator is pressed first and the display shows the function followed by a set of parentheses The number is entered between the parentheses and then the key is pressed The expression is displayed in line 1 and the result is shown in line 2 The following examples illustrate the differences 1 18 Getting Started Example Calculate 3 42 first in RPN mode and then in ALG mode Keys Display Description MODE 5 SRPH Enter RPN mode if necessary WAA 8 3 Enter the number EE Wea x i S Press the square operator MODE 4 4ALG Switch to AL
239. nown when integrating no prompt occurs for the variable of integration Prompts halt execution Pressing resumes the calculation using the value for the variable you keyed in or the displayed current value of the variable if is your sole response to the prompt Flag 11 is automatically cleared after evaluation SOLVE or J FN of an equation in a program The status of flag 11 is also controlled by execution of the SF and CF operations from the keyboard or by SF and CF statements in programs Programming Techniques 14 11 Annunciators for Set Flags Flags O 1 2 3 and 4 have annunciators in the display that turn on when the corresponding flag is set The presence or absence of O 1 2 3 or 4 lets you know at any time whether any of these five flags is set or not However there is no such indication for the status of flags 5 through 11 The states of these flags can be determined by executing the FS instruction from the keyboard See Using Flags below Using Flags Pressing displays the FLAGS menu F CF FS After selecting the function you want you will be prompted for the flag number O 11 For example press EW ELAGS 1 15F 0 to set flag O press EN FLAGS 1 15F LJL0 to set flag 10 press EW FLAGS L1 1 F CJL to set flag 11 FLAGS Menu Menu Key Description SF n Set flag Sets flag n CF n Clear flag Clears flag n FS n Is flag set Tests the status of flag n A fl
240. ns sseesseeeeesesseerreeseserrreessererrrreerreree 4 4 Hyperbolie Funchonsyntstsec arse cota aemawnalenanie 4 6 Percentage FUNCTIONS ccseeeeececeeeneeteecceeeeeuaueeteceeeeasaeeeeecs 4 6 Physics Constants v asses eytepugh anno EE EAEE EE e 4 8 Conversion Functions cceeeeeeeeceeeceeceeceeeeeeeeeteeeeeeeeeeeeeeeees 4 10 Rectangular Polar Conversions cccsssseeeeeeeesteeeeeesenees 4 10 MIME CONVEFSIONS eiecit a Bove uaecdeversceeiedeensacenansemaowend 4 13 Angle Conversions pcasivessivail iavatsvossenunianheoaves ere mesure 4 13 Unit Conversions ccceeeeeceeccceeeeeeeeceeeeeeeeeeseeeeeeeeeeereeeess 4 14 Probability Functions arise aitasiartaeeriartieliaaigenaen orate 4 15 Factorial Sct sun S cs Sncoe eeu Rooacnartarte bacon thine Manse Raa pater eaer aes 4 15 GOMMA cats cad ce e ct de ayaa EEE EE E E ton haas 4 15 Probability a4 resus tecovea ter tae cas Suede ta teMiaveiaceuonse ere a a 4 15 P ris ot Numbers iis ese naa eas 4 16 Contents 3 By Fractions enni a a a a 5 1 Entering Fractions seinna E iR 5 1 Fractions in the Displayriecusiedetasttacendsisey oat Rea eure aaionlan 5 2 Display RULES ives mcctu ya exw raed aoan a A ied EE sump tb oiai 5 2 Accuracy NAICS sn iwsanecusonnen pie mrgnataasmaaran ines 5 3 Changing the Fraction Display ccccceeeeseeeeeeeeetteeeeeeeeteeeees 5 4 Setting the Maximum Denominator cseecceeeetteeeeenteeeeeeees 5 4 Choosing a Fraction Formot cs
241. nters the first new data pair 1 6866 6 ENTER 4 0 0 6 8888 Display shows n the number z BEBE of data pairs you entered We LAST x 6 6868 Brings back last x value Last 468 BEBE y is still in Y register Ee 6 BEBB Deletes the last data pair 1 6866 6 ENTER 4 0 6 6686 Reenters the last data pair 2 BEEBE 4 ENTER 2 0_ EN 4 6668 Deletes the first data pair a 1 6666 Statistical Operations 12 3 5 ENTER 2 0 5 666G Reenters the first data pair 2 BEBB There is still a total of two data pairs in the statistics registers Statistical Calculations Once you have entered your data you can use the functions in the statistics menus Statistics Menus Menu Key Description L R The linear regression menu linear estimation and curve fitting F m b See Linear Regression later in this chapter x y 6 The mean menu Y Wy See Mean below s 0 rss Sc The standard deviation menu o o See Sample Standard Deviation and Population Standard Deviation later in this chapter SUMS Wea SUMS The summation menu N Ex Ev Ex Eye Ex See Summation Statistics later in this chapter Mean Mean is the arithmetic average of a group of numbers m Press EN Y for the mean of the x values m Press 4 2_ for the mean of the y values m Press EW 7 1 gt J 2 n for
242. nts while calculating 3 4 9 T 1 1 1 Z 2 1 2 vis E xlala zlale a 1 2 3 1 The stack drops its contents The T top register replicates its contents 2 The stack lifts its contents The T register s contents are lost 3 The stack drops m Notice that when the stack lifts it replaces the contents of the T top register with the contents of the Z register and that the former contents of the T register are lost You can see therefore that the stack s memory is limited to four numbers E Because of the automatic movements of the stack you do not need to clear the X register before doing a new calculation Most functions prepare the stack to lift its contents when the next number enters the X register See appendix B for lists of functions that disable stack lift RPN The Automatic Memory Stack 2 5 How ENTER Works You know that separates two numbers keyed in one after the other In terms of the stack how does it do this Suppose the stack is again filled with 1 2 3 and 4 Now enter and add two new numbers Lifts the stack Lifts the stack and replicates the X register Does not lift the stack DOIN T Drops the stack and replicates the T register replicates the contents of the X register into the Y register The next number you key in or recall writes over the copy of the first number left in the X register The effect is simply to separate two sequentially entered numbers You can us
243. on specifying the integrand though it can be any type of equation If you want the equation to prompt for variable values instead of including INPUT instructions make sure flag 11 is set 4 End the program with a RTN Program execution should end with the value of the function in the X register Example Program Using Equation The sine integral function in the example in chapter 8 is sit ji yd x This function can be evaluated by integrating a program that defines the integrand S661 LBL Defines the function S02 SINCHI H The function as an expression Checksum and length OEEO 8 S883 RTH Ends the subroutine Checksum and length of program D57E 17 Enter this program and integrate the sine integral function with respect to x from O to 2 t 2 Keys Display Description In RPN mode MODE 2 2RAD Selects Radians mode E FN 5 Selects label S as the integrand 0 ENTER 2 2 Enters lower and upper limits of integration EY CIC INTEGRATING Integrates function from O to 2 Je displays result 1 6654 MODE 1 10EG 1 6654 Restores Degrees mode Solving and Integrating Programs 15 9 Using Integration in a Program Integration can be executed from a program Remember to include or prompt for the limits of integration before executing the integration and remember that accuracy and execution time are controlled by the display format at the time the program runs The two int
244. one variable or when known values are supplied for all variables except one then to solve for x is to find a root of the equation A root of an equation occurs where an equality or assignment equation balances exactly or where an expression equation equals zero Solving an Equation To solve an equation excluding built in equations for an unknown variable 1 Press and display the desired equation If necessary type the equation as explained in chapter 6 under Entering Equations into the Equation List Solving Equations 7 1 2 Press Wea SOLVE then press the key for the unknown variable For example press F SOLVE X to solve for x The equation then prompts for a value for every other variable in the equation 3 For each prompt enter the desired value m If the displayed value is the one you want press R S m f you want a different value type or calculate the value and press RZS For details see Responding to Equation Prompts in chapter 6 You can halt a running calculation by pressing or R S When the root is found it s stored in the relation variable and the variable value is viewed in the display In addition the X register contains the root the Y register contains the previous estimate value or Zero and the Z register contains the value of the root D value which should be zero For some complicated mathematical conditions a definitive solution cannot be found and the calculator displays HO
245. onverts it to hexadecimal 11 6 Base Conversions and Arithmetic and Logic MAM FFFFFFOOEh ENTER Wea BASE 4 4B 1H Liiidiidiiiliim rey itiiiiiiiiiigim Wea gt iigiiiies WS BASE 1DEc 546 e806 Range of Numbers 2 s complement sign changed Binary version indicates more digits The number is negative since the highest bit is 1 Displays the rest of the number by scrolling one screen Displays the rightmost window Negative decimal number The 36 bit binary number size determines the range of numbers that can be represented in hexadecimal 9 digits octal 12 digits and binary bases 36 digits and the range of decimal numbers 11 digits that can be converted to these other bases Range of Numbers for Base Conversions Base Positive Integer Negative Integer of Largest Magnitude of Largest Magnitude Hexadecimal 7 FFFFFFFFh 800000000h Octal 3777777777770 4000000000000 Binary 0111111111111111111111 10000000000000000000000 11111111111111b 0000000000000b Decimal 34 359 738 367 34 359 738 368 Numbers outside of this range can not be entered when a non decimal base is selected Base Conversions and Arithmetic and Logic 11 7 In BIN OCT HEX If a number entered in decimal base is outside the range given above then it produces the message TOO BIG Any operation using TOO BIG causes an overflow condition which substitutes the largest pos
246. oose to work problems in a left to right order For example you have already calculated 2 14 RPN The Automatic Memory Stack 4 14 7 x 3 2 by starting with the innermost parentheses 7 x 3 and working outward just as you would with pencil and paper The keystrokes were 3 ROI MIEN A If you work the problem from left to right press 4 ENTER OC GJ ENTER WENT IDA This method takes one additional keystroke Notice that the first intermediate result is still the innermost parentheses 7 x 3 The advantage to working a problem left to right is that you don t have to use to reposition operands for noncommutative functions EE and E However the first method starting with the innermost parentheses is often preferred because m It takes fewer keystrokes It requires fewer registers in the stack Note When using the left to right method be sure that no more The above example when solved left to right needed all registers in the stack at than four intermediate numbers or results will be needed at one time the stack can hold no more than four numbers one point Keys Display Description 4 ENTER 11 4 14 6668 Saves 4 and 14 as intermediate ENTER numbers in the stack 7 ENTER 3 a At this point the stack is full with numbers for this calculation E3 21 6668 Intermediate result E3 35 6688 Intermediate result RPN The Automatic Memory Stack 2 15 2
247. opulation standard deviation of x values V gt xP n fF SADIDID 0 Returns population standard deviation of y values J y 7 n A J FH a _ variable Integrates the displayed equation or the program selected by FN using lower limit of the variable of integration in the Y register and upper limit of the variable of integration in the X register LO parenthesis press to leave the parenthesis for further calculation L A vector symbol for performing vector operations m A complex number symbol for performing complex number operations 12 11 12 11 12 11 12 11 8 2 15 7 6 6 Si Operation Index Name A through Z ABS ACOS ACOSH MODE 4 4ALG ALOG ALL AND ARG ASIN ASINH ATAN ATANH Keys and Description RCL variable Value of named variable F ABS Absolute value Returns x A F ACOS Arc cosine Returns cos 1x Ea HYP Wea acos Hyperbolic arc cosine Returns cosh 1 x Activates Algebraic mode ra Common exponential Returns 10 raised to the specified power antilogarithm ESN DISPLAY 4 4ALL Displays all significant digits May have to scroll right 3 LJ to see all of the digits EW LOGIC L1 1 AND Logic operator EN ARG Replaces a complex number with its Argument 0 P ASIN Arc sine Returns sin 1 x EN HYP Wed AS
248. or reentering them and without using parentheses Work from the Parentheses Out For example evaluate 12 3 x 7 If you were working out this problem on paper you would first calculate the intermediate result of 12 3 i243 15 then you would multiply the intermediate result by 7 15 x 7 105 Evaluate the expression in the same way on the HP 35s starting inside the parentheses Keys Display Description CENTER 3 G 15 8888 Calculates the intermediate result first You don t need to press to save this intermediate result before proceeding since it is a calculated result it is saved automatically 2 12 RPN The Automatic Memory Stack Keys Display Description 165 6666 Pressing the function key produces the answer This result can be used in further calculations Now study the following examples Remember that you need to press only to separate sequentially entered numbers such as at the beginning of an expression The operations themselves E etc separate subsequent numbers and save intermediate results The last result saved is the first one retrieved as needed to carry out the calculation Calculate 2 3 10 Keys Display Description CIENEGA 14 8888 Calculates 3 10 first ooa 6 1538 Puts 2 before 13 so the division is correct 2 13 Calculate 4 14 7 x 3 2 Keys Display Description C7 ENTER 3X 21 8666 Calculates 7 x 3 goog J
249. ork in programs just as they do as functions executed from the keyboard 13 24 Simple Programming This allows you to write programs that accept numbers in any of the four bases do arithmetic in any base and display results in any base When writing programs that use numbers in a base other than 10 set the base mode both as the current setting for the calculator and in the program as an instruction Selecting a Base Mode in a Program Insert a BIN OCT or HEX instruction into the beginning of the program You should usually include a DEC instruction at the end of the program so that the calculator s setting will revert to Decimal mode when the program is done An instruction in a program to change the base mode will determine how input is interpreted and how output looks during and after program execution but it does not affect the program lines as you enter them Numbers Entered in Program Lines Before starting program entry set the base mode The current setting for the base mode determines the result of program An annunciator tells you which base is the current setting Compare the program lines below in the decimal and non decimal mode All decimal and non decimal numbers are left justified in the calculator s display Decimal mode set Binary mode set PRGM l PRGM BIN AGGES BIH AGES BIH Agia 16 Decimal number AGIA 16b Binary number can omit the sign should add the d base sign b Simple Programming 13 25
250. ormb Linear regression curve fitting and linear estimation x M EH Arithmetic mean of statistical x and y values weighted mean of statistical x values Sx SY OX OF Sample standard deviation population standard deviation Menu to access the values of 41 physics constants refer to Physics constants on page 4 8 mn Ex Ey Exe Eve Exy Statistical data summations DEC HES OCT BIN da h a amp Base conversions decimal hexadecimal octal and binary SGM INT Rmar IMTG FP IP Sign value integer division remainder from division greatest integer fractional part integer part AHD XOR OR HOT HAHD HOR Logic operators 12 12 12 12 AC 11 1 6 Getting Started FLAGS x y x 0 MEM MODE DISPLAY RV RD CLEAR Programming Instructions SF CF FS Functions to set clear and test flags L lt gt 2H Comparison tests of the X and Y registers S lt gt 2 Comparison tests of the X register and zero Other functions VRE PG Memory status bytes of memory available catalog of variables catalog of programs program labels DEG RAD GRAD ALG RPH Angular modes and operation mode Fix SCI ENG ALL 1 666 1866 xtv tye rAd Fixed scientific engineering full floating point numerical display formats radix symbol options or complex number display format in RPN mode only xiy and r6a are available HOY 2 T Functions to review the stack in ALG mode X
251. overs The allocation and requirements of user memory How to reset the calculator without atfecting memory How to clear purge all of user memory and reset the system defaults and Which operations affect stack lift Managing Calculator Memory The HP 35s has 30KB of user memory available to you for any combination of stored data variables equations or program lines SOLVE f FN and statistical calculations also require user memory The J FN operation is particularly expensive to run All of your stored data is preserved until you explicitly clear it The message MEMORY FULL means that there is currently not enough memory available for the operation you just attempted You need to clear some or all of user memory For instance you can m Clear any or all equations see Editing and Clearing Equations in chapter 6 m Clear any or all programs see Clearing One or More Programs in chapter 13 m Clear all of user memory press Wea CLEAR 3 ALL To see how much memory is available press EEW MEM The display shows the number of bytes available User Memory and the Stack B 1 To see the memory requirements of specific equations in the equation list 1 Press to activate Equation mode EM LIST TOP or the lett end of the current equation will be displayed 2 If necessary scroll through the equation list press or until you see the desired equation 3 Press Et to see the checksum hexadecimal a
252. oximations are not yet as accurate as the accuracy of f x would permit the algorithm is iterated repeated with a larger number of sample points These iterations continue using about twice as many sample points each time until the resulting approximation is as accurate as is justified considering the inherent uncertainty in f x More about Integration E 1 As explained in chapter 8 the uncertainty of the final approximation is a number derived from the display format which specifies the uncertainty for the function At the end of each iteration the algorithm compares the approximation calculated during that iteration with the approximations calculated during two previous iterations If the difference between any of these three approximations and the other two is less than the uncertainty tolerable in the final approximation the calculation ends leaving the current approximation in the X register and its uncertainty in the Y register It is extremely unlikely that the errors in each of three successive approximations that is the differences between the actual integral and the approximations would all be larger than the disparity among the approximations themselves Consequently the error in the final approximation will be less than its uncertainty provided that f x does not vary rapidly Although we can t know the error in the final approximation the error is extremely unlikely to exceed the displayed uncertainty of the approx
253. period specified above due to defects in material and workmanship when properly installed and used If HP receives notice of such defects during the warranty period HP will replace software media which does not execute its programming instructions due to such defects HP does not warrant that the operation of HP products will be uninterrupted or error free If HP is unable within a reasonable time to repair or replace any product to a condition as warranted you will be entitled to a refund of the purchase price upon prompt return of the product with proof of purchase HP products may contain remanufactured parts equivalent to new in performance or may have been subject to incidental use Warranty does not apply to defects resulting from a improper or inadequate maintenance or calibration b software interfacing parts or supplies not supplied by HP c unauthorized modification or misuse d operation outside of the published environmental specifications for the product or e improper site preparation or maintenance Support Batteries and Service A 7 6 HP MAKES NO OTHER EXPRESS WARRANTY OR CONDITION WHETHER WRITTEN OR ORAL TO THE EXTENT ALLOWED BY LOCAL LAW ANY IMPLIED WARRANTY OR CONDITION OF MERCHANTABILITY SATISFACTORY QUALITY OR FITNESS FOR A PARTICULAR PURPOSE IS LIMITED TO THE DURATION OF THE EXPRESS WARRANTY SET FORTH ABOVE Some countries states or provinces do not allow limitations on the duration of an implied warr
254. pped or if power is interrupted B 2 User Memory and the Stack Clearing Memory The usual way to clear user memory is to press W CLEAR 3 ALL However there is also 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 following MEMORY CLEAR procedure These keystrokes clear all of memory reset the calculator and restore all format and modes to their original default settings shown below Press and hold down the key 2 Press and hold down R S 3 Press Li You will be pressing three keys simultaneously When you release all three keys the display shows MEMORY CLEAR if the operation is successful User Memory and the Stack B 3 Stack registers Variables Indirect Variables Logic Cleared to zero Cleared to zero Not defined Unchanged Category CLEAR ALL MEMORY CLEAR Default Angular mode Unchanged Degrees Base mode Unchanged Decimal Contrast setting Unchanged Medium Decimal point Unchanged we Thousand separator Unchanged 1 000 Denominator c value Unchanged 4095 Display format Unchanged FIX 4 Flags Unchanged Cleared Complex mode Unchanged xiy Fraction display mode Unchanged Off Random number seed Unchanged Zero Equation pointer EQN LIST TOP EQN LIST TOP Equation
255. pproximation of the integral The integral is 1 61 0 0161 Since the uncertainty would not affect the approximation until its third decimal place you can consider all the displayed digits in this approximation to be accurate If the uncertainty of an approximation is larger than what you choose to tolerate you can increase the number of digits in the display format and repeat the integration provided that f x is still calculated accurately to the number of digits shown in the display In general the uncertainty of an integration calculation decreases by a factor of ten for each additional digit specified in the display format Example Changing the Accuracy For the integral of Si 2 just calculated specify that the result be accurate to four decimal places instead of only two Integrating Equations 8 7 Keys Display Description ES DISPLAY 2 1 6879 2 Specifies accuracy to four decimal 28C1 4 places The uncertainty from the last example is still in the display RYRY 8 66668 Rolls down the limits of integration 2 BBBBEG from the Z and T registers into the X and Y registers EQN SINGH H Displays the current equation ey x INTEGRATING Calculates the result j 1i 64EG EZDI 1 6656E 4 Note that the uncertainty is about 1 100 as large as the uncertainty of the SCI 2 result calculated previously Ly 28C1 4 g eane Restores FIX 4 format O 10E6 6 6682 Restores Degrees mode This uncertainty ind
256. press R S Repeat steps 3 and 4 for each data pair If you discover that you have made an error after you have pressed in step 3 with the 7 value prompt still visible press again displaying the value prompt and press to undo remove the last data pair If you discover that you made an error after step 4 press KEQ UJ ENTER In either case continue at step 3 After all data are keyed in press CR ENTER to see the correlation coefficient R Press RZS to see the regression coefficient B Press RZS to see the regression coefficient M Press R S to see the value prompt for the X y estimation routine 10 If you wish to estimate y based on x key in x at the value prompt then press RZS to see y Y7 11 If you wish to estimate xX based on y press until you see the value prompt key in y then press to see X 7 12 For more estimations go to step 10 or 11 16 8 Statistics Programs 13 For a new case go to step 2 Variables Used B za Statistics registers Example 1 Regression coefficient y intercept of a straight line also used for scratch Regression coefficient slope of a straight line Correlation coefficient also used for scratch The x value of a data pair when entering data the hypothetical x when projecting y or X x estimate when given a hypothetical y The y value of a data pair when entering data the hypothetical y when projecting x or y y estima
257. quation Search fails with guesses O and 10 Description Selects Equation mode Enters the equation Checksum and length Cancels Equation mode Your positive guesses for the root Selects Equation mode displays the equation Solves for x using guesses 0 005 and 5 Previous estimate is the same f x 0 Watch what happens when you use negative values for guesses Keys Display Description Hopr 1 e666 Your negative guesses for the root ENTER FZ 2 EQN 1B ITHWCK Selects Equation mode displays the equation Wes SOLVE X Solves for X displays the result G 1666 Example Find the root of the equation x x 0 3 0 5 0 Enter the equation as an expression Keys Display Description EQN Selects Equation mode 2 RCD Na Enters the equation RELI ILI WHA LI ENTER SQRTCH X 0 3 m E SHOW CE 9F36 Checksum and length LH 12 KA Cancels Equation mode First attempt to find a positive root Keys Display Description maso Your positive guesses for the ENTER JLO iB root EQN SORTCH CH 0 33 Selects Equation mode displays the left end of the equation E SOLVE Calculates the root using 6 1866 guesses O and 10 More about Solving D 11 Now attempt to find a negative root by entering guesses 0 and 10 Notice that the function is undefined for values of x between O and 0 3 since those values produce a positive denomi
258. rera e e i 9 2 Complex Operations cccccceeeccccceeeeeneeeeeeesnnaeeeeeeseneeeeeeeees 9 2 Using Complex Numbers in Polar Notation ccccccceceseeeeeees 9 5 Complex Numbers in Equations c cccccccsessseeeeeeeeseeeeeeeeeens 9 7 Complex Number in Program sscssscsssssssssssscsseseessesessseeenees 9 8 10 Vector Arithmetic cscccsscesscseeseeeesesseesseeeseeees 10 1 Vector Operations sscceseeceeeeseeeeeeeeeeeeeeeeceeececeeceeeeeeeeeeanaaea 10 1 Absolute value of the vector cc ccccssssseeeseeeeeteeeeseeeeeees 10 3 Contents 5 Dot OPOAU Ch cateuierteo an tvacysitatuaitar sea scoe teva tuasarant yeas E E 10 4 Angle between vectors s ccccccesessseeeeeeestteeeeeeeeeseeeeeeseaaes 10 5 Vectors in Equations siceecceivcccdel cage ccadasnnaedseaetectsmuanenetieaneetees 10 6 Vectors in Prograims sscccssssccsssscsssscsesseesssssesssseeesseesssseesees 10 7 Creating Vectors from Variables or Registers cc sceeeeeees 10 8 11 Base Conversions and Arithmetic and Logic 11 1 Arithmetic in Bases 2 8 and 16 0 ecceeeccccesecccaseecccenecceceneeecs 11 4 The Representation of Numbers ccccscceeeeeeeeeeeeeeeeeeeeeeees 11 6 Negative Numbers iiss cnccrevsrriu enn vede laxderdseasadanatespuboenaderinc 11 6 Reingeso hiINwin bers coccrscs c aac uneresassonesneeassiautanuaryaer 11 7 Windows for Long Binary Numbers sccceeeeceeeee
259. res the input value for P Tests for even input Increments P if input an even number Stores 3 in test divisor D EA89 47 This routine tests P to see if it is prime Finds the fractional part of P D Tests for a remainder of zero not prime If the number is not prime tries next possibility Tests to see whether all possible factors have been tried If all factors have been tried branches to the display routine Branches to test potential prime with new factor Checksum and length C6B5 53 Miscellaneous Programs and Equations 17 9 Flags Used None Program Instructions Key in the program routines press when done Key in a positive integer greater than 3 Press XEQ PJ ENTER to run program Prime number P will be displayed To see the next prime number press R S hon Variables Used P Prime value and potential prime values D Divisor used to test the current value of P Remarks No test is made to ensure that the input is greater than 3 Example What is the first prime number after 789 What is the next prime number Keys Display Description In ALG mode 7J 8 19 KEQ P Calculates next prime number ofter PI ENTER 797 8888 789 R S P Calculates next prime number ofter 2069 BEB 797 17 10 Miscellaneous Programs and Equations Cross Product in Vectors Here is an example showing how to use the program function to calculate the cross product Cross product v
260. rface area in S Sets flag 10 to display equations Displays message in equations Clears flag 10 Displays volume Displays surface area Ends program Displays label C and the length of the program in bytes Checksum and length of program Cancels program entry Simple Programming 13 17 Now find the volume and surface area of a cylinder with a radius of 2 1 2 cm and a height of 8 cm Keys Display Description In RPN mode XEQ CC ENTER R Starts executing C prompts for value R It displays whatever value happens to be in R magogo H Enters 2 1 2 as a fraction R S value Prompts for H 8 R S VOL AREA Message displayed R S y Volume in cm3 157 6736 R S Surface area in cm2 164 9336 Displaying Information without Stopping Normally a program stops when it displays a variable with VIEW or displays an equation message You normally have to press to resume execution If you want you can make the program continue while the information is displayed If the next program line after a VIEW instruction or a viewed equation contains a PSE pause instruction the information is displayed and execution continues after a 1 second pause In this case no scrolling or keyboard input is allowed The display is cleared by other display operations and by the RND operation if flag 7 is set rounding to a fraction Press Wea to enter PSE in a program The VIEW and PSE line
261. rn to the default settings This example uses RPN mode Keys Display 4 4AL L ERFA ESETE 12 345 678 6 7I8ILIL 12 345 678 ENTER EN OSI 6 12 345 678 12 345 6780 mM 8218 12345678 9 aB 123456789 meN 12 345 678 mOPN Fi 12 345 678 BBB to oho to ko Description Select full floating point precision ALL format The default format uses the comma as the thousand separator and the period as the radix Change to use the comma for the radix Note that the thousand separator automatically changes to the period Change to having no comma separator Return to the default format Complex number display format xi i F 4a Complex numbers can be displayed in a number of formats x1 x L and FOO although b is only available in ALG mode In the example below the complex number 3 4i is displayed in all three ways 1 24 Getting Started Example Display the complex number 3 4i in each of the different formats Keys Display Description MODE 4 4ALG Enable ALG mode WOAR zit Enter the complex number It displays 34 as 3i4 the default format aN DISPLAY ER 314 Change to x yi format iisti 3444 ESN DisPLAY L _ Jit Change to r a format The radius is ira or 5053 1361623542 5 and the angle is approximately EN OSA A 53 13 LA SHOWing Full 12 Digit Precision Changing the number of displayed decimal p
262. rogram entry mode 1 4 13 6 programs See program labels ALG operations 13 4 base mode 13 25 branching 14 2 14 4 14 6 14 16 calculations in 13 13 calling routines 14 1 14 2 catalog of 1 28 13 22 checksums 13 22 13 23 B 2 clearing 13 6 13 22 13 23 clearing all 13 6 13 23 comparison tests 14 7 conditional tests 14 7 14 9 14 12 14 17 15 6 data input 13 5 13 13 13 14 data output 13 5 13 14 13 18 Index 7 deleting 1 28 deleting all 1 5 deleting equations 13 7 13 20 deleting lines 13 20 designing 13 3 14 1 editing 1 4 13 7 13 20 editing equations 13 7 13 20 entering 13 6 equation evaluation 14 11 equation prompting 14 11 equations in 13 4 13 7 errors in 13 19 executing 13 10 flags 14 9 14 12 for integration 15 7 for SOLVE 15 1 D 1 fractions with 5 8 13 15 14 9 functions not allowed 13 24 indirect addressing 14 20 14 21 14 23 inserting lines 13 6 13 20 interrupting 13 19 lengths 13 22 13 23 B 2 line numbers 13 22 loop counter 14 18 looping 14 16 14 17 memory usage 13 22 messages in 13 16 13 18 moving through 13 11 not stopping 13 18 numbers in 13 7 pausing 13 19 prompting for data 13 12 purpose 13 1 resuming 13 16 return at end 13 4 routines 14 1 RPN operations 13 4 running 13 10 showing long number 13 7 stepping through 13 11 stopping 13 14 13 16 13 19 techniques 14 1 testing 13 11 using integration 15 10 using SOLVE 15 6 Index 8
263. rs or variables For optimal efficiency of the stack we have modified that notation to specify the operators after the numbers Hence the term Reverse Polish Notation or RPN The stack consists of four storage locations called registers which are stacked on top of each other These registers labeled X Y Z and T store and manipulate four current numbers The oldest number is stored in the T top register The stack is the work area for calculations RPN The Automatic Memory Stack 2 1 T 1 Part2 Pere Oldest number Partl 0 0000 L Part3 C Part2 o Partl 0 0000 Displ Part splayed X Part2 Displayed Part The most recent number is in the X register this is the number you see in the second line of the display Every register is separated into three parts m A real number or a 1 D vector will occupy part 1 part 2 and part 3 will be null in this case A complex number or a 2 D vector will occupy part 1 and part 2 part 3 will be null in this case m A 3 D vector will occupy part 1 part 2 and part 3 In programming the stack is used to perform calculations to temporarily store intermediate results to pass stored data variables among programs and subroutines to accept input and to deliver output 2 2 RPN The Automatic Memory Stack The X and Y Registers are in the Display The X and Y Registers are what you see except when a menu a message an equation
264. s or the equation and PSE lines are treated as one operation when you execute a program one line at a time 13 18 Simple Programming Stopping or Interrupting a Program Programming a Stop or Pause STOP PSE a Pressing run stop during program entry inserts a STOP instruction This will display the contents of the X register and halt a running program until you resume it by pressing from the keyboard You can use STOP rather than RTN in order to end a program without returning the program pointer to the top of memory a Pressing a during program entry inserts a PSE pause instruction This will suspend a running program and display the contents of the X register for about 1 second with the following exception If PSE immediately follows a VIEW instruction or an equation that s displayed flag 10 set the variable or equation is displayed instead and the display remains after the 1 second pause Interrupting a Running Program You can interrupt a running program at any time by pressing or R S The program completes its current instruction before stopping Press run stop to resume the program If you interrupt a program and then press XEQ GTO or EW RIN you cannot resume the program with R S Re execute the program instead XEQ label line number Error Stops If an error occurs in the course of a running program program execution halts and an error message appears in the display There is
265. s g required in this case EIRAN SIHCHI H_ ENTER SIHIK Terminates the equation m SHOW CK 6EE6 Checksum and length LH 8 KA Leaves Equation mode Now integrate this function with respect to x that is X from zero to 2 t 2 Keys Display Description MODE 2 2RAD Selects Radians mode 0 STO CXJIENTER 2 Enters limits of integration lower 2 first EQN SIHCHI H Displays the current equation Et INTEGRATING Calculates the result for Si 2 j 1 6654 Integrating Equations 8 5 Accuracy of Integration Since the calculator cannot compute the value of an integral exactly it approximates it The accuracy of this approximation depends on the accuracy of the integrand s function itself as calculated by your equation This is affected by round off error in the calculator and the accuracy of the empirical constants Integrals of functions with certain characteristics such as spikes or very rapid oscillations might be calculated inaccurately but the likelihood is very small The general characteristics of functions that can cause problems as well as techniques for dealing with them are discussed in appendix E Specifying Accuracy The display format s setting FIX SCI ENG or ALL determines the precision of the integration calculation the greater the number of digits displayed the greater the precision of the calculated integral and the greater the time required to calculate it The fewer th
266. s You can convert between rectangular and polar formats for complex numbers degrees radians and gradients for angle measures E E m decimal and hexagesimal formats for time and degree angles E various supported units cm in kg lb etc With the exception of the rectangular and polar conversions each of the conversions is associated with a particular key The left yellow shift of the key converts one way while the right blue shift of the same key converts the other way For each conversion of this type the number you entered is assumed to be measured using the other unit For example when using to convert a number to Fahrenheit degrees the number you enter is assumed to be a temperature measured in Celsius degrees The examples in this chapter utilize RPN mode In ALG mode enter the function first then the number to convert Rectangular Polar Conversions Polar coordinates r and rectangular coordinates x y are measured as shown in the illustration The angle 8 uses units set by the current angular mode A calculated result for will be between 180 and 180 between r and r radians or between 200 and 200 grads 4 10 Real Number Functions To convert between rectangular and polar coordinates The format for representing complex numbers is a mode setting You may enter a complex number in any format upon entry the complex number is converted to the format determined by the mode setting Here are the steps
267. s constants in the CONST menu You can press Et to view the following items CONST Menu Items Description Value C Speed of light in vacuum 299792458 m s7 Standard acceleration of gravity 9 80665 m s 2 G Newtonian constant of 6 673x10 71 m3 kg s72 gravitation Wm Molar volume of ideal gas 0 022413996 m3 mol He Avogadro constant 6 02214199x10 23 mol 1 Ro Rydberg constant 10973731 5685 m 1 el Elementary charge 1 6021 76462x10 19 C me Electron mass 9 10938 188x10 31 kg mF Proton mass 1 67262158x10 27 kg mm Neutron mass 1 674927 16x10 27 kg mH Muon mass 1 88353 109x10 28 kg k Boltzmann constant 1 3806503x10 23 J K 1 h Planck constant 6 62606876x10 34 J s fh Planck constant over 2 pi 1 05457 1596x10 34 J s a Magnetic flux quantum 2 067833636x10 15 Wb ao Bohr radius 5 291772083x10 11 m a Electric constant 8 854187817x10 12 F m F Molar gas constant 8 314472 J mol 1 k 1 F Faraday constant 96485 3415 C mol 1 u Atomic mass constant 1 66053873x10 27 kg Ho Magnetic constant 1 2566370614x10 6 NA HE Bohr magneton 9 27400899x10 24 J T HH Nuclear magneton 5 05078317x10 27 J T HF Proton magnetic moment 1 410606633x10 26 J T He Electron magnetic moment 9 28476362x1 0 24 J T un Neutron magnetic moment 9 662364x10 27 J T7 4 8 Real Number Functions Items Description Value HH Muon magnetic moment 4 490448 1310 26 J T re Classical electron ra
268. s for the unknown variable Based on the results with those two guesses SOLVE generates another better guess Through successive iterations SOLVE finds a value for the unknown that makes the value of the equation equal to zero When SOLVE evaluates an equation it does it the same way does any in the equation is treated as a For example the Ideal Gas Law equation is evaluated as Px V N x R x T This ensures that an equality or assignment equation balances at the root and that an expression equation equals zero at the root Some equations are more difficult to solve than others In some cases you need to enter initial guesses in order to find a solution See Choosing Initial Guesses for SOLVE below If SOLVE is unable to find a solution the calculator displays HO ROOT FHO See appendix D for more information about how SOLVE works Verifying the Result After the SOLVE calculation ends you can verify that the result is indeed a solution of the equation by reviewing the values left in the stack m The X register press to clear the viewed variable contains the solution root for the unknown that is the value that makes the evaluation of the equation equal to zero Solving Equations 7 7 m The Y register press IRH contains the previous estimate for the root or equals to zero This number should be the same as the value in the X register If it is not then the root returned was only an approximation and
269. s is circular so you can wrap the program pointer from the bottom to the top and reverse While program entry is active there are four ways to change the program pointer the displayed line Aa and L allows you to move from label to label If no labels are defined It will move to the top or bottom of the program To move more than one line at a time scrolling continue to hold the or key Simple Programming 13 21 m Press CILY to move the program pointer to PRGM TOP m Press CJ label nnn to move to a specific line If Program entry mode is not active if no program lines are displayed you can also move the program pointer by pressing label line number Canceling Program entry mode does not change the position of the program pointer Memory Usage If during program entry you encounter the message MEMORY FULL then there is not enough room in program memory for the line you just tried to enter You can make more room available by clearing programs or other data See Clearing One or More Programs below or Managing Calculator Memory in appendix B The Catalog of Programs MEM The catalog of programs is a list of all program labels with the number of bytes of memory used by each label and the lines associated with it Press EN 2 2F GNM to display the catalog and press or to move within the list You can use this catalog to m Review the labels in program memory and the memory cost of each labeled
270. s the initialization routine B 86668 16 16 Statistics Programs R S 57 Accepts the default value of zero for M 1 6666 R S 1 e888 Accepts the default value of 1 for S XEQ D ENTER Starts the distribution program and value prompts for X 3 R S a Enters 3 for X and starts computation of 6 6613 Q X Displays the ratio of the population smarter than everyone within three standard deviations of the mean mom 13 4984 Multiplies by the population Displays x the approximate number of blind dates in the local population that meet the criteria Since your friend has been known to exaggerate from time to time you decide to see how rare a 20 date might be Note that the program may be rerun simply by pressing R S Keys Display Description In RPN mode R S x Resumes program 3 6666 2 R S a Enters X value of 2 and calculates G e228 qX mmama 227 5612 Multiplies by the population for the x revised estimate Example 2 The mean of a set of test scores is 55 The standard deviation is 15 3 Assuming that the standard normal curve adequately models the distribution what is the probability that a randomly selected student scored at least 90 What is the score that only 10 percent of the students would be expected to have surpassed What would be the score that only 20 percent of the students would have failed to achieve Statistics Programs 16 17 Keys Display Description In RPN mo
271. s x to the Y register and y to the X register Displays the x y comparison tests menu e 229 x It x y executes next program line if x y skips next program line EW eLA s If x lt y executes next program line if x gt y skips next program line ey ANL If x lt y executes next program line if x2y skips next program line EY wyboILIDI gt If x gt y executes next program line if x lt y skips next program line BY wybILILILI 2 If x2y executes next program line if x lt y skips next program line 12 11 4 15 14 7 14 7 14 7 14 7 14 7 14 7 Operation Index G 15 Name Keys and Description Page xy E Oooo 47 If x y executes next program line if x y skips next program line B Displays the x 0 comparison tests 14 7 menu x 0 Wed x20 14 7 If x40 executes next program line if x 0 skips the next program line x lt 0 Wed x20 s 14 7 If x lt 0 executes next program line if x gt 0 skips next program line x lt 0 Wes 470 I0 lt 14 7 If x lt O executes next program line if x20 skips next program line x gt 0 fe 70 DICIL gt 14 7 If x gt 0 executes next program line if x lt O skips next program line x20 a OO ILILIL 2 14 7 If x20 executes next program line if x lt 0 skips next program line x 0 B WODILILDILIDA
272. splay The integer part of 2 47 EW ONTG 6 EIP 2QICI4 IPt2 473 7 ENTER 2 8080 The fractional part of 2 47 ENJUNTG G SFF 2 G 4 Frt2 47 gt 7 ENTER G 4700 The absolute value of 7 Fe ABS 2 7 ENTER RBS F3 The sign value of 9 EN NTS 7 1 SGN 9 SCN cr ENTER 1 8086 The greatest integer equal to EN INTG 4 4INTG HGA IMNTGe 5 33 or less than 5 3 3 ENTER 6 BABE Reviewing the Stack The or 0 key produces a menu in the display X Y Z T registers to let you review the entire contents of the stack The difference between the and the a key is the location of the underline in the display Pressing the a displays the underline on the T register pressing the displays the underline on the Y register Pressing displays the following menu SYT value Pressing Wea displays the following menu a 2 T value You can press and Wa along with or L lt to review the entire contents of the stack and recall them They will appear as REGH REGY REGZ or REGT depending on which part of the stacked was recalled and may be used in further calculations ALG Summary C 7 The value of X Y Z T register in ALG mode is the same in RPN mode After normal calculation solving programming or integrating the value of the four registers will be the same as in RPN or ALG mode and retained when you switch between ALG and RPN logic modes Integrating an Equation 1 Key in an equation
273. ss the addition key to see the result 6 ENTER z Enter 6 then place 4 in the x register 4 EW nCr 5 Press the combinations key to see the 15 result MODE 4 4ALG Switch to ALG mode 274 3 ENTER 2 3 Expression and result are both shown a ES Cr nrg 3 Enter the combination function wma nEri g Enter the 6 then move the edit cursor past the comma and enter the 4 ENTER nEri g Press Enter to see the result 15 In ALG mode the infix operators are e9 E and RA The other two argument operations use function notation of the form f x y where x and y are the first and second operands in order In RPN mode the operands for two argument operations are entered in the order Y then X on the stack That is y is the value in the y register and x is the value in the x register The x root of y EZ is the exception to this rule For example to calculate yin RPN mode press 8 ENTER 3 C2 In ALG mode the equivalent operation is keyed in as EW C7 3 2 8 ENTER As with the single argument operations some of the two argument operations display differently in RPN mode than in ALG mode These differences are summarized in the table below 1 20 Getting Started Key In RPN RPN Program In ALG Equation ALG Program y A w xy y XROOT For commutative operations such as and X the order of the operands does not affect the calculated result If you mistakenly enter t
274. ssccssssessseseseeseeseeeees D 1 Contents How SOLVE Finds a Root cccccccseescccuseccceceecccaseccceaesesceneencs D 1 Interpreting Results lt iseiscs ceventaiaiiazevudntudgsondstiwestondubauds iapdesianades D 3 When SOLVE Cannot Find a Roots scicisiocariinwhancniantant D 8 Reine SOT Etrente sci acta de Sack n e a E eae D 13 E More about Integration ssscsccsscesecesesseeeseeees E 1 How the Integral Is Evaluated 5 0caccadsaxasncvdsanugguatsedanvenentqoecunyeanes E 1 Conditions That Could Cause Incorrect Results 00eeeeeeeeeees E 2 Conditions That Prolong Calculation Time esceeeeeceeeeteeeeeeees E 7 Fi MOSSOQ CS EE ET F 1 G Operation Index sscccssccssscessscessccsceesseceseeseees G 1 Contents 11 Part Basic Operation Getting Started Watch for this symbol in the margin It identifies examples or keystrokes that are shown in RPN mode and must be performed differently in ALG mode Appendix C explains how to use your calculator in ALG mode Important Preliminaries Turning the Calculator On and Off To turn the calculator on press LEJ ON is printed on the bottom of the key To turn the calculator off press EW C That is press and release the EN shift key then press which has OFF printed in yellow above it Since the calculator has Continuous Memory turning it off does not affect any information you ve stored To conserve energy the calculator
275. stack operation 2 5 9 2 maximum of function D 8 mean menu 12 4 means statistics calculating 12 4 normal distribution 16 11 memory amount available 1 28 clearing 1 5 1 29 A 1 A 4 B 1 B 3 clearing equations 6 9 clearing programs 1 28 13 6 13 22 clearing statistics registers 12 2 clearing variables 1 28 full A 1 maintained while off 1 1 programs 13 21 B 2 size 1 28 B 1 stack 2 1 Index 6 usage B 1 MEMORY CLEAR A 4 B 3 F 3 MEMORY FULL B 1 F 3 menu keys 1 6 menus example of using 1 8 general operation 1 6 leaving 1 4 1 8 list of 1 6 messages clearing 1 4 displaying 13 16 13 18 in equations 13 16 responding to 1 27 F 1 summary of F minimum of function D 8 modes See angular mode base mode Equation mode Fraction display mode Program entry mode MODES menu angular mode 4 4 money finance 17 1 multiplication dividision 10 2 N negative numbers 1 15 9 3 11 6 nested routines 14 2 15 11 normal distribution 16 11 numbers See binary numbers hex numbers octal numbers variables bases 10 1 13 25 changing sign of 1 15 9 3 clearing 1 4 1 5 1 17 complex 9 1 display format 1 21 11 6 E in 1 15 A 1 editing 1 4 1 17 exchanging 2 4 finding parts of 4 17 fractions in 1 26 5 1 in equations 6 5 in programs 13 7 internal representation 11 6 large and small 1 15 1 17 negative 1 15 9 3 11 6 pertorming arithmetic calculations 1 18 periods and commas in 1 23 A 1 precision D 13 prime
276. step 4 4 The self test produces one of these two results The calculator displays 355 QK if it passed the self test Go to step 5 The calculator displays 355 FATL followed by a one digit number if it failed the self test If you received the message because you pressed a key out of order reset the calculator hold down LCE press and do the self test again If you pressed the keys in order but got this message repeat the self test to verify the results If the calculator fails again it requires service see page A 8 Include a copy of the fail message with the calculator when you ship it for service 5 To exit the self test reset the calculator hold down and press GTO Pressing and starts a continuous self test that is used at the factory You can halt this factory test by pressing any key A 6 Support Batteries and Service Warranty HP 35s Scientific Calculator Warranty period 12 months HP warrants to you the end user customer that HP hardware accessories and supplies will be free from defects in materials and workmanship after the date of purchase for the period specified above If HP receives notice of such defects during the warranty period HP will at its option either repair or replace products which prove to be defective Replacement products may be either new or like new HP warrants to you that HP software will not fail to execute its programming instructions after the date of purchase for the
277. t into the calculator nor search through the functions printed on the keyboard Exiting Menus Whenever you execute a menu function the menu automatically disappears as in the above example If you want to leave a menu without executing a function you have three options 1 8 Getting Started E Pressing backs out of the 2 level CLEAR or MEM menu one level at a time Refer to WER CLEAR in the table on page 1 5 m Pressing or cancels any other menu Keys Display DAUA 123 5678 8 ESN DISPLAY iF 25C1 4 JEHG 4ALL Le or 123 5673_ m Pressing another menu key replaces the old menu with the new one Keys Display WWA i23 5678_ 8 mr IFI 25C yg ZENG 4ALL Wea CLEAR ik 2VARS og ZALL 4E Ka 123 5678 RPN and ALG Modes The calculator can be set to perform arithmetic operations in either RPN Reverse Polish Notation or ALG Algebraic mode In Reverse Polish Notation RPN mode the intermediate results of calculations are stored automatically hence you do not have to use parentheses In Algebraic mode ALG you perform arithmetic operations using the standard order of operations To select RPN mode Press 5 SEPH to set the calculator to RPN mode When the calculator is in RPN mode the RPN annunciator is on Getting Started 1 9 To select ALG mode Press 4 4ALG to set the calculator to ALG mode When the calculator is in ALG mode the ALG annunciator is on E
278. te when given a hypothetical x Statistical accumulation and computation Fit a straight line to the data below Make an intentional error when keying in the third data pair and correct it with the undo routine Also estimate y for an x value of 37 Estimate x for a y value of 101 X 40 5 Y 104 5 Keys In RPN mode KEQ 40 LIS R S 38 6 37 9 36 2 35 1 34 6 102 100 97 5 95 5 94 Display Description a7 Starts straight line routine 1 6666 Y Enters x value of data pair value Statistics Programs 16 9 EN wA R S 3 E WARS WARS x 2 8888 Y 164 5606 x 3 8888 Enters y value of data pair Enters x value of data pair Enters y value of data pair Now intentionally enter 379 instead of 37 9 so that you can see how to correct incorrect entries R S Keys In RPN mode 3 7 9 R S KEQ U ENTER b E b 7 AWARS ARs a G Ea Le D b L Le k a b Le b LJ LJ LJ va 7 R S R S R S R S R S x lt m m Z m 7 Display Y7 162 6666 a7 4 6666 K 3 6666 Y7 162 6666 KF 4 6666 Y 166 6666 K T BEE Y7 o7 o 5666 a7 6 6666 Y7 25 50666 A7 r BBBG R 6 9955 16 10 Statistics Programs Description Enters wrong x value of data pair Retrieves prompt Deletes the last pair Now proceed with the correct data entry Enters correct x
279. te B 4 disabling B 4 enabling B 4 not affecting B 5 operation 2 5 standard deviations calculating 12 6 12 7 grouped data 16 18 normal distribution 16 11 standard deviation menu 12 6 12 7 statistical data See statistics registers clearing 1 5 12 2 correcting 12 2 entering 12 1 initializing 12 2 one variable 12 2 precision 12 10 sums of variables 12 11 two variable 12 2 statistics calculating 12 4 curve fitting 12 8 16 1 distributions 16 11 grouped data 16 18 one variable data 12 2 operations 12 1 two variable data 12 2 statistics menus 12 1 12 4 statistics registers See statistical data accessing 12 12 clearing 1 5 12 2 contain summations 12 1 12 11 12 12 correcting data 12 2 initializing 12 2 no fractions 5 2 viewing 12 11 STO 3 2 13 12 STO arithmetic 3 6 STOP 13 19 storage arithmetic 3 6 subroutines See routines sums of statistical variables 12 11 Index 10 syntax equations 6 14 6 19 13 16 T tangent trig 4 4 9 3 A 2 C 6 temperatures converting units 4 14 limits for calculator A 2 test menus 14 7 testing the calculator A 4 A 5 time formats 4 13 time value of money 17 1 T register 2 5 trigonometric functions 4 4 9 3 C 6 troubleshooting A 4 A 5 turning on and off 1 1 TVM 17 1 twos complement 11 4 11 6 two variable statistics 12 2 U uncertainty integration 8 2 8 6 units conversions 4 14 V variable catalog 1 28 3 4 variables accessing stack register contents B arithm
280. tering in programs 13 7 evaluating 6 10 6 11 6 12 7 7 13 4 14 11 functions 6 5 6 16 G 1 in programs 13 4 13 7 13 24 14 11 integrating 8 2 lengths 6 19 13 7 B 2 list of See equation list long 6 7 Index 3 memory in 13 16 multiple roots 7 9 no root 7 8 numbers in 6 5 numeric value of 6 10 6 11 7 1 7 7 13 4 operation summary 6 3 parentheses 6 5 6 6 6 15 precedence of operators 6 14 prompt for values 6 11 6 13 prompting in programs 14 11 15 1 15 8 roots 7 1 scrolling 6 7 13 7 13 16 solving 7 1 D 1 stack usage 6 11 storing variable value 6 12 syntax 6 14 13 16 TVM equation 17 1 types of 6 9 uses 6 1 variables in 6 3 7 1 with I J 14 23 error messages F 1 errors clearing 1 4 correcting 2 8 F 1 estimation statistical 12 8 16 1 executing programs 13 10 exponential curve fitting 16 1 exponential functions 1 16 4 1 9 3 C5 exponents of ten 1 15 1 16 expression equations 6 10 6 11 7 1 F J FN See integration not programmable 5 10 toggles display mode 5 1 A 2 toggles flag 14 9 factorial function 4 15 financial calculations 17 1 FIX format 1 21 See also display format flags annunciators 14 12 Index 4 clearing 14 12 default states 14 9 equation evaluation 14 11 equation prompting 14 11 fraction display 14 10 meanings 14 9 operations 14 12 overflow 14 9 setting 14 12 testing 14 9 14 12 unassigned 14 9 flow diagrams 14 2 FN in programs 15 6 15 10 integrating programs 15
281. ters In ALG mode use B 2 and Wea lt to see the rest of the characters The and keys are active for stepping through an equation list a catalog of variables lines of a program menu pages or programs in the program catalog The alphabetic keys are active Attention Indicates a special condition or an error Battery power is low 1 6 1 6 13 1 14 Getting Started Keying in Numbers The minimum and maximum values that the calculator can handle are 9 9999999999949 If the result of a calculation is beyond this range the error message OVERFLOW appears momentarily along with the A annunciator The overflow message is then replaced with the value closest to the overflow boundary that the calculator can display The smallest numbers the calculator can distinguish from zero are 1047 If you enter a number between these values the calculator will display O upon entry Likewise if the result of calculation lies between these two values the result will be displayed as zero Entering numbers beyond the maximum range above will result in an error message INYALID DATA clearing the error message returns you to the previous entry for correction Making Numbers Negative The key changes the sign of a number E To key in a negative number type the number then press CA m n ALG mode you may press key before or after typing the number m To change the sign of a number that was entered pr
282. that a power of 10 follows G 6 Operation Index Name Keys and Description Page ENG n ENG Jand ENG ENTER ex EXP F ra FIX n Eat FLAGS FN label FP EOD EENG Selects Engineering display with n digits following the first digit n O through 11 Causes the exponent display for the number being displayed to change in multiple of 3 Separates two numbers keyed in sequentially completes equation entry evaluates the displayed equation and stores result if appropriate Copies x into the Y register lifts y into the Z register lifts z into the T register and loses t Activates or cancels toggles Equation entry mode a Le Natural exponential Returns e raised to the x power Wea LE Natural exponential Returns e raised to the specitied power Lal Converts C to F Turns on and off Fraction display mode DISPLAY LF 1 n Selects Fixed display with n decimal places O lt n lt 11 Displays the menu to set clear and test flags label Selects labeled program as the current function used by SOLVE and J FN Lal 5 SFP Fractional part of x 1 22 1 19 6 4 6 11 2 6 6 3 13 7 4 1 Operation Index Name Keys and Description Page FS n GAL GRAD GTO C label nnn GTO C E HEX ey HYP gt HMS HMS gt C 3 IN IDIV EN HAG
283. the curves and the relevant equations are shown below The internal regression functions of the HP 35s are used to compute the regression coefficients Statistics Programs 16 1 Straight Line Fit Exponential Curve Fit s E y y y B Mx x Logarithmic Curve Fit Power Curve Fit L P y y y B MInx y BxM x To fit logarithmic curves values of x must be positive To fit exponential curves values of y must be positive To fit power curves both x and y must be positive A LOGEHEG 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 12 16 2 Statistics Programs Program Listing Program Lines Description In RPN mode 2661 LBL This routine sets the status for the straight line model 5662 CF 6 Clears flag O the indicator for In X S663 CF i Clears flag 1 the indicator for In Y S864 CTO Z661 Branches to common entry point Z Checksum and length 8E85 12 L i LEL L This routine sets the status for the logarithmic model Lage SFB Sets flag O the indicator for In X Lees CF i Clears flag 1 the indicator for In Y Lee4 GTO Z661 Branches to common entry point Z Checksum and length AD1B 12 E i LEL E This routine sets the status for the exponential model E 2 CFE Clears flag O the indicator for In X
284. the equation list HBa or WEY Jumps to the top or bottom of the equation list EN Shows the displayed equation s checksum verification value and length bytes of memory EN UNDO Recovers the most recently deleted element or equation Cc Leaves Equation mode You can also use equations in programs this is discussed in chapter 13 Entering and Evaluating Equations 6 3 Entering Equations into the Equation List The equation list is a collection of equations you enter The list is saved in the calculator s memory Each equation you enter is automatically saved in the equation list To enter an equation You can make an equation as long as you want it is limited only by the amount of available memory 1 Make sure the calculator is in its normal operating mode usually with a number in the display For example you can t be viewing the catalog of variables or programs 2 Press EQN The EQN annunciator shows that Equation mode is active and an entry from the equation list is displayed 3 Start typing the equation The previous display is replaced by the equation you re entering the previous equation isn t affected If you make a mistake press L or EW UNDO as required 4 Press ENTER to terminate the equation and see it in the display The equation is automatically saved in the equation list right after the entry that was displayed when you started typing If you press instead the eq
285. the weighted mean of the x values using the y values as weights or frequencies The weights can be integers or non integers 12 4 Statistical Operations Example Mean One Variable Production supervisor May Kitt wants to determine the average time that a certain process takes She randomly picks six people observes each one as he or she carries out the process and records the time required in minutes 15 5 9 25 10 0 12 5 12 0 8 5 Calculate the mean of the times Treat all data as x values Keys Display Description Wes CLEAR 4 42 Clears the statistics registers MYO Bey 1 8888 Enters the first time WAALA Enters the remaining data six WUWA pepe data points accumulated WBW DE x ev EM Calculates the mean time to 11 2917 complete the process Example Weighted Mean Two Variables A manufacturing company purchases a certain part four times a year Last year s purchases were Price per Part x 4 25 4 60 4 70 4 10 Number of Parts y 250 800 900 1000 Find the average price weighted for the purchase quantity for this part Remember to enter y the weight frequency before x the price Keys Display Description Wes CLEAR 4 42 Clears the statistics registers WO ENTER 4 J Enters data displays n LO LO ENTER 4 L Lo ILO ENTER LALJ 966 BAGE oy 3 6088 SHS Statistical Operations 1
286. tion one digit before the or radix mark with up to 11 decimal places and up to three digits in the exponent After the prompt SCI_ type in the number of decimal places to be displayed For 10 or 11 places press L LO or LJU The mantissa part of the number will always be less than 10 For example in the number 1 2346E5 the 2 3 4 and 6 are the decimal digits you see when the calculator is set to SCI 4 display mode The 5 following the E is the exponent of 10 1 2346 x 105 If you enter or calculate a number that has more than 12 digits the additional precision is not maintained Engineering Format EHG ENG format displays a number in a manner similar to scientific notation except that the exponent is a multiple of three there can be up to three digits before the or radix mark This format is most useful for scientific and engineering calculations that use units specified in multiples of 103 such as micro milli and kilo units After the prompt ENG_ type in the number of digits you want after the first significant digit For 10 or 11 places press JLO or LJUN For example in the number 123 46E3 the 2 3 4 and 6 are the significant digits after the first significant digit you see when the calculator is set to ENG 4 display mode The 3 following the E is the multiple of 3 exponent of 10 123 46 x 103 Pressing R LENG or EN ENG will cause the exponent disp
287. tion contains an and the left side contains more than just a single variable For example x 2 y 2 r 2 is an equality Assignments The equation contains an and the left side contains just a single variable For example A 0 5 x b x h is an assignment Entering and Evaluating Equations 6 9 m Expressions The equation does not contain an For example x3 1 is an expression When you re calculating with an equation you might use any type of equation although the type can affect how it s evaluated When you re solving a problem for an unknown variable you ll probably use an equality or assignment When you re integrating a function you ll probably use an expression Evaluating Equations One of the most useful characteristics of equations is their ability to be evaluated to generate numeric values This is what enables you to calculate a result from an equation It also enables you to solve and integrate equations as described in chapters 7 and 8 Because many equations have two sides separated by the basic value of an equation is the difference between the values of the two sides For this calculation in an equation is essentially treated as The value is a measure of how well the equation balances The HP 35s has two keys for evaluating equations and XEQ Their actions differ only in how they evaluate assignment equations E XEQ returns the value of the equation regardless of the
288. tor then 2 3 is displayed as 35 4 because the exact fraction is approximately 3 3333 5 a little above 3 5 Similarly 2 3 is displayed as 78 3 54 because the true numerator is a little above 3 Sometimes an annunciator is lit when you wouldn t expect it to be For example if you enter 2 2 3 you see Z 2 34 even though that s the exact number you entered The calculator always compares the fractional part of the internal value and the 12 digit value of just the fraction If the internal value has an integer part its fractional part contains less than 12 digits and it can t exactly match a fraction that uses all 12 digits Changing the Fraction Display In its default condition the calculator displays a fractional number according to certain rules However you can change the rules according to how you want fractions displayed a You can set the maximum denominator that s used m You can select one of three fraction formats The next few topics show how to change the fraction display Setting the Maximum Denominator For any fraction the denominator is selected based on a value stored in the calculator If you think of fractions as a b c then c corresponds to the value that controls the denominator The c value defines only the maximum denominator used in Fraction display mode the specific denominator that s used is determined by the fraction format discussed in the next topic 5 4 Fractions To set t
289. type of equation m ENTER returns the value of the equation unless it s an assignmenttype equation For an assignment equation returns the value of the right side only and also enters that value into the variable on the left side it stores the value in the variable The following table shows the two ways to evaluate equations 6 10 Entering and Evaluating Equations Type of Equation Result for ENTER Result for Equality g x f x g x f x Example x2 y2 r2 x2 y2 r2 Assignment y f x f x y f x Example A 0 5xbxh 0 5xbxh A 05xbxh Expression f x f x Example x3 1 x3 1 x Also stores the result in the left hand variable A for example To evaluate an equation 1 Display the desired equation See Displaying and Selecting Equations above 2 Press or The equation prompts for a value for each variable needed If the base of a number in the equation is different from the current base the calculator automatically changes the result to the current base 3 For each prompt enter the desired value m f the displayed value is good press R S m If you want a different value type the value and press R S Also see Responding to Equation Prompts later in this chapter To halt a calculation press or R S The message INTERRUPTED js shown in line 2 The evaluation of an equation takes no values from the stack it uses only numbers
290. uation from the equation list You can halt a running integration calculation by pressing or and the message INTERRUPTED will appear line 2 However the calculation cannot be resumed No information about the integration is available until the calculation finishes normally Pressing while an integration calculation is running will cancel the operation In this case you should start again from the beginning To write a program for FN The program can use equations ALG or RPN operations in whatever combination is most convenient 1 Begin the program with a label This label identifies the function that you want to integrate FH abel 2 Include an INPUT instruction for each variable including the variable of integration INPUT instructions enable you to integrate with respect to any variable in a multi variable function INPUT for the variable of integration is ignored by the calculator so you need to write only one program that contains a separate INPUT instruction for every variable including the variable of integration If you include no INPUT instructions the program uses the values stored in the variables or entered at equation prompts 3 Enter the instructions to evaluate the function m A function programmed as a multi line RPN or ALG sequence must calculate the function values you want to integrate 15 8 Solving and Integrating Programs m A function programmed as an equation is usually included as an expressi
291. uation is saved but Equation mode is turned off Equations can contain variables numbers vectors functions and parentheses they re described in the following topics The example that follows illustrates these elements Variables in Equations You can use any of the calculator s variables in an equation A through Z I and J You can use each variable as many times as you want For information about 1 and J see Indirectly Addressing Variables and Labels in chapter 14 To enter a variable in an equation press variable When you press the A Z annunciator shows that you can press a variable key to enter its name in the equation 6 4 Entering and Evaluating Equations Numbers in Equations You can enter any valid number in an equation including base 2 8 and 16 real complex and fractional numbers Numbers are always shown using ALL display format which displays up to 12 characters To enter a number in an equation you can use the standard number entry keys including LJ G4 and LE Do not use for subtraction Functions in Equations You can enter many HP 35s functions in an equation A complete list is given under Equation Functions later in this chapter Appendix G Operation Index also gives this information When you enter an equation you enter functions in about the same way you put them in ordinary algebraic equations n an equation certain functions are normally shown betw
292. ulation rstc54 ta darth ocak eeeoreeintonachadnauecias 2 14 AIEE ETE EN T vanereeaeereae 2 16 Storing Data into Variables scssesseesseeseeeeees 3 1 Storing and Recalling Numbers 5 tvceetinieevedeaveaervaasvasdustemensameaere 3 2 Viewing a Variable i amp sx stven stain vtetatanannaaturateands santssenda probisandnins 3 4 Contents Using the MEM Catalog ia tins aca oasvataats ashostauusdnatesauuanoaspncaendenonne 3 4 The VAR CGtGIOG atic ata suitat we evvekaa tosunves towds aude iota ansaws taaataua 3 4 Arithmetic with Stored Variables ccceceeeesseeeeeeeeeeeeeeeeeeees 3 6 Storage ATIMMEHS ckats seit aisuransumcou eetaseaenuleanoneiyutansatunodtuG mnie 3 6 RecallvArithinnietiees ccuises sven catsa pega gat aaataanaanosinse cuss aay ont 3 7 Exchanging x with Any Variable 0 cccccscseeceeeeeeteeeeeeeenneeeees 3 8 The Variables I and ads sass ice alta sl aiahee yaa oacitraeee 3 9 Real Number Functions ccssccssssssscceseecsseeeeeees 4 1 Exponential and Logarithmic Functions cccsseeseeeeeeeeteeeees 4 1 Quotient and Remainder of Division cc ccceeseeeeesteeeeeeteeees 4 2 Powe r FUNCH ONS oeeo eaten vars deer davareiasv ete ges a aas aa E A eden sens 4 2 TriGGnoMmethy sat hH eH aah Bailes A Re ees 4 3 Entering Tiesa even assis edeua EE toes E ah E E SERE veces 4 3 Setting the Angular Mode 1 35ic ccslvasdvisasstssagisauheocsunmseencansn 4 4 Trigonometric Functio
293. umber such as a constant in a calculation Remember to enter the constant second just before executing the arithmetic operation so that the constant is the last number in the X register and therefore can be saved and retrieved with Wea f Example 96 704 52 3947 52 3947 Calculate 2 10 RPN The Automatic Memory Stack oT an z aa _ SI vfer CVS oer Sn x eso AS eave cen aor vst a r zZ 149 0987 Lel 52 3947 Keys Display Description mopa 26 7646 Enters first number ENTER Hoama 149 0957 Intermediate result 7 3 52 3947 Brings back display from before 4 E 2 8457 Final result Example Two close stellar neighbors of Earth are Rigel Centaurus 4 3 light years away and Sirius 8 7 light years away Use c the speed of light 9 5 x 1015 meters per year to convert the distances from the Earth to these stars 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 RPN The Automatic Memory Stack 2 11 Keys Display Description 4 3 ENTER 4 3888 Light years to Rigel Centaurus WHAHA Seis Speed of light c bx 4 6856616 Meters to R Centaurus mope asx 7 5660E15 Retrieves c E3 2 2650E16 Meters to Sirius Chain Calculations in RPN Mode In RPN mode the automatic lifting and dropping of the stack s contents let you retain intermediate results without storing
294. very small non zero value for f x is often acceptable because it might result from approximating numbers with limited 12 digit precision D 2 More about Solving Interpreting Results The SOLVE operation will produce a solution under either of the following conditions m If it finds an estimate for which f x equals zero See figure a below m If it finds an estimate where f x is not equal to zero but the calculated root is a 1 2 digit number adjacent to the place where the function s graph crosses the x axis see figure b below This occurs when the two final estimates are neighbors that is they differ by 1 in the 12th digit and the function s value is positive for one estimate and negative for the other Or they are 0 10 499 or 0 10 499 In most cases f x will be relatively close to zero f x f x a x x To obtain additional information about the result press see the previous estimate of the root x which was left in the Y register Press again to see the value of f x which was left in the Z register If f x equals zero or is relatively small it is very likely that a solution has been found However if f x is relatively large you must use caution in interpreting the results Example An Equation With One Root Find the root of the equation 2x3 4x2 6x 8 0 Enter the equation as an expression More about Solving D 3 Keys Display Description EQN Select Equat
295. w the three splay flags 7 8 and 9 and the message display flag 10 are used in this program are listed as MESSAGE and are entered as equations 1 Set Equation entry mode by pressing the EQN annunciator turns on 2 Press for ea 3 Press REL letter for each alpha character in the message press Wea SPACE ch space character ENTER to insert the message in the current program line and end Equation entry mode 14 14 Programming Techniques Fei FBZ FRES Fee4 FEBS FEBE FRE FEBS FRE Fei Feil Fe1i2 Fis Fei4 FiS Feie Fei Feis F619 Fe26 Fee21 Fe 22 F235 Fe24 F 25 Fe26 Fe2r Program Lines In RPN mode LBL F CFF CFS CF 3 SF if DEC INPUT WV INPUT D RCL WV DECIMAL PSE STOP RCL D Ct RCL W MOST PRECISE PSE STOP SF FACTOR DEHOM PSE STOP SF FIED DEWOM PSE STOP GTO Feel Description Begins the fraction program Clears three fraction flags Displays messages Selects decimal base Prompts for a number Prompts for denominator 2 4095 Displays message then shows the decimal number Sets c value and sets flag 7 Displays message then shows the fraction Sets flag 8 Displays message then shows the fraction Sets flag 9 Displays message then shows the fraction Goes to beginning of program Checksum and length BE54 123 Programming Techniques 14 15 Use the above program to see the different forms of
296. with its absolute value press WB For complex numbers and vectors the absolute value of 1 a complex number in r6a format is r 2 a complex number in xiy format is 4 x y 3 a vector A1 A2 A3 An is A JA as A tent Argument value To extract the argument of a complex number use EW ARG The argument of a complex number 1 in r6a format is a 2 in xiy format is Atan y x Sign value To indicate the sign of x press EEN UNTG 1 1 86H If the x value is negative 1 0000 is displayed if zero 0 0000 is displayed if positive 1 0000 is displayed Real Number Functions 4 17 Greatest integer To obtain the greatest integer equal to or less than given number press EN NTG 4 4 INTC Example This example summarizes many of the operations that extract parts of numbers To calculate Press Display The integer part of 2 47 MOI4IZIEINTG 6 EIF 2 6888 The fractional part of 2 47 QJ 4IIGA INIG 5 SFP amp 47ee FA The absolute value of 7 Jaa 7 BBB The sign value of 9 OMN 1856H 1 66668 The greatest integer equal to 5 3 EZ ED INTG 4 6 6886 or less than 5 3 4INTG The RND function 0 rounds x internally to the number of digits specified by the display format The internal number is represented by 12 digits Refer to chapter 5 for the behavior of RND in Fraction display mode 4 18 Real Number Functions Fractions In Ch
297. xample Suppose you want to calculate 1 2 3 In RPN mode you enter the first number press the ENTER key enter the second number and finally press the arithmetic operator key LE In ALG mode you enter the first number press L enter the second number and finally press the ENTER key RPN mode ALG mode 1 2 1 2 In ALG mode the results and the calculations are displayed In RPN mode only the results are displayed not the calculations Note You can choose either ALG Algebraic or RPN Reverse Polish Notation mode for your calculations Throughout the manual the w a in the margin indicates that the examples or keystrokes in RPN mode must be performed differently in ALG mode Appendix C explains how to use your calculator in ALG mode 1 10 Getting Started Undo key The Undo Key The operation of the Undo key depends on the calculator context but serves largely to recover from the deletion of an entry rather than to undo any arbitrary operation See The Last X Register in Chapter 2 for details on recalling the entry in line 2 of the display after a numeric function is executed Press EW UNDO immediately after using or to recover m an entry that you deleted m an equation deleted while in equation mode a program line deleted while in program mode In addition you can use Undo to recover the value of a register just cleared using the CLEAR menu The Undo operation must imme
298. y 6 0221 x 1023 in A 3 2 Storing Data into Variables Keys Display Description Hamama f 8etees_ Avogadro s number wA LIRO 6 B221EZ3A__ E prompts for variable ENTER 6 B221E23A Stores a copy of Avogadro s number 6 B221E23 in A This also terminates digit entry Ke Clears the number in the display RCL A Z The A Z annunciator Turns on CENTER R Copies Avogadro s number from A 6 B221E23 the display To recall the value stored in a variable use the Recall command The display of this command differs slightly from RPN to ALG mode as the following example illustrates Example In this example we recall the value of 1 75 that we stored in the variable G in the last example This example assumes the HP 35s is still in ALG mode at the start Keys Display Description G Pressing simply activates A Z 1 7588 mode no command is pasted into line 1 In ALG mode Recall can be used to paste a variable into an expression in the command line Suppose we wish to evaluate 15 2xG with G 1 75 from above Keys Display Description www 15 286 RCL 11 5066 We now proceed to switch to RPN mode and recall the value of G Storing Data into Variables 3 3 Keys Display Description MODE 5 SRPH Switch to RPN mode RCL In RPN mode pastes the RCL _ command into the edit line G 1 7588 No need to press ENTER 1 75868 Viewing a Variable The VIEW command VIEW displays the v

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