HP 33S User manual

File name 33s-E-Manual-1008-Publication(1st).doc Page:386
Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm


HP 33s
RPN/ALG Scientific Calculator
Owner’s Manual
H
HP Part No. F2216-90020
Printed in China
Edition 1

File name 33s-E-Manual-1008-Publication(1st).doc Page : 386
Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm
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 and
fitness for a particular purpose. Hewlett–Packard Co. shall not be liable
for any errors or for incidental or consequential damages in connection with the
furnishing, performance, or use of this manual or the examples contained herein.
© Copyright 2003 Hewlett–Packard Development Company. L.P. Reproduction,
adaptation, or translation of this manual is prohibited without prior written
permission of Hewlett–Packard Company, except as allowed under the copyright
laws.
The programs that control your calculator are copyrighted and all rights are
reserved. Reproduction, adaptation, or translation of those programs without prior
written permission of Hewlett–Packard Co. is also prohibited.
4995, Murphy Canyon Rd,
Suite 301
San Diego, CA 92123
Printing History
Edition 1 November 2003

Contents
1
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Contents
Part 1. Basic Operation
1. Getting Started
Important Preliminaries.......................................................1–1
Turning the Calculator On and Off.................................1–1
Adjusting Display Contrast............................................1–1
Highlights of the Keyboard and Display ...............................1–2
Shifted Keys................................................................1–2
Alpha Keys.................................................................1–3
Backspacing and Clearing............................................1–3
Cursor keys ................................................................1–6
Using Menus ..............................................................1–6
Exiting Menus .............................................................1–9
RPN and ALG Keys ...................................................1–10
The Display and Annunciators .....................................1–11
Keying in Numbers..........................................................1–14
Making Numbers Negative ........................................1–14
Exponents of Ten .......................................................1–14
Understanding Digit Entry...........................................1–15
Range of Numbers and OVERFLOW ............................1–16
Doing Arithmetic .............................................................1–16
One–Number Functions..............................................1–17
Two–Number Functions ..............................................1–17
Controlling the Display Format ..........................................1–18
Periods and Commas in Numbers ................................1–18

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Number of Decimal Places ......................................... 1–19
SHOWing Full 12–Digit Precision ........................... 1–20
Fractions........................................................................ 1–21
Entering Fractions...................................................... 1–21
Displaying Fractions .................................................. 1–22
Messages ...................................................................... 1–23
Calculator Memory ......................................................... 1–23
Checking Available Memory ...................................... 1–24
Clearing All of Memory ............................................. 1–24
2. RPN: The Automatic Memory Stack
What the Stack Is ............................................................. 2–1
The X and Y–Registers are in the Display ........................ 2–2
Clearing the X–Register................................................ 2–2
Reviewing the stack ..................................................... 2–2
Exchanging the X– and Y–Registers in the Stack .............. 2–3
Arithmetic – How the Stack Does It ...................................... 2–4
How ENTER Works ..................................................... 2–5
How CLEAR x Works................................................... 2–6
The LAST X Register ........................................................... 2–7
Correcting Mistakes with LAST X.................................... 2–8
Reusing Numbers with LAST X....................................... 2–9
Chain Calculations in RPN mode ...................................... 2–10
Work from the Parentheses Out ................................... 2–10
Exercises.................................................................. 2–12
Order of Calculation ................................................. 2–13
More Exercises ......................................................... 2–14

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3. Storing Data into Variables
Storing and Recalling Numbers...........................................3–2
Viewing a Variable without Recalling It.................................3–3
Reviewing Variables in the VAR Catalog ...............................3–3
Clearing Variables ............................................................3–4
Arithmetic with Stored Variables ..........................................3–4
Storage Arithmetic .......................................................3–4
Recall Arithmetic .........................................................3–5
Exchanging x with Any Variable..........................................3–6
The Variable "i" ................................................................3–7
4. Real–Number Functions
Exponential and Logarithmic Functions .................................4–1
Quotient and Remainder Division ........................................4–2
Power Functions ................................................................4–2
Trigonometry ....................................................................4–3
Entering π..................................................................4–3
Setting the Angular Mode.............................................4–4
Trigonometric Functions ................................................4–4
Hyperbolic Functions..........................................................4–6
Percentage Functions..........................................................4–6
Physics Constants ..............................................................4–8
Conversion Functions .........................................................4–9
Coordinate Conversions .............................................4–10
Time Conversions ......................................................4–12
Angle Conversions.....................................................4–13
Unit conversions........................................................4–13
Probability Functions........................................................4–14

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Factorial .................................................................. 4–14
Gamma................................................................... 4–14
Probability ............................................................... 4–14
Parts of Numbers ............................................................ 4–16
Names of Functions......................................................... 4–17
5. Fractions
Entering Fractions ............................................................. 5–1
Fractions in the Display...................................................... 5–2
Display Rules.............................................................. 5–2
Accuracy Indicators..................................................... 5–3
Longer Fractions.......................................................... 5–4
Changing the Fraction Display............................................ 5–5
Setting the Maximum Denominator ................................ 5–5
Choosing a Fraction Format.......................................... 5–5
Examples of Fraction Displays ....................................... 5–6
Rounding Fractions............................................................ 5–8
Fractions in Equations........................................................ 5–9
Fractions in Programs ........................................................ 5–9
6. Entering and Evaluating Equations
How You Can Use Equations .............................................. 6–1
Summary of Equation Operations........................................ 6–3
Entering Equations into the Equation List ............................... 6–4
Variables in Equations ................................................. 6–4
Numbers in Equations ................................................. 6–5
Functions in Equations.................................................. 6–5
Parentheses in Equations .............................................. 6–6
Displaying and Selecting Equations ..................................... 6–6

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Editing and Clearing Equations ...........................................6–7
Types of Equations.............................................................6–9
Evaluating Equations..........................................................6–9
Using ENTER for Evaluation ........................................6–11
Using XEQ for Evaluation ...........................................6–12
Responding to Equation Prompts ..................................6–12
The Syntax of Equations ...................................................6–13
Operator Precedence.................................................6–13
Equation Functions.....................................................6–15
Syntax Errors ............................................................6–18
Verifying Equations..........................................................6–18
7. Solving Equations
Solving an Equation...........................................................7–1
Understanding and Controlling SOLVE .................................7–5
Verifying the Result ......................................................7–6
Interrupting a SOLVE Calculation ...................................7–7
Choosing Initial Guesses for SOLVE................................7–7
For More Information .......................................................7–11
8. Integrating Equations
Integrating Equations ( ∫FN)...............................................8–2
Accuracy of Integration ......................................................8–5
Specifying Accuracy ....................................................8–6
Interpreting Accuracy ...................................................8–6
For More Information .........................................................8–8
9. Operations with Complex Numbers
The Complex Stack............................................................9–1
Complex Operations .........................................................9–2

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Using Complex Numbers in Polar Notation........................... 9–5
10. Base Conversions and Arithmetic
Arithmetic in Bases 2, 8, and 16....................................... 10–2
The Representation of Numbers......................................... 10–4
Negative Numbers.................................................... 10–4
Range of Numbers.................................................... 10–5
Windows for Long Binary Numbers ............................. 10–5
11. Statistical Operations
Entering Statistical Data................................................... 11–1
Entering One–Variable Data....................................... 11–2
Entering Two–Variable Data........................................ 11–2
Correcting Errors in Data Entry.................................... 11–2
Statistical Calculations..................................................... 11–4
Mean...................................................................... 11–4
Sample Standard Deviation ........................................ 11–6
Population Standard Deviation .................................... 11–6
Linear regression....................................................... 11–7
Limitations on Precision of Data....................................... 11–10
Summation Values and the Statistics Registers ................... 11–11
Summation Statistics ................................................ 11–11
The Statistics Registers in Calculator Memory .............. 11–12
Access to the Statistics Registers ................................ 11–12
Part 2. Programming
12. Simple Programming
Designing a Program ...................................................... 12–3

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Selecting a Mode......................................................12–3
Program Boundaries (LBL and RTN) ..............................12–3
Using RPN, ALG and Equations in Programs..................12–4
Data Input and Output ...............................................12–4
Entering a Program..........................................................12–5
Keys That Clear.........................................................12–6
Function Names in Programs.......................................12–6
Running a Program..........................................................12–9
Executing a Program (XEQ).........................................12–9
Testing a Program......................................................12–9
Entering and Displaying Data .........................................12–11
Using INPUT for Entering Data ..................................12–11
Using VIEW for Displaying Data................................12–13
Using Equations to Display Messages.........................12–14
Displaying Information without Stopping .....................12–17
Stopping or Interrupting a Program ..................................12–17
Programming a Stop or Pause (STOP, PSE)...................12–17
Interrupting a Running Program .................................12–18
Error Stops .............................................................12–18
Editing a Program .........................................................12–18
Program Memory ..........................................................12–19
Viewing Program Memory ........................................12–19
Memory Usage .......................................................12–20
The Catalog of Programs (MEM)................................12–20
Clearing One or More Programs ...............................12–21
The Checksum.........................................................12–21
Nonprogrammable Functions .......................................... 12–22
Programming with BASE................................................. 12–22

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Selecting a Base Mode in a Program......................... 12–23
Numbers Entered in Program Lines ............................ 12–23
Polynomial Expressions and Horner's Method ................... 12–24
13. Programming Techniques
Routines in Programs....................................................... 13–1
Calling Subroutines (XEQ, RTN) .................................. 13–2
Nested Subroutines ................................................... 13–3
Branching (GTO) ............................................................ 13–4
A Programmed GTO Instruction................................... 13–5
Using GTO from the Keyboard .................................... 13–5
Conditional Instructions.................................................... 13–6
Tests of Comparison (x?y, x?0) ................................... 13–7
Flags....................................................................... 13–8
Loops.......................................................................... 13–16
Conditional Loops (GTO).......................................... 13–17
Loops With Counters (DSE, ISG) ................................ 13–18
Indirectly Addressing Variables and Labels ....................... 13–21
The Variable "i"...................................................... 13–21
The Indirect Address, (i) ........................................... 13–22
Program Control with (i) ........................................... 13–23
Equations with (i) .................................................... 13–25
14. Solving and Integrating Programs
Solving a Program .......................................................... 14–1
Using SOLVE in Program.................................................. 14–5
Integrating a Program...................................................... 14–7
Using Integration in a Program ....................................... 14–10
Restrictions on Solving and Integrating ............................. 14–11

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15. Mathematics Programs
Vector Operations ...........................................................15–1
Solutions of Simultaneous Equations.................................15–12
Polynomial Root Finder...................................................15–20
Coordinate Transformations ............................................ 15–32
16. Statistics Programs
Curve Fitting...................................................................16–1
Normal and Inverse–Normal Distributions .........................16–11
Grouped Standard Deviation ..........................................16–17
17. Miscellaneous Programs and Equations
Time Value of Money.......................................................17–1
Prime Number Generator .................................................17–6
Part 3. Appendixes and Reference
A. Support, Batteries, and Service
Calculator Support ........................................................... A–1
Answers to Common Questions .................................... A–1
Environmental Limits.......................................................... A–2
Changing the Batteries...................................................... A–2
Testing Calculator Operation ............................................. A–4
The Self–Test.................................................................... A–5
Warranty........................................................................ A–6
Service ........................................................................... A–7
Regulatory information...................................................... A–9
B. User Memory and the Stack
Managing Calculator Memory ............................................B–1

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Resetting the Calculator ..................................................... B–2
Clearing Memory ............................................................. B–3
The Status of Stack Lift ....................................................... B–4
Disabling Operations .................................................. B–5
Neutral Operations ..................................................... B–5
The Status of the LAST X Register......................................... B–6
C. ALG: Summary
About ALG ......................................................................C–1
Doing Two–number Arithmetic in ALG..................................C–2
Simple Arithmetic........................................................C–2
Power Functions ..........................................................C–2
Percentage Calculations ...............................................C–3
Permutation and Combination .......................................C–4
Quotient and Remainder Division ..................................C–4
Parentheses Calculations....................................................C–5
Chain Calculations ...........................................................C–5
Reviewing the Stack ..........................................................C–6
Coordinate Conversions.....................................................C–7
Integrating an Equation .....................................................C–8
Operations with Complex Numbers.....................................C–8
Arithmetic in Bases 2, 8, and 16....................................... C–10
Entering Statistical Two–Variable data................................C–11
D. More about Solving
How SOLVE Finds a Root ................................................... D–1
Interpreting Results ............................................................ D–2
When SOLVE Cannot Find a Root ....................................... D–8
Round–Off Error ............................................................. D–14

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Underflow......................................................................D–14
E. More about Integration
How the Integral Is Evaluated.............................................. E–1
Conditions That Could Cause Incorrect Results ....................... E–2
Conditions That Prolong Calculation Time ............................. E–7
F. Messages
G. Operation Index
Index

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Part 1
Basic Operation

Getting Started
1–1
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1
Getting Started
Important Preliminaries
Turning the Calculator On and Off
To turn the calculator on, press Å. ON is printed below the key.
To turn the calculator off, press ºÄ. That is, press and release the ºshift
key, then press Å(which has OFF printed in purple above it). Since the
calculator has Continuous Memory, turning it off does not affect any information
you've stored.
To conserve energy, the calculator turns itself off after 10 minutes of no use. If you
see the low–power indicator ( ã) in the display, replace the batteries as soon as
possible. See appendix A for instructions.
Adjusting Display Contrast
Display contrast depends on lighting, viewing angle, and the contrast setting. To
increase or decrease the contrast, hold down the Åkey and press Ùor Ã.

1–2 Getting Started
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Highlights of the Keyboard and Display
Shifted Keys
Each key has three functions: one printed on its face, a left–shifted function
(Green), and a right–shifted function (Purple). The shifted function names are
printed in green and purple above each key. Press the appropriate shift key (¹
or º) before pressing the key for the desired function. For example, to turn the
calculator off, press and release the ºshift key, then press Å.

Getting Started
1–3
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Pressing ¹or ºturns on the corresponding ßor àannunciator symbol at
the top of the display. The annunciator remains on until you press the next key. To
cancel a shift key (and turn off its annunciator), press the same shift key again.
Alpha Keys
Right-shifted
function
Left-shifted
function
Letter for
alphabetic key
G
Most keys have a letter written next to them, as shown above. Whenever you
need to type a letter (for example, a variable or a program label), the A..Z
annunciator appears in the display, indicating that the alpha keys are
"active".
Variables are covered in chapter 3; labels are covered in chapter 6.
Backspacing and Clearing
One of the first things you need to know is how to clear: how to correct numbers,
clear the display, or start over.

1–4 Getting Started
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Keys for Clearing
Key Description
~Backspace.
 Keyboard–entry mode:
Erases the character immediately to the left of "_" (the
digit–entry cursor) or backs out of the current menu. (Menus
are described in "Using Menus" on page 1–6.) If the number
is completed (no cursor), ~clears the entire number.
 Equation–entry mode:
Erases the character immediately to the left of "" (the
equation–entry cursor). If a number entry in your equation is
complete, ~erases the entire number. If the number is not
complete, ~erases the character immediately to the left of
"_" (the number–entry cursor). "_" changes back to "" when
number entry is complete.
~also clears error messages, and deletes the current program
line during program entry.
ÅClear or Cancel.
Clears the displayed number to zero or cancels the current
situation (such as a menu, a message, a prompt, a catalog, or
Equation–entry or Program–entry mode).