HP HP-28S User manual

HP-28S
Flin- HEWLETT
~I:.. PACKARD

Hp·28S
Advanced Scientific Calculator
Owner's Manual
r/i;' HEWLETT
.:~ PACKARD
Edition 4 November 1988
Reorder Number 00028-90066

Notice
For warranty and regulatory information for this calculator, see pages 291
and 295.
This manual and any examples contained herein are provided
"as is" and
are subject to change without notice. Hewlett-Packard Company makes
no
warranty ofany 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 keystroke programs
contained herein.
© Hewlett-Packard Co. 1988. All rights reserved. Reproduction, adapta-
tion, or translation of this manual
is prohibited without prior written per-
mission of Hewlett-Packard Company, except as allowed under the copy-
right 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.
Corvallis Division
1000 N.E. Circle Blvd.
Corvallis,
OR 97330, U.S.A.
Printing History
Edition 1
Edition 2
Edition 3
Edition 4
November 1987
April 1988
June 1988
November 1988
Mfg. No. 00028-90067
Mfg. No. 00028-90128
Mfg. No. 00028-90130
Mfg. No. 00028-90147

Welcome to the HP·28S
Congratulations! With the HP-28S you can easily solve complicated
problems, including problems you couldn't solve on a calculator be-
fore. The HP-28S combines powerful numerical computation with a
new dimension-symbolic computation. You can formulate a problem
symbolically, find a symbolic solution that shows the global behavior
of the problem, and obtain numerical results from the symbolic solu-
tion.
The HP-28S offers the following features:
• Algebraic
manipulation. You can expand, collect, or rearrange terms
in an expression, and you can symbolically solve an equation for a
variable.
• Calculus.
You can calculate derivatives, indefinite integrals, and
definite integrals.
• Numerical solutions. Using
HP Solve on the HP-28S, you can solve
an expression or equation for any variable. You can also solve a
system of linear equations. With multiple data types, you can use
complex numbers, vectors, and matrices as easily as real numbers.
• Plotting. You can plot expressions, equations, and statistical data.
•
Unit conversion. You can convert between any equivalent combina-
tions of the 120 built-in units. You can also define your own units.
• Statistics.
You can calculate single-sample statistics, paired-sample
statistics, and probabilities.
• Binary
number bases. You can calculate with binary, octal, and
hexadecimal numbers and perform bit manipulations.
• Direct entry for algebraic formulas, plus RPN logic for interactive
calculations.
Welcome to the HP·28S 3

The HP-28S Owner's Manual (this manual) contains three parts. Part 1,
"Fundamentals," demonstrates how to work some simple problems.
Part 2, "Summary of Calculator Features," builds on part 1 to help
you apply those examples to your own problems. Part 3, "Program-
ming," describes
programming features and demonstrates them in a
series
of programming examples.
The HP-28S Reference Manual gives detailed information about com-
mands. It is a dictionary of menus, describing the concepts and
commands for each menu.
We recommend that you first work through the examples in part 1 of
the Owner's Manual to get comfortable with the calculator, and then
look at part 2 to gain a broader understanding of the calculator's op-
eration. When you want to know more about a particular command,
look it up in the Reference Manual. When you want to learn about
programming, read part 3 of the Owner's Manual.
These manuals show you how to use the HP-28S to do math, but
they don't teach math. We assume that you're already familiar with
the relevant mathematical principles. For example, to use the calculus
features
of the HP-28S effectively, you should know elementary
calculus.
On the other hand, you don't need to understand all the math topics
in the HP-28S to use those parts of interest to you. For example, you
don't need to understand calculus to use the statistical capabilities.
4 Welcome to the HP-285

Contents
15 How To Use This Manual
15 What's in This Manual
16 For More Information
Part 1: Fundamentals
1
2
Getting Started
Preliminaries
Opening and Closing the Case
18
18
18
19
20
20
21
21
25
25
31
Locating the Battery Door and Printer Port
Turning the HP-28S On and Off
Clearing All Memory (Memory Reset)
Adjusting the Display Contrast
34
36
36
37
39
40
Keyboard Calculations
An Overview of the Calculator
Major Features and Concepts
The Catalog of Commands
Doing Arithmetic
Entering and Displaying Numbers
Changing the Decimal Point
Selecting
Number Display Mode
Keying In Numbers
One-Number Functions
41 Two-Number Functions
41 Addition and Subtraction
41 Multiplication and Division
42 Powers and Roots
43 Percentages
Contents 5

43 Swapping Levels 1 and 2
44
Clearing Objects From the Stack
45 Chain Calculations
47
If You Execute the Wrong Function
3 48
Using Variables
48 Introduction to Variables
49 Creating a Numerical Variable
50
Recalling a Numerical Variable
50
Evaluating a Numerical Variable
51
Changing the Value of a Variable
52 Purging a Variable
52
Changing the Name of a Variable
54 Creating a Program Variable
56
Recalling a Program Variable
56
Evaluating a Program Variable
57
Quoted and Unquoted Names
4 58
Repeating Calculations
58
Creating an Expression
60
Creating a Directory
63
Using the Solver To Repeat a Calculation
66
Using a Different Set of Values
68
Using a Different Expression
71 Returning to HOME
72 Summary
5
73
Real-Number Functions
73 Trigonometric Functions
73
Selecting Angle Mode
74 Using 7r
76
Converting Angular Measure
77
Logarithmic, Exponential, and Hyperbolic
Functions
78 Other Real Functions
79
Defining New Functions
6 Contents

6
82 Complex-Number Functions
82 Using Complex Numbers
84 Using Polar Coordinates
86 A User Function for Polar Addition
7 89
Plotting
91 Printing a Plot
91 Changing the Scale of the Plot
93 Translating the Plot
94 Redefining the Corners of the Plot
97 Plotting Equations
8
98
The Solver
98 Finding a Zero of an Expression
100 Finding a Minimum or Maximum
103 Time Value of Money
9 107 Symbolic Solutions
107
Finding the Zeros of a Quadratic Expression
109 Isolating a Variable
110 Expanding and Collecting
112
Using FORM
10 117 Calculus
117 Differentiating an Expression
118 Step-by-Step Differentiation
120
Complete Differentiation
120 Integrating an Expression
121 Symbolic Integration
of Polynomials
122 Numerical Integration of Expressions
Contents 7

11 124
Vectors and Matrices
124 Vectors
124 Keying In a Vector
125 Multiplying and Dividing a Vector by a Number
125 Adding and Subtracting Vectors
126 Finding the Cross Product
126 Finding the Dot Product
126 Matrices
127 Keying In a Matrix
127 Viewing a Large Matrix
128 Inverting a Matrix
128 Finding the Determinant
128 Multiplying Two Arrays
128 Multiplying Two Matrices
129 Multiplying a Matrix and a Vector
130 Solving a System of Linear Equations
12 131 Statistics
132
Entering Data
133 Editing Data
134 Single-Sample Statistics
134
Finding the Mean
135 Finding the Standard Deviation
135 Finding the Variance
135
Paired-Sample Statistics
136 Specifying a Pair of Columns
136 Finding the Correlation
136 Finding the Covariance
137 Finding the Linear Regression
137 Finding Predicted Values
13 138 Binary Arithmetic
138 Selecting the Wordsize
139 Selecting the Base
139 Entering Binary Integers
140 Calculating With Binary Integers
8 Contents

14
15
Part
16
17
141
141
143
144
146
147
149
149
150
151
152
152
Unit Conversion
The UNITS Catalog
Converting Units
Converting Unit Strings
Checking for the Correct Units
User
Functions for Unit Conversion
Printing
Printing the Display
Printing a Running Record
Printing Level 1
Printing the Stack
Printing a Variable
2: Summary of Calculator Features
154 Objects
155 Real Numbers
155 Complex Numbers
156 Binary Integers
156 Strings
157
Arrays
158 Lists
159 Names
160 Programs
161
Algebraics
161 Expressions
162 Equations
163 Symbolic Constants
164 Operations, Commands, and Functions
Contents 9

18 166 The Command Line
166 The Cursor Menu
168 Some Entry Keys
169
Object Delimiters and Separators
169
Entry Modes
171 Exceptions
171 Manual Selection of Entry Modes
172 How the Cursor Indicates Modes
173 Executing the Command Line
173 Editing Existing Objects
174 Recovering Command Lines
175 The Command Line as a String
19 176 The Stack
176 Review of Stack Concepts
177 Viewing the Stack
177 Manipulating the Stack
179 Local Variables
179 Recovering the Last Arguments
180 Restoring the Stack
181 The Stack as a List
20 182 Memory
182 User Memory
182 Global Variables
183 Directories
187 Recovery Features
188 Low Memory
190 Maximizing Performance
21 192 Menus
193 Menus of
Commands
194 Menus of Operations
194 Menus of Variables
195 Custom Menus
10 Contents

22 196
Catalog of Commands
197 Finding a Command
197 Checking Command Use
23 198
Evaluation
199
Data-Class Objects
199 Name-Class Objects
200
Evaluation of Local Names
200
Evaluation of Global Names
201
Procedure-Class Objects
201
Evaluation of Programs
202
Evaluation of Algebraics
203 Evaluation of Functions
24 205 Modes
205
General Modes
207 Entry and Display Modes
210 Recovery Modes
211 Mathematical Exceptions
212
Printing Modes
25 215
System Operations
216 Printing the Display
216
Contrast Control
216
Clearing Operations
216 Attention
217 System Halt
217
Memory Reset
Contents 11

218 Test Operations
218 Repeating Test
219 Keyboard Test
Part 3: Programming
26
222 Program Structures
222 Local-Variable Structure
223
Conditional Structures
226
IF ... THEN ... ELSE ... END
226 IFTE (If-Then-Else-End Function)
227 IF ... THEN ... END
227 1FT (If- Then-End Command)
227 Error Traps
228 Definite Loop Structures
228 START ... NEXT
229
FOR counter ... NEXT
230
... increment STEP
231
Indefinite Loop Structures
231 DO ... UNTIL ... END
232 WHILE ... REPEAT ... END
233
Nested Program Structures
27
234 Interactive Programs
234
Asking for Input
235
Asking for a Choice
235
A More Complicated Example
28 240 Programming Examples
241 Box Functions
241
BOXS (Surface of a Box)
244
BOXS Without Local Variables
245
BOXR (Ratio of Surface to Volume of a Box)
246
Fibonacci Numbers
247
FIBl (Fibonacci Numbers, Recursive Version)
248
FIB2 (Fibonacci Numbers, Loop Version)
249 Comparison of FIBl and FIB2
250
Single-Step Execution
12 Contents

253 Expanding and Collecting Completely
253 MULTI (Multiple Execution)
255 EXCO (Expand and Collect Completely)
257 Displaying a Binary Integer
257 PAD (Pad With Leading Spaces)
258 PRESERVE (Save and Restore Previous Status)
259 BDISP (Binary Display)
262 Summary Statistics
263 SUMS (Summary Statistics Matrix)
265 1;GET (Get an Element of 1;COV)
266 1;X2 (Sum of Squares of x)
266 1;Y2 (Sum of Squares of y)
267 1;XY (Sum of Products of x and y)
270 Median of Statistics Data
270 SORT (Sort a List)
272 LMED (Median of a List)
273 MEDIAN (Median of Statistics Data)
275 Changing Directories
276 UP (Move to a Parent Directory)
277 DOWN (Move to a Subdirectory)
Contents 13

Appendixes & Indexes
A
B
c
D
282
282
286
289
289
289
291
293
295
296
302
306
Assistance, Batteries, and Service
Answers to Common Questions
Batteries
Calculator
Maintenance
Environmental Limits
Determining If the Calculator Requires Service
Limited One-Year Warranty
If the Calculator Requires Service
Regulatory
Information
Notes for RPN Calculator Users
Notes for Algebraic Calculator Users
Menu Map
327 Key Index
332 Subject Index
14 Contents

How To Use This Manual
If you have the time and inclination, you can read this manual from
front to back, working every example.
If not, we recommend the fol-
lowing
approach for getting started.
1. Read the first five chapters in part 1, "Fundamentals," to get
comfortable with the calculator.
2. There are two appendixes that compare the HP-28S with other
styles of calculators.
• If you're familiar with other Hewlett-Packard calculators that
use RPN, read appendix B, "Notes for RPN Calculator Users,"
on page 296.
• If you're familiar with calculators that use a form of algebraic
entry,
read appendix C, "Notes for Algebraic Calculator Us-
ers," on page 302.
3. If you're interested in a topic covered later in part 1, you can
skip ahead and try the examples in that chapter.
What's in This Manual
Part 1, "Fundamentals," demonstrates how to work some simple prob-
lems. While solving these problems you'll learn the basics about HP-
28S operations, object types, and menus.
Part 2, "Summary of Calculator Features," builds on part 1. It provides
more detail about how to use the calculator, including options and
features not discussed in part 1. Using part 2, you can extend the
examples in part 1 to solve your own problems.
How to Use This Manual 15

Part 3, "Programming," describes the programming features of the
HP-28S. The last chapter, "Programming Examples," contains a series
of
short programs that demonstrate programming techniques.
For More Information
As you work the examples in this manual, you may have questions
about the features demonstrated or mentioned in the examples. Both
this
manual and the Reference Manual contain additional
information.
• If you have problems, see "Answers to Common Questions" on
page 282.
• For a brief description
of what each key does, see "Key Index" on
page 327.
• For a brief description
of the commands in each menu, see appen-
dix D, "Menu Map," on page 306.
• For
detailed information about a menu, look in the Reference Man-
ual. All menus (plus some additional topics) appear in alphabetical
order. The contents of the dictionary are listed on the back cover of
the Reference Manual.
• For detailed information about a particular command, look in the
"Operation Index" at the back of the Reference Manual. There
you'll find a reference to a dictionary entry (usually a menu) and a
page reference to the particular command.
16 How To Use This Manual

Fundamentals
Page 18
1: Getting Started
34 2: Doing Arithmetic
48 3: Using Variables
58 4: Repeating Calculations
73 5: Real-Number Functions
82 6: Complex-Number Functions
89 7: Plotting
98
8: The Solver
107 9: Symbolic Solutions
117 10: Calculus
124 11: Vectors and Matrices
131 12: Statistics
138
13: Binary Arithmetic
141 14: Unit Conversions
149
15: Printing

1
Getting Started
This chapter first describes the calculator's basic features, then dem-
onstrates a simple calculation. Next, an annotated illustration of the
keyboard highlights the major features of the keyboard and display.
Last, you'll
learn about the catalog of commands, which is a handy
guide to commands and how to use them.
Preliminaries
This section describes the calculator's basic features.
Opening and Closing the Case
The calculator forms its own case, opening and closing like a book. To
open the calculator, hold it with the hinge away from you and open it
with your thumbs.
18 1: Getting Started

To close the calculator, fold the two sides together and press until you
hear a click.
You can fold back the left-hand side of the caI,.::ulator until it is back-
to-back
with the right-hand keyboard. This is handy for field work-
when you want to hold the calculator in one hand and operate it with
the other-or to save space on a desk.
Locating the Battery Door and Printer Port
With the calculator open, note the location of the battery door and the
printer port.
;+--..;- Printer port
~~.;....-----.;- Battery door
The HP-28S is powered by three N-cell alkaline batteries. Batteries
are
included with the calculator. If the batteries are not already in-
stalled, follow
the instructions that start on page 286.
1: Getting Started 19