Representation of Numbers, Negative Numbers | HP 35s Scientific

() b

 ()

 

() 

() 

Changes to base 2; BIN annunciator on. This terminates digit entry, so no

is needed between

the numbers.

Result in binary base. Result in hexadecimal base. 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 12510 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 0 (positive). A negative number is the 2's complement of its positive binary number.

Keys:



()

Display:Description:

 Enters a positive, decimal number; then converts it to hexadecimal.

11-6Base Conversions and Arithmetic and Logic

Image 164

HP 35s Scientific manual Representation of Numbers, Negative Numbers,  , 

Contents

HP 35s scientific calculator Users guide Printing History Contents Storing Data into Variables Viewing a Variable ContentsRPN The Automatic Memory Stack Real-Number Functions Quotient and Remainder of DivisionTrigonometry Entering π Hyperbolic Functions Fractions Entering and Evaluating Equations Solving Equations Integrating EquationsOperations with Complex Numbers Vector Arithmetic 10-1 Base Conversions and Arithmetic and Logic 11-1 Statistical Operations 12-110-7 Creating Vectors from Variables or Registers 10-8 Part 2. Programming Simple Programming 13-1 Programming Techniques 14-1 Support, Batteries, and Service Part 3. Appendixes and ReferenceSolving and Integrating Programs 15-1 Statistics Programs 16-1 More about Solving User Memory and the StackALG Summary Round-Off Error More about IntegrationMessages Operation Index How the Integral Is Evaluated Contents Part Page Adjusting Display Contrast Getting StartedImportant Preliminaries Turning the Calculator On and Off 2Getting Started Highlights of the Keyboard and DisplayShifted Keys Alpha Keys Cursor KeysFunction Key Left-shifted function Right-shifted Letter for alphabetic  Clear or Cancel Backspacing and ClearingKeys for Clearing 4Getting Started Key Description Clear menu       Using Menus ˆ ˆ   HP 35s Menus Chapter Name 6Getting Started Programming Instructions Other functions Exiting Menus or  8 RPN and ALG Modes Keys Display KeysDisplay RPN mode ALG mode 10Getting Started Undo key Display and Annunciators First Line Second LineAnnunciators 12Getting Started HP 35s Annunciators Meaning Chapter EQN 14Getting Started Exponents of Ten Keying in NumbersMaking Numbers Negative 16Getting Started z Understanding Entry Cursor Range of Numbers and Overflow  18Getting Started Performing Arithmetic CalculationsSingle Argument or Unary Operations Key RPN,RPN Program ALG, Equation, ALG Program Two Argument or Binary Operations   Õ Controlling the Display Format Key RPN, RPN Program ALG, Equation, ALG Program 22Getting Started Periods and Commas in Numbers   Complex number display format  ,  ,  88 24Getting Started SHOWing Full 12-Digit Precision 8  8×  26Getting Started FractionsEntering Fractions Messages  É  28Getting Started Calculator MemoryChecking Available Memory Clearing All of Memory 30Getting Started RPN The Automatic Memory Stack RPN The Automatic Memory StackWhat the Stack Is 2RPN The Automatic Memory Stack Reviewing the Stack X and Y-Registers are in the DisplayClearing the X-Register 4RPN The Automatic Memory Stack Exchanging the X- and Y-Registers in the StackPress  Arithmetic How the Stack Does It How Enter Works 6RPN The Automatic Memory Stack How to Clear the Stack Filling the stack with a constant Last X Register 8RPN The Automatic Memory Stack Correcting Mistakes with Last Reusing Numbers with Last  Ù    Chain Calculations in RPN Mode Work from the Parentheses Out     Exercises Order of Calculation      More Exercises        18RPN The Automatic Memory Stack Storing Data into Variables AKeys DisplayDescription Storing and Recalling Numbers 2Storing Data into VariablesPress letter-key  Press letter-key    AG  Using the MEM Catalog Viewing a VariableVAR catalog 4Storing Data into Variables C D E Arithmetic with Stored Variables Storage Arithmetic6Storing Data into Variables Storage arithmetic uses , , , or  Recall Arithmetic Exchanging x with Any Variable  DD E A Variables I and J 10Storing Data into Variables Exponential and Logarithmic Functions Real-Number Functions Power Functions Quotient and Remainder of Division    Trigonometry Entering π Setting the Angular Mode Trigonometric FunctionsOption Description Annunciator 4Real-Number Functions   Hyperbolic Functions Percentage Functions     8Real-Number Functions Physics ConstantsConst Menu Items Description Value Items Description Value 10Real-Number Functions Conversion FunctionsRectangular/Polar Conversions 30o 12Real-Number Functions 86  Time ConversionsAngle Conversions Unit Conversions Probability Functions FactorialGamma Probability 16Real-Number Functions  Parts of Numbers Integer partFractional part Absolute value 18Real-Number Functions To calculatePressDisplay   FractionsEntering Fractions 2Fractions Fractions in the DisplayDisplay Rules Accuracy Indicators Entered Value Internal Value Displayed Fraction 4Fractions Setting the Maximum DenominatorChanging the Fraction Display  Choosing a Fraction Format 6Fractions   j To Get This Fraction Format Change These Flags Rounding Fractions Examples of Fraction Displays Fractions in Equations Fractions in Programs 10Fractions Entering and Evaluating Equations How You Can Use EquationsEntering and Evaluating Equations = .25 π d2 l Value      D 2Entering and Evaluating Equations Summary of Equation Operations Key Operation 4Entering and Evaluating Equations Entering Equations into the Equation ListVariables in Equations Numbers in Equations Functions in Equations Displaying and Selecting Equations Parentheses in Equations   Ö  Editing and Clearing Equations 8Entering and Evaluating Equations Types of Equations Evaluating Equations 10Entering and Evaluating Equations Using Enter for Evaluation Type of Equation Result for  Result for  12Entering and Evaluating Equations Using XEQ for Evaluation       Responding to Equation Prompts 14Entering and Evaluating Equations Syntax of EquationsOperator Precedence Order Operation Example Equations Meaning Σxy Equation Functions16Entering and Evaluating Equations RPN Operation Equation function Perimeter = a + b + h sin1θ + sin1φ 18Entering and Evaluating Equations Area =  Õ Syntax ErrorsVerifying Equations 20Entering and Evaluating Equations Solving Equations Solving an EquationSolving Equations Markup ⋅ Cost = Price 2Solving Equations = v0 t + 1/2 g t  G    P     P    Solving built-in Equation  6Solving Equations  Understanding and Controlling SolveVerifying the Result 8Solving Equations Interrupting a Solve CalculationChoosing Initial Guesses for Solve Solving Equations 10Solving Equations = 40 H ⋅ 20 H ⋅ 4 ⋅ HType in the equation Equation H  value 4H   For More Information 12Solving Equations Integrating Equations Integrating Equations Integrating Equations FN 2Integrating Equations J0 x = π 0 cosx sin t dt   4Integrating Equations = t X SinxX  Accuracy of Integration Specifying AccuracyInterpreting Accuracy 6Integrating Equations 8        8 8Integrating Equations Operations with Complex Numbers Form  2Operations with Complex Numbers Complex StackComplex Operations Functions for One Complex Number, z To Calculate Press 8  6 8  6 6 6Display Description 4Operations with Complex Numbers Using Complex Numbers in Polar Notation ?  ?  ?  6Operations with Complex Numbers Complex Numbers in Equations 6 ? ? Program lines ALG mode Complex Number in Program          Vector Arithmetic Vector ArithmeticVector operations    Õ 3  Absolute value of the vector  3  Dot product   3 3 10-4Vector Arithmetic Angle between vectors  Õ  3   10-6Vector Arithmetic Vectors in Equations3   Vectors in Programs Program lines Description 10-8Vector Arithmetic Creating Vectors from Variables or RegistersThen hC Õ hA Base Conversions and Arithmetic and Logic Base MenuMenu label Description Base Conversions and Arithmetic and Logic 11-2Base Conversions and Arithmetic and Logic    Õ  11-4Base Conversions and Arithmetic and Logic Arithmetic in Bases 2, 8,Logic Menu          Representation of Numbers Negative Numbers   Range of Numbers Using base in program and equations Windows for Long Binary Numbers    Statistical Operations Statistical OperationsEntering Statistical Data Correcting Errors in Data Entry Entering One-Variable DataEntering Two-Variable Data 12-2Statistical Operations   Initial x, y Corrected x, y Statistical Calculations MeanStatistics Menus Menu Key Description      Sample Standard Deviation     Population Standard Deviation Linear Regression 12-8Statistical Operations  ˆ Õ ˆLinear Regression Menu        12-10Statistical Operations Limitations on Precision of Data Summation Values and the Statistics Registers Summation Statistics Access to the Statistics Registers 12-12Statistical Operations Statistical Operations 12-14Statistical Operations Programming Page Simple Programming Simple Programming Area = πx2 13-2Simple Programming Selecting a Mode KeysDisplay In ALG modeDesigning a Program  X  Using RPN, ALG and Equations in Programs Program Boundaries LBL and RTN13-4Simple Programming  letter-key Data Input and Output Strengths of RPN Operations Entering a Program 13-6Simple Programming Clear functions and backspace key 13-8Simple Programming Function Names in ProgramsA RPN mode ER  R  Running a Program Executing a Program XEQ 13-10Simple Programming  Testing a ProgramKeys Display Description RPN mode Entering and Displaying Data 13-12Simple Programming Using Input for Entering Data RPN mode ALG mode 13-14Simple Programming Using View for Displaying Data 13-16Simple Programming Using Equations to Display Messages  ÇR ÇH Keys RPN mode  R H V  R R H  V OL  A RE A    V  S     Displaying Information without Stopping  13-18Simple Programming C  value Error Stops Stopping or Interrupting a ProgramProgramming a Stop or Pause STOP, PSE Interrupting a Running Program Editing a Program 13-20Simple Programming Program Memory Viewing Program Memory 13-22Simple Programming Memory UsageCatalog of Programs MEM Clearing One or More Programs Checksum Nonprogrammable Functions Programming with Base   Numbers Entered in Program Lines Selecting a Base Mode in a ProgramDecimal mode set Ax4 + Bx3 + Cx2 + Dx + E Polynomial Expressions and Horners Method13-26Simple Programming   A X     A  13-28Simple Programming Programming Techniques Routines in ProgramsCalling Subroutines XEQ, RTN Programming Techniques Nested Subroutines 14-2Programming Techniques A2 + b2 + c2 + d2 A2 + B2 Branching GTO14-4Programming Techniques Using GTO from the Keyboard Programmed GTO Instruction Conditional Instructions 14-6Programming Techniques Tests of Comparison x?y, x?0 Test Menus Program Lines Description RPN mode 14-8Programming Techniques Flags Meanings of Flags 14-10Programming Techniques Flag Fraction-Control FlagsClear Programming Techniques Flags Menu 14-12Programming Techniques … takes the natural log of the X-input S  value   value  14-14Programming Techniques Number 14-16Programming Techniques LoopsF      Conditional Loops GTO Loops with Counters DSE, ISG 14-18Programming Techniques Programming Techniques 14-20Programming Techniques Indirectly Addressing Variables and LabelsVariables I and J Indirect Address, I and J If I/J contains Then I/J will address 14-22Programming Techniques Unnamed indirect variables Program Control with I/JEquations with I/J 14-24Programming Techniques Solving and Integrating Programs Solving and Integrating ProgramsSolving a Program 15-2Solving and Integrating Programs V= N x R x T Keys Display Description ALG mode Program Lines Description ALG modeG P  value   value   H     LP   label  variable Using Solve in a Program15-6Solving and Integrating Programs Program Lines In RPN mode Integrating a Program 15-8Solving and Integrating Programs  S   X Sin  label   variable Using Integration in a Program15-10Solving and Integrating Programs Restrictions on Solving and Integrating 15-12Solving and Integrating Programs Statistics Programs Statistics ProgramsCurve Fitting = B + MIn 16-2Statistics Programs Program Listing 16-4Statistics Programs    16-6Statistics Programs Determines if D001 or B001 should be run 16-8Statistics Programs S            Logarithmic Exponential Power Normal and Inverse-Normal Distributions  Qx = 0.5 − σ 12π xx e−x −x ⎟σ 2 ⎟2dx 16-12Statistics Programs This routine initializes the normal distribution program Program Lines 16-14Statistics Programs Program Lines S  16-16Statistics ProgramsTo the inverse Program D  ∑ x f Grouped Standard Deviation16-18Statistics Programs   16-20Statistics Programs Register Summation Σ f Summation Σ x i f Index variable used to indirectly address the correctStatistics register    U     16-24Statistics Programs Miscellaneous Programs and Equations Time Value of MoneyMiscellaneous Programs and Equations TVM equation is P 4I NÕ I KeysDisplay In RPN mode    17-4Miscellaneous Programs and Equations P  value    I  17-6Miscellaneous Programs and Equations Prime Number Generator   17-8Miscellaneous Programs and Equations Tests to see whether all possible factors have been tried   17-10Miscellaneous Programs and Equations Cross Product in Vectors 17-12Miscellaneous Programs and Equations z 17-14Miscellaneous Programs and Equations Appendixes and Reference Page Support, Batteries, and Service Support, Batteries, and Service A-1Calculator Support Answers to Common Questions 2Support, Batteries, and Service Environmental Limits Support, Batteries, and Service A-3 Changing the Batteries Testing Calculator Operation 4Support, Batteries, and Service Support, Batteries, and Service A-5 Self-Test 6Support, Batteries, and Service Warranty Support, Batteries, and Service A-7 8Support, Batteries, and Service Customer Support Support, Batteries, and Service A-9 Emea 10Support, Batteries, and Service Support, Batteries, and Service A-11 Invent 12Support, Batteries, and Service Support, Batteries, and Service A-13 Yyyy+ 14Support, Batteries, and Service User Memory and the Stack B-1 User Memory and the StackManaging Calculator Memory Resetting the Calculator 2User Memory and the Stack Clearing Memory User Memory and the Stack B-3 Default Status of Stack LiftCategory 4User Memory and the Stack User Memory and the Stack B-5 Disabling OperationsNeutral Operations 6User Memory and the Stack Status of the Last X Registerˆ ˆ Accessing Stack Register Contents 8User Memory and the Stack ALG Summary About ALG, ALG Summary C-1 Doing Two argument Arithmetic in ALG Simple Arithmetic Power Functions Percentage Calculations Parentheses Calculations Permutations and CombinationsQuotient and Remainder Of Division xÕ 4  Õ  Trigonometric Functions Hyperbolic functions Reviewing the Stack ALG Summary C-7 8ALG Summary Integrating an EquationOperations with Complex Numbers 6 ALG Summary C-9 8Ë 4 66 6Õ4 6 Entering Statistical Two-Variable Data 12ALG Summary z ΣZ6   ˆ Õ ˆ ALG Summary C-13 14ALG Summary More about Solving D-1 More about SolvingHow Solve Finds a Root 2More about Solving Function Whose Roots Can Be Found Interpreting Results More about Solving D-3  X  X X X 4More about Solving X XX   6More about Solving XÕ  X   X4X Õ  More about Solving D-7 8More about Solving When Solve Cannot Find a Root X   More about Solving D-9  X  X    X  10More about Solving X4 X ÕÕ More about Solving D-11 X   12More about Solving More about Solving D-13 Round-Off Error X   14More about Solving More about Integration More about IntegrationHow the Integral Is Evaluated Conditions That Could Cause Incorrect Results 2More about Integration ∞ xe−xdx   4More about Integration More about Integration 6More about Integration Conditions That Prolong Calculation Time   8More about Integration More about Integration 10More about Integration Messages Messages F-1 2Messages Or program. This might take a while Messages F-3 4Messages    Solve include EQN and PGM modecannot find FN each uses a level, they can also generate this error Messages F-5 6Messages Operation Index G-1 Operation IndexName Keys and Description 2Operation Index ×Ø Operation Index G-3 = 4Operation Index Operation Index G-5  Denominator 6Operation Index Operation Index G-7 Natural exponentiallabel  Fractional part 8Operation Index   Operation Index G-9Input variable variable  Integer part ISG variable variable  10Operation IndexLBL label label Natural logarithm Operation Index G-11 RCL variable Pause Degrees to radians. Returns 2π/360 12Operation Index Operation Index G-13 14Operation Index Hyperbolic TangentView variable variable XEQ label label ÕÕ ≠Õ≤ Operation Index G-15 16Operation Index =y?14-7 Menu ≠0? 11-4 Power Operation Index G-17 18Operation Index Index Index-1 Index-2 Index-3 EQN List TOP 6-7, F-2 Index-4 Index-5 Index-6 Index-7 Index-8 Index-9 Index-10 Index-11 Angle between two vectors Index-12