17-8Miscellaneous Programs and Equations, | HP 33s Scientific

Program Listing:

Program Lines:		Description
(In ALG mode)
& &	This routine displays prime number P.
& #$
Checksum and length: AA7A		6
' '	This routine adds 2 to P.
'
' -
Checksum and length: 8696		21

! ª ! º65¸ º/¸@ !- !

This routine stores the input value for P.

Tests for even input.

Increments P if input an even number. Stores 3 in test divisor, D.

Checksum and length: D0B8 87

% % % % ª % % º/@ % ! ' % % º %º65¸

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.

17–8Miscellaneous Programs and Equations

Image 290

HP 33s Scientific manual 17-8Miscellaneous Programs and Equations, #$ , ,

Contents

Hp 33s scientific calculator Printing History Contents RPN The Automatic Memory Stack Clearing the X-Register Storing Data into Variables Fractions in Programs How You Can Use Equations Summary of Equation Operations For More Information Complex Stack Complex Operations ContentsSolving an Equation Accuracy of Integration Programming 12-6 12-4Data Input and Output 12-4 Entering a Program 12-5 12-7 13-3 13-113-2 Branching GTO 13-4 Vector Operations 15-1 Managing Calculator Memory ContentsPart 3. Appendixes and Reference 15-12 Disabling Operations Neutral Operations Resetting the Calculator Clearing MemoryRound-Off Error Contents About ALG Conditions That Prolong Calculation Time UnderflowHow the Integral Is Evaluated Page Part Basic OperationPage Important Preliminaries Adjusting Display ContrastGetting Started Turning the Calculator On and Off 2Getting Started Highlights of the Keyboard and DisplayShifted Keys Alpha Keys Cursor Keys 4Getting Started Silver Paint KeysBackspacing and Clearing Equation-entry mode Keyboard-entry modeAre described in Using Menus on page 1-7. If ¾ when number entry is complete 6Getting Started Programming Instructions Using MenusHP 33s Menus Chapter Name Numeric Functions Description Other functions8Getting Started To use a menu function Exiting Menus KeysDisplay To select ALG mode RPN mode ALG modeTo select RPN mode RPN and ALG Keys Display and Annunciators First Line Second Line 2 3 HP 33s Annunciators Meaning Chapter12Getting Started RAD or §,¨ Exponents of Ten Keying in NumbersMaking Numbers Negative Keys Display Description Other Exponent Functions Understanding Digit EntryKeying in Exponents of Ten Keys Display Doing ArithmeticRange of Numbers and Overflow 16Getting Started , \, , Qor T One-Number FunctionsTwo-Number Functions Key in the number. You dont need to press ‘ ‘3 z Controlling the Display FormatPeriods and Commas in Numbers D, , \, ,Q Scientific Format Number of Decimal PlacesFixed-Decimal Format % Engineering Format SHOWing Full 12-Digit Precision20Getting Started ALL Format KeysDisplayDescription FractionsEntering Fractions 22Getting Started DisplayDescription MessagesDisplaying Fractions Clearing All of Memory Calculator MemoryChecking Available Memory 24Getting Started RPN The Automatic Memory Stack RPN The Automatic Memory StackWhat the Stack Is 2RPN The Automatic Memory Stack X and Y-Registers are in the DisplayClearing the X-Register Rµ Roll Up Reviewing the Stack¶ Roll Down 4RPN The Automatic Memory Stack Arithmetic How the Stack Does ItExchanging the X- and Y-Registers in the Stack How Enter Works Lost 6RPN The Automatic Memory Stack Using a Number Twice in a RowHow Clear x Works Filling the stack with a constant Last X Register 8RPN The Automatic Memory Stack Correcting Mistakes with Last, \, , Qor T Wrong One-Number Function Mistake Reusing Numbers with Last› 96.704 + 10RPN The Automatic Memory Stack Chain Calculations in RPN mode Work from the Parentheses Out 12RPN The Automatic Memory Stack Order of Calculation SolutionExercises 16.3805x5 = 181.0000 ‘14 ‘ More Exercises14RPN The Automatic Memory Stack ⋅ 0.8 ⎟ 12.5 − 0.73 = Page Storing Data into Variables Storing Data into Variables To recall a copy of a number from a variable to the display Storing and Recalling Numbers2Storing Data into Variables Example Storing Numbers To review the values at any or all non-zero variables Viewing a Variable without Recalling ItReviewing Variables in the VAR Catalog Storage Arithmetic Clearing VariablesArithmetic with Stored Variables 4Storing Data into Variables Recall Arithmetic Result 3 That is, x 6Storing Data into Variables Exchanging x with Any VariableLzE Variable Page Real-Number Functions Real-Number FunctionsExponential and Logarithmic Functions To Calculate Press Power FunctionsQuotient and Remainder of Division 2Real-Number Functions To Calculate Press Result TrigonometryEntering π Option Description Annunciator Setting the Angular ModeTrigonometric Functions 4Real-Number Functions NzR Programming Note 6Real-Number Functions Hyperbolic FunctionsPercentage Functions ‘x Q 16.12 ‘ 15.76 T . 8Real-Number Functions Physics ConstantsConst Menu Items Description Value To insert a constant Conversion FunctionsItems Description Value To convert between rectangular and polar coordinates Coordinate Conversions10Real-Number Functions Example Polar to Rectangular Conversion Example Conversion with Vectors To convert between decimal fractions and minutes-seconds Time Conversions12Real-Number Functions Example Converting Time Formats To Convert Press Displayed Results Angle ConversionsUnit Conversions To convert an angle between degrees and radians Gamma Probability FunctionsFactorial Probability Display KeysExample Combinations of People Parts of Numbers 16Real-Number Functions Names of Functions Page Fractions Entering Fractions 2Fractions Fractions in the DisplayDisplay Rules Accuracy Indicators Entered Value Internal Value Displayed Fraction 4Fractions Changing the Fraction DisplayLonger Fractions Setting the Maximum Denominator Choosing a Fraction Format Fraction How 2.77 Is Displayed Format Examples of Fraction DisplaysTo Get This Fraction Format Change These Flags 6Fractions Denominator Fixed Rounding FractionsFraction Number Entered and Fraction Displayed Format ¼ Fractions in Equations 8Fractions Fractions in Programs Page Entering and Evaluating Equations Entering and Evaluating EquationsHow You Can Use Equations Example Calculating with an Equation 2Entering and Evaluating Equations ZNzZLL Key Operation Enters and leaves Equation modeSummary of Equation Operations 4Entering and Evaluating Equations Entering Equations into the Equation ListVariables in Equations To enter an equation Numbers in Equations Functions in Equations LR d Displaying and Selecting EquationsParentheses in Equations ZLC z To view a long equation Editing and Clearing Equations——— To select an equation 8Entering and Evaluating Equations Types of Equations Evaluating Equations Fx ¼ Type of Equation Result for ‘10Entering and Evaluating Equations To evaluate an equation Using Enter for Evaluation Example Evaluating an Equation with Enter 12Entering and Evaluating Equations Using XEQ for EvaluationResponding to Equation Prompts Example Evaluating an Equation with XEQ ‘5 g Syntax of EquationsOperator Precedence „ To display digits hidden by the prompt, press 14Entering and Evaluating Equations Order Operation ExampleEquations Meaning Equation Functions Σxy Example Perimeter of a Trapezoid Operation Equation function16Entering and Evaluating Equations Perimeter = a + b + h Example Area of a Polygon HLA ’.25 zLN zLD 2 zR NqLN `qONqLN `‘Cos π / n Area = 18Entering and Evaluating Equations Syntax ErrorsVerifying Equations Example Checksum and Length of an Equation Solving Equations Solving EquationsSolving an Equation Markup ⋅ Cost = Price 2Solving Equations LD dLVZLT › Example Solving the Equation of Linear Motion Value 4Solving Equations HL P zZL T Example Solving the Ideal Gas Law Equation LV q Understanding and Controlling Solve Verifying the Result 6Solving Equations Interrupting a Solve Calculation Choosing Initial Guesses for Solve Example Using Guesses to Find a Root 8Solving Equations ZL H 40 H 10Solving Equations For More Information Page Integrating Equations Integrating Equations 2Integrating Equations Integrating Equations ≥ FNJ0 x = π1 ≥0π cos x sin t dt ≥ 0π f t Value = ≥ t 4Integrating EquationsExample Sine Integral Accuracy of Integration 6Integrating Equations Specifying AccuracyInterpreting Accuracy Example Specifying Accuracy Example Changing the Accuracy 8Integrating Equations Its uncertainty indicates + iy Operations with Complex NumbersComplex Stack To enter a complex number To do an operation with one complex number Complex Operations2Operations with Complex Numbers Functions for One Complex Number, z To Calculate Press To do an arithmetic operation with two complex numbers 4Operations with Complex Numbers ‘2 ‘ ‘4 2 5 ‘ ‘2 Using Complex Numbers in Polar Notation2 3 ‘ 6Operations with Complex Numbers Example Vector Addition Operations with Complex Numbers Page Menu label Description Base Conversions and ArithmeticBase Menu Base Conversions and Arithmetic Arithmetic in Bases 2, 8, 10-2Base Conversions and Arithmetic Keys Display ˜˜ Representation of NumbersNegative Numbers 10-4Base Conversions and Arithmetic Range of Numbers 7FFFFFFFF Windows for Long Binary Numbers 10-6Base Conversions and Arithmetic Statistical Operations Statistical OperationsEntering Statistical Data Entering Two-Variable Data Correcting Errors in Data EntryEntering One-Variable Data 11-2Statistical Operations ‘20 Initial x, y Corrected x, y400 Statistics Menus Key Description Statistical CalculationsMean 11-4Statistical Operations Price per Part Example Weighted Mean Two Variables· Number of Parts y Uº Sample Standard DeviationPopulation Standard Deviation 11-6Statistical Operations Keys DisplayDescription Linear Regressionσº Linear Regression Menu Nitrogen Applied 11-8Statistical OperationsExample Curve Fitting Grain Yield Limitations on Precision of Data 70, y 11-10Statistical Operations Summation Values and the Statistics RegistersSummation Statistics Normalizing Close, Large Numbers Example Viewing the Statistics Registers Access to the Statistics RegistersStatistics Registers in Calculator Memory # ™ ´º¸/ ™ ´¸/ ™ ´º/ ™ ´¸/ ™ ´º/ ‡ 11-12Statistical Operations Programming Page Simple Programming RPN mode 5 !Nz ALG mode 5 !zN‘Simple Programming Example a Simple Program Display Description RPN mode ALG modeRPN mode 12-2Simple Programming Program Boundaries LBL and RTN Selecting a ModeDesigning a Program Program Labels Strengths of RPN Operations Using RPN, ALG and Equations in ProgramsData Input and Output ALG Operations Entering a Program To enter a program into memory To enter an equation in a program line Keys That Clear12-6Simple Programming Example Entering a Labeled Program RPN modeFunction Names in Programs 12-8Simple Programming HN ZLR Example Entering a Program with an Equation Executing a Program XEQ Testing a ProgramRunning a Program NzX Example Testing a Program 12-10Simple Programming @ Using Input for Entering DataEntering and Displaying Data 12-12Simple Programming To use the Input function in a program Using View for Displaying Data To respond to a prompt Example INPUT, VIEW, and Messages in a Program Using Equations to Display Messages12-14Simple Programming ›p NzLR LR z › LH = 2π R2 + 2π RH = 2π R R + H Displaying Information without Stopping 12-16Simple Programming Programming a Stop or Pause STOP, PSE Error StopsStopping or Interrupting a Program Interrupting a Running Program To delete a program line Editing a Program12-18Simple Programming To insert a program line Program Memory Viewing Program Memory Clearing One or More Programs Memory UsageCatalog of Programs MEM 12-20Simple Programming Checksum To clear all programs from memory Programming with Base Selecting a Base Mode in a ProgramNonprogrammable Functions V Numbers Entered in Program Lines Decimal mode set Hexadecimal mode setPolynomial Expressions and Horners Method Ax4 + Bx3 + Cx2 + Dx + E 12-24Simple Programming Keys Display ALG mode‰X Checksum and length E41A Page Programming Techniques Programming TechniquesRoutines in Programs Calling Subroutines XEQ, RTN 13-2Programming Techniques Nested Subroutines Example a Nested Subroutine A2 + B2 Branching GTO13-4Programming Techniques Using GTO from the Keyboard Programmed GTO Instruction Conditional Instructions 13-6Programming Techniques Tests of Comparison x?y, x?0 Test Menus 13-8Programming Techniques Program Lines Description RPN modeFlags !- % ! ! ! º¸@ ! Set FlagFraction-Control Flags Status Clear 13-10Programming Techniques Annunciators for Set Flags Using FlagsFlags Menu Menu Key Description Example Using Flags 13-12Programming Techniques $ @ $ $ @ $ Program Lines Description RPN mode 13-14Programming Techniques Example Controlling the Fraction Display Program Lines Description Loops 13-16Programming Techniques . ! º6¸@ ! #$ ! Conditional Loops GTO ! ! Loop-Control Number Loops with Counters DSE, ISG13-18Programming Techniques $ $ $ ! $ 13-20Programming Techniques Indirectly Addressing Variables and LabelsVariable Indirect Address If i contains Then i will address Example Choosing Subroutines With Program Control with13-22Programming Techniques ! L - L & %1L2 If i holds Then XEQi callsProgram lines Example Loop Control With Equations with 13-24Programming Techniques 1L2 L Page Solving and Integrating Programs Solving and Integrating ProgramsSolving a Program To solve a programmed function V= N x R x T Example Program Using ALG14-2Solving and Integrating Programs Pressure ⋅ volume. Pressure ⋅ volume 14-4Solving and Integrating Programs Example Program Using EquationLP z LV ’ LN z LR z LT ‘ @ @ ‘10 !@ # / / label #variable Using Solve in a Program14-6Solving and Integrating Programs Example Solve in a Program To integrate a programmed function Program Lines In RPN modeIntegrating a Program 14-8Solving and Integrating Programs To write a program for ≥ FN / label Using Integration in a ProgramSin Example ≥ FN in a Program 14-10Solving and Integrating Programs≥ G variable Restrictions on Solving and Integrating Page Mathematics Programs Mathematics ProgramsVector Operations = R cosP = arctan V1 = X i + Y j + Z k V2=U i + V j + W k 15-2Mathematics Programs= XU + YV + ZW X2 + Y2 + Z2 and P Program Listing Program Lines Description ALG mode 15-4Mathematics Programs Goes to the vector-addition routine 15-6Mathematics Programs Program Instructions Flags UsedRemarks 15-8Mathematics Programs Variables Used XR 15-10Mathematics Programs@ 07 g !@ 125 g @ AX + DY + GZ = J BX + EY + HZ = K CX + FY + IZ = L Solutions of Simultaneous Equations15-12Mathematics Programs % 15-14Mathematics Programs Mathematics Programs 15-16Mathematics Programs Flags Used 15-18Mathematics Programs Scratch @ @ Polynomial Root Finder15-20Mathematics Programs @ @ X2 + J Lx + K M = Where J = a3/2 = y0 /2X2 + J + Lx + K + M = ⋅ the sign of JK a1/2 15-22Mathematics Programs Polynomial 15-24Mathematics Programs ! B2= -a2 Checksum and length C7A6B0 =a04a0 a32 a12 B1 = a3a1 4a0 15-26Mathematics Programs JK. a1 + L + M 15-28Mathematics Programs Terms and Coefficients Order 15-30Mathematics Programs %/ Coordinate Transformations 15-32Mathematics Programs Old coordinate System 15-34Mathematics Programs Checksum and length 8C82 15-36Mathematics Programs Remark Ÿ @ 15-38Mathematics Programs Statistics Programs Statistics ProgramsCurve Fitting = B + MIn 16-2Statistics Programs Description 16-4Statistics Programs #$ #$ 16-6Statistics Programs 16-8Statistics Programs XS%@ 40.5 g &@ value 104.5 g %@ 38.6 g &@ %@ 37.9 g &@ / / %@ 16-10Statistics Programs/ Logarithmic Exponential Power Normal and Inverse-Normal Distributions 16-12Statistics Programs Function 16-14Statistics Programs ª º ª -+. H % ! XS@ Variable used temporarily to pass the value S ⋅ 2 π toInverse program 16-16Statistics Programs Grouped Standard Deviation 2f − 16-18Statistics Programs Updates ƒxi 2fi in register Increments or decrements N 16-20Statistics Programs %@ @ Group/ XU/ %@ 13 g @ / %@ 16-22Statistics Programs%@ %@ Miscellaneous Programs and Equations Miscellaneous Programs and EquationsTime Value of Money ›LI …LN `QLI ›LF z 17-2Miscellaneous Programs and Equations Solve instructions 17-4Miscellaneous Programs and Equations Keys Display Description RPN modešas Retains 5750 in B calculates monthly interest rate Prime Number Generator 17-6Miscellaneous Programs and Equations LBL Y 17-8Miscellaneous Programs and Equations #$ No test is made to ensure that the input is greater than 17-10Miscellaneous Programs and Equations Appendixes and Reference Page Calculator Support Support, Batteries ServiceSupport, Batteries, and Service A-1 Answers to Common Questions Changing the Batteries 2Support, Batteries, and ServiceEnvironmental Limits Support, Batteries, and Service A-3 To install batteries Do not mutilate, puncture, or dispose of batteries Testing Calculator Operation4Support, Batteries, and Service Fire. The batteries can burst or explode ™Ÿ˜—š Support, Batteries, and Service A-5Self-Test Warranty 6Support, Batteries, and Service Europe Country Telephone numbers ServiceSupport, Batteries, and Service A-7 America Country Telephone numbers 8Support, Batteries, and ServiceAsia Pacific Country Telephone numbers Canada Support, Batteries, and Service A-9Regulatory Information 10Support, Batteries, and Service Japan User Memory and the Stack User Memory and the StackManaging Calculator Memory Resetting the Calculator 2User Memory and the Stack Category DefaultClearing Memory Neutral Operations Status of Stack LiftDisabling Operations 4User Memory and the Stack Vlabel nnnn EQN FDISP € θ ,r Status of the Last X Register6User Memory and the Stack ALG Summary C-1 ALG SummaryAbout ALG Simple Arithmetic Power FunctionsDoing Two-number Arithmetic in ALG 2ALG Summary ALG Summary C-3 Percentage Calculations‘27 Q… 16.12 T Permutations and CombinationsQuotient and Remainder Of Division 4ALG Summary Keys Display Description ALG Summary C-5 Reviewing the Stack 6ALG Summary Coordinate Conversions ALG Summary C-7 8ALG Summary Integrating an EquationQ3 z To view the result of complex operations Operations with Complex NumbersALG Summary C-9 Complex Operations 10ALG Summary 2 ›3 `` Q2 › ALG Summary C-11 ºy4 ÃË2Ë5 ¹cº  ºy3 ÃË  Initial x, y Corrected x, y 12ALG Summary 20 ALG Summary C-13Page More about Solving D-1 More about SolvingHow Solve Finds a Root 2More about Solving Function Whose Roots Can Be Found Example An Equation With One Root Interpreting ResultsMore about Solving D-3 4More about Solving Example An Equation with Two Roots / More about Solving D-5/ -%. 6More about Solving LX `’1.5 Example Discontinuous Function − 1= More about Solving D-7 When Solve Cannot Find a Root 8More about Solving More about Solving D-9 Example a Relative Minimum 10More about Solving Example An Asymptote More about Solving D-11 ⎟ x + 0.3 − 0.5 =#LX q LX ›3 ``… Example Find the root of the equation Example a Local Flat Region 12More about Solving!1%ª1%-22 Round-Off Error More about Solving D-13 Underflow 14More about Solving More about Integration More about IntegrationHow the Integral Is Evaluated Conditions That Could Cause Incorrect Results 2More about Integration ≥0∞ xe −x dx ‡ LX zLX ` 4More about Integration More about Integration 6More about Integration Conditions That Prolong Calculation Time 8More about Integration . More about Integration Page Messages Messages F-1 2Messages Or program. This might take a while Messages F-3 # variable 4Messages Self-Test Messages Operation Index G-1 Operation IndexName Keys and Description h ˜or —j 2Operation Index Operation Index G-3 Polar to rectangular coordinates P 4Operation Index M Operation Index G-5 ›Complex 6Operation IndexGComplex Change sign …Complex Subtraction Operation Index G-7 VRadians to degrees 8Operation IndexRHyperbolic DSE variable Mvariable Wlabel Operation Index G-9Natural exponential ?Fractional part label 10Operation IndexGTO label Vlabel Nnnn Input variable ‰variable ”I”Operation Index G-11 Integer part ISG variable Lvariable Natural logarithm 12Operation IndexLBL label •label Common logarithm FPause Operation Index G-13Permutations of n items WDegrees to radians 14Operation Index Operation Index G-15 16Operation Index Operation Index G-17 18Operation Index If x=0, skips the next program Line ≤0? 13-7 Operation Index G-19≠0? 13-7 11-10 Given an x-value Power Returns y raised to the xth power 20Operation Index Index Index-1 Index-2 Index-3 Index-4 Index-5 Index-6 Index-7 Index-8 Index-9 Index-10 Index-11 Index-12 RPN Index-13 Index-14 View Index-15