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    HP-15C 
    Owner’s Handbook 
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
    HP Part Number: 00015-90001 
    Edition 2.4, Sep 2011   
    						
    							 
     
    Legal Notice 
    This  manual  and  any  examples contained  herein  are  provided  “as  is” 
    and  are  subject  to  change  without  notice.  Hewlett-Packard  Company 
    makes  no  warranty  of  any  kind  with  regard  to  this manual,  including, 
    but  not  limited  to,  the  implied  warranties  of  merchantability  non-
    infringement  and  fitness  for  a particular  purpose.  In  this  regard,  HP 
    shall  not  be  liable  for  technical  or  editorial  errors  or  omissions 
    contained in the manual. 
    Hewlett-Packard  Company  shall  not  be  liable  for  any  errors  or 
    incidental or consequential damages in connection with the furnishing, 
    performance, or use of this manual or the examples contained herein.  
    Copyright © 2011 Hewlett-Packard Development Company, LP. 
    Reproduction,  adaptation,  or  translation  of  this  manual  is  prohibited 
    without  prior  written  permission  of  Hewlett-Packard  Company,  except 
    as allowed under the copyright laws. 
     
     
     
     
    Hewlett-Packard Company 
    Palo Alto, CA 
    94304 
    USA  
    						
    							 
    3 
    Introduction 
    Congratulations! Whether  you are  new to HP calculators or  an experienced 
    user,  you  will  find  the  HP-15C a  powerful  and  valuable  calculating  tool. 
    The HP-15C provides: 
     448  bytes  of  program  memory  (one  or  two  bytes  per  instruction)  and 
    sophisticated  programming  capability,  including  conditional  and 
    unconditional branching, subroutines, flags, and editing. 
     Four advanced mathematics capabilities: complex number calculations, 
    matrix calculations, solving for roots, and numerical integration. 
     Direct and indirect storage in up to 67 registers. 
    This  handbook  is  written  for  you,  regardless  of  your  level  of  expertise. 
    The beginning part covers all the basic functions of the HP-15C and how to 
    use  them. The  second  part covers programming and is  broken  down  into 
    three subsections – The Mechanics, Examples, and Further Information – in 
    order  to  make  it  easy  for  users  with  varying  backgrounds  to  find  the 
    information  they  need.  The last part  describes  the  four  advanced 
    mathematics capabilities. 
    Before  starting these  sections,  you  may  want  to  gain  some  operating  and 
    programming  experience  on  the  HP-15C  by  working  through  the 
    introductory material, The HP-15C: A Problem Solver, on page 12. 
    The  various  appendices  describe  additional  details  of  calculator  operation, 
    as  well  as  warranty  and  service  information.  The  Function  Summary  and 
    Index and the Programming Summary and Index at the back of this manual 
    can  be  used  for  quick  reference  to  each  function  key  and  as  a  handy  page 
    reference to more comprehensive information inside the manual. 
    Also  available  from  Hewlett-Packard  is  the HP-15C  Advanced  Functions 
    Handbook, which  provides  applications  and  technical  descriptions  for  the 
    root-solving, integration, complex number, and matrix functions. 
    Note: You  certainly  do  not need  to  read  every  part  of  the  manual 
    before  delving  into  the  HP-15C  Advanced  Functions  if  you  are 
    already  familiar  with  HP  calculators.  The  use  of _ and f 
    requires a knowledge of HP-15C programming.  
    						
    							 
    4 
    Contents 
    The HP-15C: A Problem Solver  ....................................  12 
    A Quick Look at v  .................................................  12 
    Manual Solutions  ............................................................  13 
    Programmed Solutions  .....................................................  14 
    Part I: HP-15C Fundamentals  ................................  17 
    Section 1: Getting Started  ..........................................  18 
    Power On and Off  ..........................................................  18 
    Keyboard Operation  .......................................................  18 
    Primary and Alternate Functions  .....................................  18 
    Prefix Keys  ..................................................................  19 
    Changing Signs  ...........................................................  19 
    Keying in Exponents  .....................................................  19 
    The CLEAR Keys  ........................................................  20 
    Display Clearing: ` and −  ...................................  21 
    Calculations  ...................................................................  22 
    One-Number Functions  .................................................  22 
    Two-Number Functions and v  ...............................  22 
    Section 2: Numeric Functions  .....................................  24 
    Pi  ..................................................................................  24 
    Number Alteration Functions  ............................................  24 
    One-Number Functions  ....................................................  25 
    General Functions  ........................................................  25 
    Trigonometric Operations  ..............................................  26 
    Time and Angle Conversions  .........................................  26 
    Degrees/Radians Conversions  .......................................  27 
    Logarithmic Functions  ...................................................  28 
    Hyperbolic Functions  ....................................................  28 
    Two-Number Functions  ....................................................  29 
    The Power Function  ......................................................  29 
    Percentages  .................................................................  29 
    Polar and Rectangular Coordinate Conversions  ...............  30 
    Section 3: The Automatic Memory Stack, LAST X, and 
    Data Storage  ........................................................  32  
    						
    							 Contents 5 
     
    The Automatic Memory Stack and Stack Manipulation  ........  32 
    Stack Manipulation Functions  ........................................  33 
    The LAST X Register and K  .......................................  35 
    Calculator Functions and the Stack  .................................  36 
    Order of Entry and the v Key  ...............................  37 
    Nested Calculations  .....................................................  38 
    Arithmetic Calculations With Constants  ...........................  39 
    Storage Register Operations  ............................................  42 
    Storing and Recalling Numbers  .....................................  42 
    Clearing Data Storage Registers  ....................................  43 
    Storage and Recall Arithmetic  ........................................  43 
    Overflow and Underflow  ..............................................  45 
    Problems ........................................................................  45 
    Section 4: Statistics Functions  .....................................  47 
    Probability Calculations  ...................................................  47 
    Random Number Generator  .............................................  48 
    Accumulating Statistics  .....................................................  49 
    Correcting Accumulated Statistics  ...................................  52 
    Mean  ..........................................................................  53 
    Standard Deviation  .......................................................  53 
    Linear Regression  .........................................................  54 
    Linear Estimation and Correlation Coefficient  ...................  55 
    Other Applications  .......................................................  57 
    Section 5: The Display and Continuous Memory  ...........  58 
    Display Control  ..............................................................  58 
    Fixed Decimal Display  ..................................................  58 
    Scientific Notation Display  ............................................  59 
    Engineering Notation Display  ........................................  59 
    Mantissa Display  .........................................................  60 
    Round-Off Error  ............................................................  60 
    Special Displays  .............................................................  60 
    Annunciators  ...............................................................  60 
    Digit Separators  ...........................................................  61 
    Error Display  ...............................................................  61 
    Overflow and Underflow  ..............................................  61 
    Low-Power Indication  ....................................................  62 
    Continuous Memory  ........................................................  62 
    Status  .........................................................................  62  
    						
    							6 Contents 
     
    Resetting Continuous Memory  ........................................  63 
    Part II: HP-15C Programming  ...............................  65 
    Section 6: Programming Basics  ..................................  66 
    The Mechanics  ...............................................................  66 
    Creating a Program  .....................................................  66 
    Loading a Program  ......................................................  66 
    Intermediate Program Stops  ...........................................  68 
    Running a Program .......................................................  68 
    How to Enter Data  ........................................................  69 
    Program Memory  .........................................................  70 
    Further Information  ..........................................................  74 
    Program Instructions  .....................................................  74 
    Instruction Coding  ........................................................  74 
    Memory Configuration  ..................................................  75 
    Program Boundaries  .....................................................  77 
    Unexpected Program Stops  ...........................................  78 
    Abbreviated Key Sequences  ..........................................  78 
    User Mode  ..................................................................  79 
    Polynomial Expressions and Horners Method  ..................  79 
    Nonprogrammable Functions .........................................  80 
    Problems  ........................................................................  81 
    Section 7: Program Editing  ........................................  82 
    The Mechanics  ...............................................................  82 
    Moving to a Line in Program Memory  .............................  82 
    Deleting Program Lines  .................................................  83 
    Inserting Program Lines  .................................................  83 
    Examples  .......................................................................  83 
    Further Information  ..........................................................  85 
    Single-Step Operations  .................................................  85 
    Line Position  ................................................................  86 
    Insertions and Deletions  ................................................  87 
    Initializing Calculator Status  ..........................................  87 
    Problems ........................................................................  87 
    Section 8: Program Branching and Controls  .................  90 
    The Mechanics  ...............................................................  90 
    Branching  ...................................................................  90 
    Conditional Tests ..........................................................  91  
    						
    							 Contents 7 
     
    Flags  ..........................................................................  92 
    Examples  .......................................................................  93 
    Example: Branching and Looping  ...................................  93 
    Example: Flags  ............................................................  95 
    Further Information  ..........................................................  97 
    GoTo  ..........................................................................  97 
    Looping  ......................................................................  98 
    Conditional Branching  ..................................................  98 
    Flags  ..........................................................................  98 
    The System Flags: Flags 8 and 9  ....................................  99 
    Section 9: Subroutines ...............................................  101 
    The Mechanics  ...............................................................  101 
    GoTo Subroutine and Return  ..........................................  101 
    Subroutine Limits  ..........................................................  102 
    Examples  .......................................................................  102 
    Further Information  ..........................................................  105 
    The Subroutine Return  ...................................................  105 
    Nested Subroutines  ......................................................  105 
    Section 10: The Index Register and Loop Control  ...........  106 
    The V and % Keys  ....................................................  106 
    Direct Versus Indirect Data Storage With 
    The Index Register  .....................................................  106 
    Indirect Program Control With the Index Register  .............  107 
    Program Loop Control  ...................................................  107 
    The Mechanics  ...............................................................  107 
    Index Register Storage and Recall  ..................................  107 
    Index Register Arithmetic  ...............................................  108 
    Exchanging the X-Register  .............................................  108 
    Indirect Branching With V  .........................................  108 
    Indirect Flag Control With V  ......................................  109 
    Indirect Display Format Control With V  .......................  109 
    Loop Control with Counters: I and e  ..................  109 
    Examples  .......................................................................  111 
    Examples: Register Operations  .......................................  111 
    Example: Loop Control With s  .................................  112 
    Example: Display Format Control ....................................  114 
    Further Information  ..........................................................  115 
    Index Register Contents  .................................................  115  
    						
    							8 Contents 
     
    I and e  ..........................................................  116 
    Indirect Display Control ...........................................  116 
    Part III: HP-15C Advanced Functions  ....................  119 
    Section 11: Calculating With Complex Numbers  ..........  120 
    The Complex Stack and Complex Mode  ............................  120 
    Creating the Complex Stack  ..........................................  120 
    Deactivating Complex Mode  .........................................  121 
    Complex Numbers and the Stack  ......................................  121 
    Entering Complex Numbers  ........................................... 121 
    Stack Lift in Complex Mode  ........................................... 124 
    Manipulating the Real and Imaginary Stacks  ..................  124 
    Changing Signs  ..........................................................  124 
    Clearing a Complex Number  .......................................  125 
    Entering a Real Number  ...............................................  128 
    Entering a Pure Imaginary Number  ...............................  129 
    Storing and Recalling Complex Numbers  .......................  130 
    Operations With Complex Numbers  ................................  130 
    One-Number Functions  ................................................  131 
    Two-Number Functions  .................................................  131 
    Stack Manipulation Functions  .......................................  131 
    Conditional Tests  .........................................................  132 
    Complex Results from Real Numbers  ..............................  133 
    Polar and Rectangular Coordinate Conversions  .................  133 
    Problems  .......................................................................  135 
    For Further Information  ...................................................  137 
    Section 12: Calculating With Matrices  ........................  138 
    Matrix Dimensions  .........................................................  140 
    Dimensioning a Matrix  .................................................  141 
    Displaying Matrix Dimensions  .......................................  142 
    Changing Matrix Dimensions  ........................................  142 
    Storing and Recalling Matrix Elements  ..............................  143 
    Storing and Recalling All Elements in Order  ...................  143 
    Checking and Changing Matrix Elements Individually  .....  145 
    Storing a Number in All Elements of a Matrix  .................  147 
    Matrix Operations  .........................................................  147 
    Matrix Descriptors  .......................................................  147 
    The Result Matrix  .........................................................  148  
    						
    							 Contents 9 
     
    Copying a Matrix  .......................................................  149 
    One-Matrix Operations  ................................................  149 
    Scalar Operations  .......................................................  151 
    Arithmetic Operations  ..................................................  153 
    Matrix Multiplication  ...................................................  154 
    Solving the Equation AX = B ..........................................  156 
    Calculating the Residual  ...............................................  159 
    Using Matrices in LU Form  ............................................  160 
    Calculations With Complex Matrices  ...............................  160 
    Storing the Elements of a Complex Matrix  ......................  161 
    The Complex Transformations Between ZP and Z   .............  164 
    Inverting a Complex Matrix  ..........................................  165 
    Multiplying Complex Matrices  ......................................  166 
    Solving the Complex Equation AX = B  ............................  168 
    Miscellaneous Operations Involving Matrices  .....................  173 
    Using a Matrix Element With Register Operations  ............  173 
    Using Matrix Descriptors in the Index Register  .................  173 
    Conditional Tests on Matrix Descriptors  ..........................  174 
    Stack Operation for Matrix Calculations  ............................  174 
    Using Matrix Operations in a Program  ..............................  176 
    Summary of Matrix Functions  ...........................................  177 
    For Further Information  ....................................................  179 
    Section 13: Finding the Roots of an Equation  ................  180 
    Using _  .................................................................  180 
    When No Root Is Found  ..................................................  186 
    Choosing Initial Estimates  ................................................  188 
    Using _ in a Program  ..............................................  192 
    Restriction on the Use of _  .......................................  193 
    Memory Requirements  .....................................................  193 
    For Further Information  ....................................................  193 
    Section 14: Numerical Integration  ..............................  194 
    Using f .......................................................................  194 
    Accuracy of f  .............................................................  200 
    Using f in a Program  ..................................................  203 
    Memory Requirements  .....................................................  204 
    For Further Information  ....................................................  204  
    						
    							10 Contents 
     
     
    Appendix A: Error Conditions  ....................................  205 
    Appendix B: Stack Lift and the LAST X Register  ...............  209 
    Digit Entry Termination  ....................................................  209 
    Stack Lift  ........................................................................  209 
    Disabling Operations  ...................................................  210 
    Enabling Operations  ....................................................  210 
    Neutral Operations  ......................................................  211 
    LAST X Register ...............................................................  212 
    Appendix C: Memory Allocation  ................................  213 
    The Memory Space  .........................................................  213 
    Registers  .....................................................................  213 
    Memory Status (W) ..................................................  215 
    Memory Reallocation  ......................................................  215 
    The m % Function  ................................................  215 
    Restrictions on Reallocation  ...........................................  216 
    Program Memory  ............................................................  217 
    Automatic Program Memory Reallocation  ........................  217 
    Two-Byte Program Instructions  .......................................  218 
    Memory Requirements for the Advanced Functions  .............  218 
    Appendix D: A Detailed Look at _  ......................  220 
    How _ Works  .......................................................  220 
    Accuracy of the Root  .......................................................  222 
    Interpreting Results  ..........................................................  226 
    Finding Several Roots  ......................................................  233 
    Limiting the Estimation Time  ..............................................  238 
    Counting Iterations  .......................................................  239 
    Specifying a Tolerance  .................................................  239 
    For Advanced Information ................................................  239 
    Appendix E: A Detailed Look at f  ...........................  240 
    How f Works  .............................................................  240 
    Accuracy, Uncertainty, and Calculation Time  .....................  241 
    Uncertainty and the Display Format ...................................  245 
    Conditions That Could Cause Incorrect Results  ....................  249 
    Conditions That Prolong Calculation Time  ..........................  254 
    Obtaining the Current Approximation to an Integral  ...........  257 
    For Advanced Information ................................................  258  
    						
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