HP 35s Scientific Calculator Bedienungsanleitung

HP 35s scientific calculatoruser's guideHEdition 1HP part number F2215AA-90001

8 ContentsClearing One or More Programs...13-23The Checksum ...

5-8 FractionsExamples of Fraction DisplaysThe following table shows how the number 2.77 is displayed in the three fraction formats for two /c values.T

Fractions 5-9Example: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

5-10 FractionsFractions in ProgramsYou can use a fraction in a program just as you can in an equation; numerical values are shown in their entered for

Entering and Evaluating Equations 6-16Entering and Evaluating EquationsHow You Can Use EquationsYou can use equations on the HP 35s in several ways:

6-2 Entering and Evaluating EquationsBy comparing the checksum and length of your equation with those in the example, you can verify that you've

Entering and Evaluating Equations 6-3Summary of Equation OperationsAll equations you create are saved in the equation list. This list is visible whene

6-4 Entering and Evaluating EquationsEntering Equations into the Equation ListThe equation list is a collection of equations you enter. The list is sa

Entering and Evaluating Equations 6-5Numbers in EquationsYou can enter any valid number in an equation, including base 2, 8 and 16, real, complex, and

6-6 Entering and Evaluating EquationsParentheses in EquationsYou can include parentheses in equations to control the order in which operations are per

Entering and Evaluating Equations 6-7To display equations: 1. Press . This activates Equation mode and turns on the EQN annunciator. The display show

Contents 915.Solving and Integrating Programs...15-1Solving a Program...

6-8 Entering and Evaluating EquationsEditing and Clearing EquationsYou can edit or clear an equation that you're typing. You can also edit or cle

Entering and Evaluating Equations 6-9To clear a saved equation:Scroll the equation list up or down until the desired equation is in line 2 of the disp

6-10 Entering and Evaluating Equations Expressions. The equation does not contain an "=". For example, x3 + 1 is an expression.When you&apo

Entering and Evaluating Equations 6-11To evaluate an equation:1. Display the desired equation. (See "Displaying and Selecting Equations" abo

6-12 Entering and Evaluating Equations If the equation is an assignment, only the right–hand side is evaluated. The result is returned to the X–regis

Entering and Evaluating Equations 6-13Example: Evaluating an Equation with XEQ.Use the results from the previous example to find out how much the volu

6-14 Entering and Evaluating Equations To change the number, type the new number and press . This new number writes over the old value in the X–regi

Entering and Evaluating Equations 6-15So, for example, all operations inside parentheses are performed before operations outside the parentheses.Examp

6-16 Entering and Evaluating EquationsEquation FunctionsThe following table lists the functions that are valid in equations. Appendix G, "Operati

Entering and Evaluating Equations 6-17Eight of the equation functions have names that differ from their equivalent operations:E

10 ContentsB. User Memory and the Stack...B-1Managing Calculator Memory...

6-18 Entering and Evaluating EquationsThe next equation also obeys the syntax rules. This equation uses the inverse function, , instead of

Entering and Evaluating Equations 6-19You can enter the equation into the equation list using the following keystrokes: Õ

6-20 Entering and Evaluating EquationsKeys: Display: Description: ( ×as required)πDisplays the desired equation. (hold)Di

Solving Equations 7-17Solving EquationsIn chapter 6 you saw how you can use  to find the value of the left–hand variable in an assignment–type equati

7-2 Solving Equations2. Press  then press the key for the unknown variable. For example, press  X to solve for x. The equation then prompts for a

Solving Equations 7-3g (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 ).Calc

7-4 Solving EquationsExample: Solving the Ideal Gas Law Equation.The Ideal Gas Law describes the relationship between pressure, volume, temperature, a

Solving Equations 7-5A 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

7-6 Solving EquationsSolving built-in EquationThe 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+G

Solving Equations 7-7Understanding and Controlling SOLVESOLVE first attempts to solve the equation directly for the unknown variable. If the attempt f

Contents 11How SOLVE Finds a Root ... D-1Interpreting Results...

7-8 Solving Equations The Y–register (press ) contains the previous estimate for the root or equals to zero. This number should be the same as the v

Solving Equations 7-9These sources are used for guesses whether you enter guesses or not. If you enter only one guess and store it in the variable, th

7-10 Solving EquationsExample: 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 vol

Solving Equations 7-11It seems reasonable that either a tall, narrow box or a short, flat box could be formed having the desired volume. Because the t

7-12 Solving EquationsThe dimensions of the desired box are 50 × 10 × 15 cm. If you ignored the upper limit on the height (20 cm) and used initial est

Integrating Equations 8-18Integrating EquationsMany problems in mathematics, science, and engineering require calculating the definite integral of a f

8-2 Integrating EquationsIntegrating Equations ( ∫ FN) To integrate an equation:1. If the equation that defines the integrand's function isn&apos

Integrating Equations 8-3Example: Bessel Function.The Bessel function of the first kind of order 0 can be expressed asFind the Bessel function for x–v

8-4 Integrating EquationsNow calculate J0(3) with the same limits of integration. You must re-specify the limits of integration (0, π) since they were

Integrating Equations 8-5Enter the expression that defines the integrand's function: If the calculator attempted to evaluate this function at x =

12 Contents

8-6 Integrating EquationsAccuracy of IntegrationSince the calculator cannot compute the value of an integral exactly, it approximates it. The accuracy

Integrating Equations 8-7Example: Specifying Accuracy.With the display format set to SCI 2, calculate the integral in the expression for Si(2) (from t

8-8 Integrating EquationsThis uncertainty indicates that the result might be correct to only three decimal places. In reality, this result is accurate

Operations with Complex Numbers 9-19Operations with Complex NumbersThe HP 35s can use complex numbers in the form   It has operations for comp

9-2 Operations with Complex NumbersThe Complex StackA complex number occupies part 1 and part 2 of a stack level. In RPN mode, the complex number occu

Operations with Complex Numbers 9-3Functions for One Complex Number, zTo do an arithmetic operation with two complex numbers:1. Enter the first comple

9-4 Operations with Complex NumbersExamples:Here are some examples of trigonometry and arithmetic with complex numbers:Evaluate sin (2i3)Evaluate the

Operations with Complex Numbers 9-5Evaluate , where z = (1i 1). Using Complex Numbers in Polar NotationMany applications use real numbers in polar fo

9-6 Operations with Complex NumbersYou can do a complex operation with numbers whose complex forms are different; however, the result form is dependen

Operations with Complex Numbers 9-7Evaluate 1i1+3θ 10+5θ 30Complex Numbers in EquationsYou can type complex numbers in equations. When an equation is

Part 1Basic Operation

9-8 Operations with Complex NumbersComplex Number in ProgramIn a program, you can type a complex number. For example, 1i2+3θ 10+5θ 30 in program is:Wh

Vector Arithmetic 10-110Vector ArithmeticFrom a mathematical point of view, a vector is an array of 2 or more elements arranged into a row or a column

10-2 Vector ArithmeticCalculate [1.5,-2.2]+[-1.5,2.2]Calculate [-3.4,4.5]-[2.3,1.4]Multiplication and divisions by a scalar: 1. Enter a vector2. Enter

Vector Arithmetic 10-3Calculate [3,4]x5Calculate [-2,4]÷2Absolute value of the vectorThe absolute value function “ABS”, when applied to a vector, prod

10-4 Vector ArithmeticDot productFunction DOT is used to calculate the dot product of two vectors with the same length. Attempting to calculate the do

Vector Arithmetic 10-5Angle between vectorsThe angle between two vectors, A and B, can be found asθ= ACOS(AB/ )Find the angle between two vectors:

10-6 Vector ArithmeticVectors in EquationsVectors can be used in equations and in equation variables exactly like real numbers. A vector can be entere

Vector Arithmetic 10-7Vectors in ProgramsVectors can be used in program in the same way as real and complex numbers For example, [5, 6] +2 x [7, 8] x

10-8 Vector ArithmeticCreating Vectors from Variables or Registers It is possible to create vectors containing the contents of memory variables, stack

Base Conversions and Arithmetic and Logic 11-111Base Conversions and Arithmetic and LogicThe BASE menu (  ) allows you to enter numbers and force th

11-2 Base Conversions and Arithmetic and LogicExamples: Converting the Base of a Number. The following keystrokes do various base conversions.Convert

Base Conversions and Arithmetic and Logic 11-3you can use  menu to enter base-n sign b/o/d/h following the operand to represent 2/8/10/16 base number

11-4 Base Conversions and Arithmetic and LogicLOGIC MenuThe “AND”, “OR”, “XOR”, “NOT”, “NAND”, “NOR” can be used as logic functions. Fraction, complex

Base Conversions and Arithmetic and Logic 11-5 The result of an operation is always an integer (any fractional portion is truncated).Whereas conversi

11-6 Base Conversions and Arithmetic and LogicThe Representation of NumbersAlthough the display of a number is converted when the base is changed, its

Base Conversions and Arithmetic and Logic 11-7Range of NumbersThe 36-bit binary number size determines the range of numbers that can be represented in

11-8 Base Conversions and Arithmetic and LogicIn BIN/OCT/HEX, If a number entered in decimal base is outside the range given above, then it produces t

Statistical Operations 12-112Statistical OperationsThe statistics menus in the HP 35s provide functions to statistically analyze a set of one– or two–

12-2 Statistical OperationsEntering One–Variable Data1. Press  ()to clear existing statistical data.2. Key in each x–value and press .3. The disp

Statistical Operations 12-3To correct statistical data:1. Reenter the incorrect data, but instead of pressing , press  . This deletes the value(s)

Getting Started 1-11Getting StartedImportant PreliminariesTurning the Calculator On and OffTo turn the calculator on, press . ON is printed on the bo

12-4 Statistical OperationsStatistical CalculationsOnce you have entered your data, you can use the functions in the statistics menus.Statistics Menus

Statistical Operations 12-5Example: Mean (One Variable).Production supervisor May Kitt wants to determine the average time that a certain process take

12-6 Statistical OperationsSample Standard DeviationSample standard deviation is a measure of how dispersed the data values are about the mean sample

Statistical Operations 12-7Population Standard DeviationPopulation standard deviation is a measure of how dispersed the data values are about the mean

12-8 Statistical OperationsL.R. (Linear Regression) Menu To find an estimated value for x (or y), key in a given hypothetical value for y (or x), the

Statistical Operations 12-9 Enters data; displays n.Five data pairs entered. ÕÕ ()

12-10 Statistical OperationsWhat if 70 kg of nitrogen fertilizer were applied to the rice field? Predict the grain yield based on the above statistics

Statistical Operations 12-11Summation Values and the Statistics RegistersThe statistics registers are six unique locations in memory that store the ac

12-12 Statistical OperationsAccess to the Statistics RegistersThe statistics register assignments in the HP 35s are shown in the following table. Summ

Statistical Operations 12-13You can load a statistics register with a summation by storing the number (-27 through -32) of the register you want in I

1-2 Getting StartedHighlights of the Keyboard and DisplayShifted KeysEach key has three functions: one printed on its face, a left–shifted function (y

12-14 Statistical Operations

Part 2Programming

Simple Programming 13-113Simple ProgrammingPart 1 of this manual introduced you to functions and operations that you can use manually, that is, by pre

13-2 Simple ProgrammingThis very simple program assumes that the value for the radius is in the X– register (the display) when the program starts to r

Simple Programming 13-3Try running this program to find the area of a circle with a radius of 5:We will continue using the above program for the area

13-4 Simple ProgrammingProgram Boundaries (LBL and RTN)If you want more than one program stored in program memory, then a program needs a label to mar

Simple Programming 13-5 Using RPN operations (which work with the stack, as explained in chapter 2). Using ALG operations (as explained in appendix

13-6 Simple ProgrammingFor output, you can display a variable with the VIEW instruction, you can display a message derived from an equation, you can d

Simple Programming 13-75. End the program with a return instruction, which sets the program pointer back to   after the program runs. Press .

Getting Started 1-3Pressing  or  turns on the corresponding or  annunciator symbol at the top of the display. The annunciator remains on until yo

13-8 Simple Programming      Now, erase line A002, and line A004 changes to “A003 GTO A002”Function Names in Programs

Simple Programming 13-9A different checksum means the program was not entered exactly as given here.Example: Entering a Program with an Equation.The f

13-10 Simple ProgrammingRunning a ProgramTo run or execute a program, program entry cannot be active (no program–line numbers displayed; PRGM off). Pr

Simple Programming 13-11Testing a ProgramIf you know there is an error in a program, but are not sure where the error is, then a good way to test the

13-12 Simple ProgrammingEntering and Displaying DataThe calculator's variables are used to store data input, intermediate results, and final resu

Simple Programming 13-13Using INPUT for Entering DataThe INPUT instruction (   Variable ) stops a running program and displays a prompt for the give

13-14 Simple Programming2. In the beginning of the program, insert an INPUT instruction for each variable whose value you will need. Later in the prog

Simple Programming 13-15 To cancel the INPUT prompt, press . The current value for the variable remains in the X–register. If you press  to resume

13-16 Simple ProgrammingUsing Equations to Display MessagesEquations aren't checked for valid syntax until they're evaluated. This means you

Simple Programming 13-17Keys:(In RPN mode)Display: Description:  R   H  πCalculates the volume. Checksum and length o

NoticeREGISTER YOUR PRODUCT AT: www.register.hp.comTHIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN AREPROVIDED “AS IS” AND ARE SUBJECT TO CHANGE WITHOUT

1-4 Getting StartedBackspacing and ClearingAmong the first things you need to know are how to clear an entry, correct a number, and clear the entire d

13-18 Simple ProgrammingNow find the volume and surface area–of a cylinder with a radius of 2 1/2 cm and a height of 8 cm.Displaying Information witho

Simple Programming 13-19Stopping or Interrupting a Program Programming a Stop or Pause (STOP, PSE)  Pressing  (run/stop) during program entry insert

13-20 Simple ProgrammingEditing a ProgramYou can modify a program in program memory by inserting, deleting, and editing program lines. If a program li

Simple Programming 13-213. Moving the cursor”_” and press  repeatedly to delete the unwanted number or function, then retype the rest of the program

13-22 Simple Programming Press   to move the program pointer to  . Press   label nnn to move to a specific line.If Program–entry mode

Simple Programming 13-23  where 67 is the number of bytes used by the program.Clearing One or More ProgramsTo clear a specific program from

13-24 Simple ProgrammingFor example, to see the checksum for the current program (the "cylinder" program):If your checksum does not match th

Simple Programming 13-25This allows you to write programs that accept numbers in any of the four bases, do arithmetic in any base, and display results

13-26 Simple ProgrammingPolynomial Expressions and Horner's MethodSome expressions, such as polynomials, use the same variable several times for

Simple Programming 13-27Now evaluate this polynomial for x = 7.Keys:(In RPN mode)Display: Description:    A   X  

Getting Started 1-5Keys for Clearing (continued)Key DescriptionThe CLEAR menu (       )contains options for clearing x (the n

13-28 Simple ProgrammingA more general form of this program for any equation Ax4 + Bx3 + Cx2 + Dx + E would be:      

Programming Techniques 14-114Programming TechniquesChapter 13 covered the basics of programming. This chapter explores more sophisticated but useful t

14-2 Programming Techniques If you plan to have only one program in the calculator memory, you can separate the routine in various labels. If you pla

Programming Techniques 14-3MAIN program(Top level)End of programAttempting to execute a subroutine nested more than 20 levels deep causes an  

14-4 Programming TechniquesIn RPN mode,Branching (GTO)As we have seen with subroutines, it is often desirable to transfer execution to a part of the p

Programming Techniques 14-5A Programmed GTO InstructionThe GTO labelinstruction (press  label line number) transfers the execution of a running pro

14-6 Programming Techniques To  :  . To a specific line number: label line number (line number < 1000). For example, A. For ex

Programming Techniques 14-7 Comparison tests. These compare the X–and Y–registers, or the X–register and zero. Flag tests. These check the status of

14-8 Programming TechniquesExample:The "Normal and Inverse–Normal Distributions" program in chapter 16 uses the x<y? conditional in routi

Programming Techniques 14-9FlagsA flag is an indicator of status. It is either set (true) or clear (false). Testing a flag is another conditional test

1-6 Getting StartedUsing MenusThere 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.

14-10 Programming TechniquesFlagStatusFraction–Control Flags789Clear(Default)Fraction display off; display real numbers in the current display format.

Programming Techniques 14-11 Flag 10 controls program execution of equations: When flag 10 is clear (the default state), equations in running program

14-12 Programming TechniquesAnnunciators for Set FlagsFlags 0, 1, 2, 3 and 4 have annunciators in the display that turn on when the corresponding flag

Programming Techniques 14-13It is good practice in a program to make sure that any conditions you will be testing start out in a known state. Current

14-14 Programming TechniquesIf you replace lines S002 and S003 by SF0 and SF1, then flags 0 and 1 are set so lines S006 and S010 take the natural loga

Programming Techniques 14-15Program Lines:(In RPN mode)Description:  Begins the fraction program.  Clears three fraction flags. 

14-16 Programming TechniquesUse the above program to see the different forms of fraction display:LoopsBranching backwards — that is, to a label in a p

Programming Techniques 14-17This routine is an example of an infinite loop. It can be used to collect the initial data. After entering the three value

14-18 Programming TechniquesLoops with Counters (DSE, ISG)When you want to execute a loop a specific number of times, use the   (increment; skip if

Programming Techniques 14-19 ii is the interval for incrementing and decrementing (must be two digits or unspecified). This value does not change. An

Getting Started 1-7To use a menu function:1. Press a menu key to display a set of menu items.2. Press Õ Ö × Ø to move the underline to the item you wa

14-20 Programming Techniques          Press L, then press  Z to see that the loop–control numbe

Programming Techniques 14-21The Indirect Address, (I) and (J)Many functions that use A through Z (as variables or labels) can use (I) or (J) to refer

14-22 Programming TechniquesThe INPUT(I) ,INPUT(J) and VIEW(I) ,VIEW(J)operations label the display with the name of the indirectly–addressed variable

Programming Techniques 14-23You can not solve or integrate for unnamed variables or statistic registers.Program Control with (I)/(J)Since the contents

14-24 Programming TechniquesNote:1. If you want to recall the value from an undefined storage address, the error message “ ”will be shown”.

Solving and Integrating Programs 15-115Solving and Integrating ProgramsSolving a ProgramIn chapter 7 you saw how you can enter an equation — it's

15-2 Solving and Integrating Programs1. Begin the program with a label. This label identifies the function that you want SOLVE to evaluate (label).

Solving and Integrating Programs 15-3To begin, put the calculator in Program mode; if necessary, position the program pointer to the top of program me

15-4 Solving and Integrating ProgramsExample: Program Using Equation.Write a program that uses an equation to solve the "Ideal Gas Law."Now

Solving and Integrating Programs 15-5Keys:(In RPN mode)Display: Description:LStores previous pressure. HSelects program “H.”P

1-8 Getting StartedSome menus, like the CONST and SUMS, have more than one page. Entering these menus turns on the  or  annunciator. In these menus,

15-6 Solving and Integrating ProgramsUsing SOLVE in a ProgramYou can use the SOLVE operation as part of a program.If appropriate, include or prompt fo

Solving and Integrating Programs 15-7Integrating a ProgramIn chapter 8 you saw how you can enter an equation (or expression) — it's added to the

15-8 Solving and Integrating Programs2. Select the program that defines the function to integrate: press   label. (You can skip this step if you&apo

Solving and Integrating Programs 15-9 A function programmed as an equation is usually included as an expression specifying the integrand — though it

15-10 Solving and Integrating ProgramsUsing Integration in a ProgramIntegration can be executed from a program. Remember to include or prompt for the

Solving and Integrating Programs 15-11Restrictions on Solving and IntegratingThe SOLVE variable and ∫ FN d variable instructions cannot call a routine

15-12 Solving and Integrating Programs

Statistics Programs 16-116Statistics ProgramsCurve FittingThis program can be used to fit one of four models of equations to your data. These models a

16-2 Statistics ProgramsTo fit logarithmic curves, values of x must be positive. To fit exponential curves, values of y must be positive. To fit power

Statistics Programs 16-3Program Listing:Program Lines:(In RPN mode)Description   This routine sets, the status for the straight–line model.

Getting Started 1-9 Pressing  backs out of the 2–level CLEAR or MEM menu, one level at a time. Refer to  in the table on page 1–5. Pressing  or

16-4 Statistics Programs   If flag 0 is set . . .  . . . takes the natural log of the X–input.   Stores that value for the corre

Statistics Programs 16-5   Displays, prompts for, and, if changed, stores x–value in X.  If flag 0 is set . . .   Branche

16-6 Statistics ProgramsChecksum and length: 889C 18   This subroutine calculates for the logarithmic model.      

Statistics Programs 16-7        Calculates = (Y/B ) 1/M  Goes to O005Checksum and length: 8524 21

16-8 Statistics ProgramsFlags Used:Flag 0 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 inpu

Statistics Programs 16-913. For a new case, go to step 2.Variables Used:Example 1:Fit a straight line to the data below. Make an intentional error whe

16-10 Statistics ProgramsNow intentionally enter 379 instead of 37.9 so that you can see how to correct incorrect entries.Enters y–value

Statistics Programs 16-11Example 2:Repeat example 1 (using the same data) for logarithmic, exponential, and power curve fits. The table below gives yo

16-12 Statistics ProgramsThis program uses the built–in integration feature of the HP 35s to integrate the equation of the normal frequency curve. The

Statistics Programs 16-13Program Listing:Program Lines:(In RPN mode)Description   This routine initializes the normal distribution program.

1-10 Getting StartedTo select ALG mode: Press 9{() to set the calculator to ALG mode. When the calculator is in ALG mode, the ALG annunciator is

16-14 Statistics Programs   Adds the correction to yield a new Xguess.    Tests to see if the correction is signific

Statistics Programs 16-15Flags Used:None.Remarks:The accuracy of this program is dependent on the display setting. For inputs in the area between ±3 s

16-16 Statistics Programs4. After the prompt for S, key in the population standard deviation and press . (If the standard deviation is 1, just press

Statistics Programs 16-17Since your friend has been known to exaggerate from time to time, you decide to see how rare a "2σ" date might be.

16-18 Statistics ProgramsThus, we would expect that only about 1 percent of the students would do better than score 90.Grouped Standard DeviationThe s

Statistics Programs 16-19This program allows you to input data, correct entries, and calculate the standard deviation and weighted mean of the grouped

16-20 Statistics Programs Updates in register -30.     Increments (or decrements) N.      

Statistics Programs 16-21Flags Used:None.Program Instructions:1. Key in the program routines; press  when done.2. Press S to start entering new dat

16-22 Statistics ProgramsYou erred by entering 14 instead of 13 for x3. Undo your error by executing routine U:Group 123456xi5813152237fi17 26 37 43 7

Statistics Programs 16-23Displays the counter.Prompts for the fifth xi.Prompts for the fifth fi.Displays t

Getting Started 1-11Undo keyThe Undo KeyThe operation of the Undo key depends on the calculator context, but serves largely to recover from the deleti

16-24 Statistics Programs

Miscellaneous Programs and Equations 17-117Miscellaneous Programs and EquationsTime Value of MoneyGiven any four of the five values in the "Time–

17-2 Miscellaneous Programs and EquationsEquation Entry:Key in this equation:Remarks:The TVM equation require

Miscellaneous Programs and Equations 17-3The order in which you're prompted for values depends upon the variable you're solving for.SOLVE in

17-4 Miscellaneous Programs and EquationsVariables Used:Example:Part 1. You are financing the purchase of a car with a 3–year (36–month) loan at 10.5%

Miscellaneous Programs and Equations 17-5The answer is negative since the loan has been viewed from the borrower's perspective. Money received by

17-6 Miscellaneous Programs and EquationsPart 2. What interest rate would reduce the monthly payment by $10?Part 3. Using the calculated interest rate

Miscellaneous Programs and Equations 17-7Prime Number GeneratorThis program accepts any positive integer greater than 3. If the number is a prime numb

17-8 Miscellaneous Programs and EquationsLBL YVIEW PrimeLBL ZP + 2 x→LBL Px P3 D→→LBL Xx = 0?yesnoStartnoyesNote: x is the value in the X-regis

Miscellaneous Programs and Equations 17-9Program Listing:Program Lines:(In ALG mode)Description   This routine displays prime number P. 

1-12 Getting StartedThe Display and AnnunciatorsThe display comprises two lines and annunciators.Entries with more than 14 characters will scroll to t

17-10 Miscellaneous Programs and EquationsFlags Used: None.Program Instructions:1. Key in the program routines; press  when done.2. Key in a positive

Miscellaneous Programs and Equations 17-11Cross Product in VectorsHere is an example showing how to use the program function to calculate the cross pr

17-12 Miscellaneous Programs and EquationsExample:Calculate the cross product of two vectors, v1=2i+5j+4k and v2=i-2j+3kProgram Lines:(In RPN mode)Des

Miscellaneous Programs and Equations 17-13Keys: Display: Description:RRun R routine to input vector valueInput v2 of x-compone

17-14 Miscellaneous Programs and Equations

Part 3Appendixes and Reference

Support, Batteries, and Service A-1ASupport, Batteries, and ServiceCalculator SupportYou can obtain answers to questions about using your calculator f

A-2 Support, Batteries, and ServiceA: Exponent of ten; that is, 2.51 × 10–13.Q: The calculator has displayed the message  . What should I do

Support, Batteries, and Service A-3Changing the BatteriesThe calculator is powered by two 3-volt lithium coin batteries, CR2032.Replace the batteries

Getting Started 1-13HP 35s AnnunciatorsAnnunciator Meaning ChapterThe " (Busy)" annunciator appears while an operation, equation, or progr

A-4 Support, Batteries, and Service5. Insert a new CR2032 lithium battery, making sure that the positive sign (+) is facing outward. 6. Remove and ins

Support, Batteries, and Service A-53. Remove the batteries (see "Changing the Batteries") and lightly press a coin against both battery cont

A-6 Support, Batteries, and Service →  →  → 9 → × → Ö → Õ →  →  → → 6 → Ø →  →  →  →  →  →  → →  →  → 4 →  →  →  →  → →  →  → →

Support, Batteries, and Service A-7WarrantyHP 35s Scientific Calculator; Warranty period: 12 months1. HP warrants to you, the end-user customer, that

A-8 Support, Batteries, and Service6. HP MAKES NO OTHER EXPRESS WARRANTY OR CONDITION WHETHER WRITTEN OR ORAL. TO THE EXTENT ALLOWED BY LOCAL LAW, ANY

Support, Batteries, and Service A-9China 010-68002397Hong Kong 2805-2563Indonesia +65 6100 6682Japan +852 2805-2563Malaysia +65 6100 6682New Zealand 0

A-10 Support, Batteries, and ServiceSwitzerland (German) 01 439 5358Switzerland (Italian) 022 567 5308United Kingdom 0207 458 0161LACountry : Telephon

Support, Batteries, and Service A-11Haiti 183 ♦ 800-711-2884Honduras 800-0-123 ♦ 800-711-2884Jamaica 1-800-711-2884Martinica 0-800-990-011 ♦ 877-219-8

A-12 Support, Batteries, and ServiceRegulatory informationFederal Communications Commission NoticeThis equipment has been tested and found to comply w

Support, Batteries, and Service A-13Houston, TX 77269-2000or call HP at 281-514-3333To identify your product, refer to the part, series, or model numb

Contents 1ContentsPart 1. Basic Operation1. Getting Started...1-1Important Preliminaries...

1-14 Getting StartedHP 35s Annunciators (continued)Annunciator Meaning Chapter,There are more characters to the left or right in the display of the

A-14 Support, Batteries, and ServiceJapanese Noticeこの装置は、 情報処理装置等電波障害自主規制協議会 （VCCI） の基準に基づ く クラ ス B 情報技術装置です。 こ の装置は、 家庭環境で使用する こ と を目的と し ていますが、 こ の装

User Memory and the Stack B-1BUser Memory and the StackThis appendix covers The allocation and requirements of user memory, How to reset the calcula

B-2 User Memory and the StackTo see the memory requirements of specific equations in the equation list:1. Press  to activate Equation mode. ( 

User Memory and the Stack B-3Clearing MemoryThe usual way to clear user memory is to press   (). However, there is also a more powerful clearin

B-4 User Memory and the StackMemory may inadvertently be cleared if the calculator is dropped or if power is interrupted.The Status of Stack LiftThe f

User Memory and the Stack B-5Disabling OperationsThe five operations , /, -, () and   () disable stack lift. A number keyed in after one

B-6 User Memory and the StackThe Status of the LAST X RegisterThe following operations save x in the LAST X register in RPN mode:Notice that /c does n

User Memory and the Stack B-7Accessing Stack Register ContentsThe values held in the four stack registers, X, Y, Z and T, are accessible in RPN mode i

B-8 User Memory and the Stack

ALG: Summary C-1CALG: SummaryAbout ALGThis appendix summarizes some features unique to ALG mode, including,  Two argument arithmetic Exponential and

Getting Started 1-15Keying in NumbersThe minimum and maximum values that the calculator can handle are ±9.99999999999499. If the result of a calculati

C-2 ALG: Summary5. Unary Minus +/-6. ×, ÷7. +, –8. =Doing Two argument Arithmetic in ALGThis discussion of arithmetic using ALG replaces the following

ALG: Summary C-3Power FunctionsIn ALG mode, to calculate a number y raised to a power x, key in y  x, then press . Percentage CalculationsThe Percen

C-4 ALG: SummaryPermutations and CombinationsExample: Combinations of People.A company employing 14 women and 10 men is forming a six–person safety co

ALG: Summary C-5If you were to key in , the calculator would calculate the result, -107.6471. However, that’s not what you want. To delay th

C-6 ALG: SummaryTrigonometric Functions Assume the unit of the angle is 9() Hyperbolic functionsTo Calculate: Press: Display:Sine of x. 

ALG: Summary C-7Parts of numbers Reviewing the StackThe  or  key produces a menu in the display— X–, Y–, Z–, T–registers, to let you review the en

C-8 ALG: SummaryThe value of X-, Y-, Z-, T-register in ALG mode is the same in RPN mode. After normal calculation, solving, programming, or integrati

ALG: Summary C-9To do an operation with one complex number:1. Select the function.2. Enter the complex number z. 3. Press  to calculate.4. The calcul

C-10 ALG: SummaryExamples:Evaluate (4 - 2/5 i)  (3 - 2/3 i)Arithmetic in Bases 2, 8, and 16Here are some examples of arithmetic in Hexadecimal, Octal

ALG: Summary C-1177608 – 43268=?1008 ÷ 58=?5A016 + 100110002 =?Entering Statistical Two–Variable DataIn ALG mode, remember to enter an (x, y) pair in

1-16 Getting StartedKeying in Powers of TenThe  key is used to enter powers of ten quickly. For example, instead of entering one million as 1000000

C-12 ALG: Summary4. The display shows n the number of statistical data pairs you have accumulated.5. Continue entering x, y–pairs. n is updated with

ALG: Summary C-13Linear RegressionLinear regression, or L.R. (also called linear estimation), is a statistical method for finding a straight line that

C-14 ALG: Summary

More about Solving D-1DMore about SolvingThis appendix provides information about the SOLVE operation beyond that given in chapter 7.How SOLVE Finds a

D-2 More about Solving If f(x) has one or more local minima or minima, each occurs singly between adjacent roots of f(x) (figure d, below).In most si

More about Solving D-3Interpreting ResultsThe SOLVE operation will produce a solution under either of the following conditions: If it finds an estima

D-4 More about SolvingNow, solve the equation to find the root:Example: An Equation with Two Roots.Find the two roots of the parabolic equation:x2 + x

More about Solving D-5Now, solve the equation to find its positive and negative roots:Certain cases require special consideration: If the function&ap

D-6 More about Solving Values of f(x) may be approaching infinity at the location where the graph changes sign (see figure b, below). This situation

More about Solving D-7Now, solve to find the root:Note the difference between the last two estimates, as well as the relatively large value for f(x).

Getting Started 1-17Other Exponent FunctionsTo calculate an exponent of ten (the base 10 antilogarithm), use  . To calculate the result of any numbe

D-8 More about SolvingNow, solve to find the root.When SOLVE Cannot Find a RootSometimes SOLVE fails to find a root. The following conditions cause th

More about Solving D-9Example: A Relative Minimum.Calculate the root of this parabolic equation:x2 – 6x + 13 = 0.It has a minimum at x = 3.Enter the e

D-10 More about SolvingNow, solve to find the root:Example: An Asymptote.Find the root of the equationEnter the equation as an expression. 

More about Solving D-11Watch what happens when you use negative values for guesses:Example: Find the root of the equation.Enter the equation as an exp

D-12 More about SolvingNow attempt to find a negative root by entering guesses 0 and –10. Notice that the function is undefined for values of x betwee

More about Solving D-13Solve for X using initial guesses of 10–8 and –10–8.Round–Off ErrorThe limited (12–digit) precision of the calculator can cause

D-14 More about Solving

More about Integration E-1EMore about IntegrationThis appendix provides information about integration beyond that given in chapter 8.How the Integral

E-2 More about IntegrationAs explained in chapter 8, the uncertainty of the final approximation is a number derived from the display format, which spe

More about Integration E-3With this number of sample points, the algorithm will calculate the same approximation for the integral of any of the functi

1-18 Getting StartedPerforming Arithmetic CalculationsThe HP 35s can operate in either RPN mode or in Algebraic mode (ALG). These modes affect how ex

E-4 More about IntegrationTry it and see what happens. Enter the function f(x) = xe–x.Set the display format to SCI 3, specify the lower and upper lim

More about Integration E-5The graph is a spike very close to the origin. Because no sample point happened to discover the spike, the algorithm assumed

E-6 More about IntegrationNote that the rapidity of variation in the function (or its low–order derivatives) must be determined with respect to the wi

More about Integration E-7In many cases you will be familiar enough with the function you want to integrate that you will know whether the function ha

E-8 More about IntegrationThis is the correct answer, but it took a very long time. To understand why, compare the graph of the function between x = 0

More about Integration E-9Because the calculation time depends on how soon a certain density of sample points is achieved in the region where the func

E-10 More about Integration

Messages F-1FMessagesThe calculator responds to certain conditions or keystrokes by displaying a message. The  symbol comes on to call your attention

F-2 Messages   Indicates the "top" of equation memory. The memory scheme is circular, so    is also the "equation&q

Messages F-3 Exponentiation error:  Attempted to raise 0 to the 0th power or to a negative power. Attempted to raise a negative number to a

Getting Started 1-19Example:Calculate 3.42, first in RPN mode and then in ALG mode.In the example, the square operator is shown on the key as  but di

F-4 Messages   SOLVE (include EQN and PGM mode)cannot find the root of the equation using the current initial guesses (see page ). These cond

Messages F-5Self–Test Messages:  Statistics error:  Attempted to do a statistics calculation with n = 0.  Attempted to calculate sx sy, , ,

F-6 Messages

Operation Index G-1GOperation IndexThis section is a quick reference for all functions and operations and their formulas, where appropriate. The listi

G-2 Operation IndexØDisplays next entry in catalog; moves to next equation in equation list; moves program pointer to next line (during program entry)

Operation Index G-3Σx2 ÕÕÕ ()Returns the sum of squares of x–values.12–11 1ΣxyÕÕÕÕÕ ()Returns the sum of products of x–and y–values.12–11 1Σ

G-4 Operation IndexA through Zvariable Value of named variable. 6–4 1ABS  Absolute value.Returns .4–17 1ACOS  Arc cosine.Returns cos –1x.4–4 1ACO

Operation Index G-5b  ()Indicates a binary number11–2 1 Displays the base–conversion menu. 11–1BIN ()Selects Binary (base 2) mode.11–1T

G-6 Operation IndexCLVARx  ()Clears indirect variables whose address is greater than the x address to zero.1–4CLSTK  ()Clears all sta

Operation Index G-7ENG n8()n Selects Engineering display with n digits following the first digit (n = 0 through 11).1–22@and2Causes the exponent

1-20 Getting StartedExampleCalculate 2+3 and 6C4, first in RPN mode and then in ALG mode.In ALG mode, the infix operators are ,  ,, , and . The

G-8 Operation IndexFS? n () nIf flag n (n = 0 through 11) is set, executes the next program line; if flag n is clear, skips the next program li

Operation Index G-9INT÷(÷) Produces the quotient of a division operation involving two integers.4–2 1INTG() Obtains the greatest intege

G-10 Operation IndexLBL label   label Labels a program with a single letter for reference by the XEQ, GTO, or FN= operations. (Used only in programs

Operation Index G-11OR> ()Logic operator11–4 1 Turns the calculator off. 1–1nPr { Permutations of n items taken r at a time. Returns n!÷(n

G-12 Operation IndexRCL+ variable  variableReturns x + variable.3–7RCL– variable  variable.Returns x – variable.3–7RCLx variable  variable.Retur

Operation Index G-13SCI n8() nSelects Scientific display with n decimal places. (n = 0 through 11.)1–22SEED  Restarts the random–number sequen

G-14 Operation IndexSTOP Run/stop.Begins program execution at the current program line; stops a running program and displays the X–register.13–19 D

Operation Index G-15  ()Given a y–value in the X–register, returns the x–estimate based on the regression line: = (y – b) ÷ m.12–11 1! * Factoria

G-16 Operation Indexx=y? ÕÕÕÕÕ ()If x=y, executes next program line;if x≠y, skips next program line.14–7 Displays the "x?0" comparison

Operation Index G-17Notes:1. Function can be used in equations. Õ ()Given an x–value in the X–register, returns the y–estimate based on the regressi

Getting Started 1-21For commutative operations such as  and , the order of the operands does not affect the calculated result. If you mistakenly ent

G-18 Operation Index

Index-1IndexSpecial Characters∫ FN. See integration% functions 4-6 1-15 in fractions 1-26π 4-3, A-2  annunciatorin fractions 5-2in fractions 5-3

Index-2binary numbers. See numbersarithmetic 11-4converting to 11-2range of 11-7scrolling 11-8typing 11-1viewing all digits 11-8borrower (finance) 17-

Index-3temperature units 4-14time format 4-13volume units 4-14coordinatesconverting 4-10correlation coefficient 12-8, 16-1cosine (trig) 4-4, 9-3, C-6c

Index-4memory in 13-16multiple roots 7-9no root 7-8numbers in 6-5numeric value of 6-10, 6-11, 7-1, 7-7, 13-4operation summary 6-3parentheses 6-5, 6-6,

Index-5Gfinds PRGM TOP 13-6, 13-21, 14-6finds program labels 13-10, 13-22, 14-5finds program lines 13-22, 14-5gamma function 4-15go to. See GTOgrads

Index-6logarithmic functions 4-1, 9-3, C-5logicAND 11-4NAND 11-4NOR 11-4NOT 11-4OR 11-4XOR 11-4loop counter 14-18, 14-23looping 14-16, 14-17Łukasiewic

Index-71-18periods and commas in 1-23, A-1precision D-13prime 17-7range of 1-17, 11-7real 4-1recalling 3-2reusing 2-6, 2-10rounding 4-18showing all di

Index-8deleting 1-28deleting all 1-5deleting equations 13-7, 13-20deleting lines 13-20designing 13-3, 14-1editing 1-4, 13-7, 13-20editing equations 13

Index-9rolling the stack 2-3, C-7root functions 4-3roots. See SOLVEchecking 7-7, D-3in programs 15-6multiple 7-9none found 7-8, D-8of equations 7-1of

1-22 Getting StartedScientific Format ()SCI format displays a number in scientific notation (one digit before the "" or "" ra

Index-10size limit 2-4, 9-2unaffected by VIEW 13-15stack lift. See stackdefault state B-4disabling B-4enabling B-4not affecting B-5operation 2-5standa

Index-11solving for 7-1, 15-1, 15-6, D-1storing 3-2storing from equation 6-12typing name 1-3viewing 3-4, 13-15, 13-18vectorsabsolute value 10-3additio

Index-12

Getting Started 1-23Example:This example illustrates the behavior of the Engineering format using the number 12.346E4. It also shows the use of the @

2 ContentsComplex number display format (, , ·‚)...1-24SHOWing Full 12–Digit Precision ...1

1-24 Getting StartedExampleEnter the number 12,345,678.90 and change the decimal point to the comma. Then choose to have no thousand separator. Fina

Getting Started 1-25ExampleDisplay the complex number 3+4i in each of the different formats.SHOWing Full 12–Digit PrecisionChanging the number of disp

1-26 Getting StartedFractionsThe HP 35s allows you to enter and operate on fractions, displaying them as either decimals or fractions. The HP 35s disp

Getting Started 1-27ExampleEnter the mixed numeral 12 3/8 and display it in fraction and decimal forms. Then enter ¾ and add it to 12 3/8. This exampl

1-28 Getting Started Any other key also clears the message, though the key function is not enteredIf no message is displayed, but the  annunciator a

Getting Started 1-29Clearing All of MemoryClearing all of memory erases all numbers, equations, and programs you've stored. It does not affect mo

1-30 Getting Started

RPN: The Automatic Memory Stack 2-12RPN: The AutomaticMemory StackThis chapter explains how calculations take place in the automatic memory stack in R

2-2 RPN: The Automatic Memory StackThe most "recent" number is in the X–register: this is the number you see in the second line of the displ

RPN: The Automatic Memory Stack 2-3The X and Y–Registers are in the DisplayThe X and Y–Registers are what you see except when a menu, a message, an eq

Contents 3Using the MEM Catalog ... 3-4The VAR catalog...

2-4 RPN: The Automatic Memory StackWhat was in the X–register rotates into the T–register, the contents of the T–register rotate into the Z–register,

RPN: The Automatic Memory Stack 2-5Arithmetic – How the Stack Does ItThe contents of the stack move up and down automatically as new numbers enter the

2-6 RPN: The Automatic Memory StackHow ENTER WorksYou know that  separates two numbers keyed in one after the other. In terms of the stack, how does

RPN: The Automatic Memory Stack 2-7Filling the stack with a constantThe replicating effect of  together with the replicating effect of stack drop (fr

2-8 RPN: The Automatic Memory Stack1. Lifts the stack2. Lifts the stack and replicates the X–register.3. Overwrites the X–register.4. Clears x by over

RPN: The Automatic Memory Stack 2-9Correcting Mistakes with LAST X Wrong Single Argument FunctionIf you execute the wrong single argument function, us

2-10 RPN: The Automatic Memory StackExample:Suppose you made a mistake while calculating16 × 19 = 304There are three kinds of mistakes you could have

RPN: The Automatic Memory Stack 2-11Example:Two close stellar neighbors of Earth are Rigel Centaurus (4.3 light–years away) and Sirius (8.7 light–year

2-12 RPN: The Automatic Memory StackChain Calculations in RPN ModeIn RPN mode, the automatic lifting and dropping of the stack's contents let you

RPN: The Automatic Memory Stack 2-13Now study the following examples. Remember that you need to press  only to separate sequentially-entered numbers,

4 Contents5. Fractions...5-1Entering Fractions ...

2-14 RPN: The Automatic Memory StackExercisesCalculate:Solution: Calculate:Solution:Calculate:(10 – 5) ÷ [(17 – 12

RPN: The Automatic Memory Stack 2-154 ÷ [14 + (7 × 3) – 2]by starting with the innermost parentheses (7 × 3) and working outward, just as you would wi

2-16 RPN: The Automatic Memory StackMore ExercisesPractice using RPN by working through the following problems:Calculate:(14 + 12) × (18 – 12) ÷ (9 –

RPN: The Automatic Memory Stack 2-17A Solution:     

2-18 RPN: The Automatic Memory Stack

Storing Data into Variables 3-13Storing Data into VariablesThe HP 35s has 30 KB of memory, in which you can store numbers, equations, and programs. Nu

3-2 Storing Data into VariablesIn ALG mode, you can store an expression into a variable; in this case, the value of the expression is stored in the va

Storing Data into Variables 3-3To recall the value stored in a variable, use the Recall command. The display of this command differs slightly from RP

3-4 Storing Data into VariablesViewing a Variable The VIEW command () displays the value of a variable without recalling that value to the x-registe

Storing Data into Variables 3-5Example: 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 cle

Contents 5Operator Precedence... 6-14Equation Functions...

3-6 Storing Data into VariablesTo leave the VAR catalog at any time, press either  or . An alternate method to clearing a variable is simply to sto

Storing Data into Variables 3-7Recall ArithmeticRecall arithmetic uses , , , or  to do arithmetic in the X–register using a recalled number an

3-8 Storing Data into VariablesExample:Suppose the variables D, E, and F contain the values 1, 2, and 3. Use storage arithmetic to add 1 to each of th

Storing Data into Variables 3-9Example:The Variables "I" and "J"There are two variables that you can access directly: the variable

3-10 Storing Data into Variables

Real–Number Functions 4-14Real–Number FunctionsThis chapter covers most of the calculator's functions that perform computations on real numbers,

4-2 Real–Number FunctionsQuotient and Remainder of DivisionYou can use ()and () to produce the integer quotient and integer remainder,

Real–Number Functions 4-3In RPN mode, to calculate a root x of a number y (the xth root of y), key in y  x, then press . For y < 0, x must be an

4-4 Real–Number FunctionsSetting the Angular ModeThe angular mode specifies which unit of measure to assume for angles used in trigonometric functions

Real–Number Functions 4-5Example:Show that cosine (5/7)π radians and cosine 128.57° are equal (to four significant digits). Programming Note:Equations

6 ContentsDot product ...10-4Angle between vectors...

4-6 Real–Number FunctionsHyperbolic FunctionsWith x in the display:Percentage FunctionsThe percentage functions are special (compared with  and  ) b

Real–Number Functions 4-7Suppose that the $15.76 item cost $16.12 last year. What is the percentage change from last year's price to this year&ap

4-8 Real–Number FunctionsPhysics ConstantsThere are 41 physics constants in the CONST menu. You can press  to view the following items.CONST MenuIt

Real–Number Functions 4-9To insert a constant:1. Position your cursor where you want the constant inserted.2. Press   to display the physics constan

4-10 Real–Number FunctionsConversion FunctionsThe HP 35s supports four types of conversions. You can convert between: rectangular and polar formats f

Real–Number Functions 4-11To convert between rectangular and polar coordinates: The format for representing complex numbers is a mode setting. You ma

4-12 Real–Number FunctionsExample: Conversion with Vectors.Engineer P.C. Bord has determined that in the RC circuit shown, the total impedance is 77.8

Real–Number Functions 4-13Time ConversionsThe HP 35s can convert between decimal and hexagesimal formats for numbers. This is especially useful for ti

4-14 Real–Number FunctionsTo convert an angle between degrees and radians: ExampleIn this example, we convert an angle measure of 30° to π/6 radians.U

Real–Number Functions 4-15Probability FunctionsFactorialTo calculate the factorial of a displayed non-negative integer x (0 ≤ x ≤ 253), press  * (the

Contents 7Part 2. Programming13.Simple Programming...13-1Designing a Program ...

4-16 Real–Number FunctionsThe RANDOM function uses a seed to generate a random number. Each random number generated becomes the seed for the next rand

Real–Number Functions 4-17Parts of NumbersThese functions are primarily used in programming.Integer partTo remove the fractional part of x and replace

4-18 Real–Number FunctionsGreatest integerTo obtain the greatest integer equal to or less than given number, press  ().Example:This example su

Fractions 5-15FractionsIn Chapter 1, the section Fractions introduced the basics of entering, displaying, and calculating with fractions. This chapte

5-2 FractionsIf you didn't get the same results as the example, you may have accidentally changed how fractions are displayed. (See "Changin

Fractions 5-3Accuracy IndicatorsThe accuracy of a displayed fraction is indicated by the  and  annunciators at the right of the display. The calcula

5-4 FractionsThis is especially important if you change the rules about how fractions are displayed. (See "Changing the Fraction Display" la

Fractions 5-5 To set the maximum denominator value, enter the value and then press . Fraction-display mode will be automatically enabled. The value

5-6 Fractions2. In ALG mode, you can use the result of a calculation as the argument for the /c function. With the value in line 2, simply press . T

Fractions 5-7You can change flags 8 and 9 to set the fraction format using the steps listed here. (Because flags are especially useful in programs, th