HP HP-20S User manual

Scientific Calculator
Owner’s Manual
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. Separates two numbers.
. Executes a program.
. Activates blue-labeled keys.
. Activates yellow-labeled keys.
. On; clears display, cancels
operation.
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11. A through F keys for labels, built-
in programs, hexadecimal digits.
12. Annunciator Line.

HP-20S Scientific Calculator
Owner’s Manual
fi HEWLETT
PACKARD
Edition 5 August 1992
Part Number 00020-90001
@ The contents of this manual are printed on recycled paper.

Notice
For warranty and regulatory information for this calculator, see pages 117
and 120.
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 keystroke programs
contained herein.
o Hewlett-Packard Co. 1988. All rights reserved. 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.
Corvallis Division
1000 N.E. Circle Blvd.
Corvallis, OR 97330, U.S.A.
Printing History
Edition 1 April 1988
Edition 2 September 1988
Edition 3 June 1989
Edition 4 August 1991
Edition 5§ August 1992

Welcome to the HP-20S
Your HP-20S is another example of the superior quality and attention
to detail in engineering and manufacturing that have marked
Hewlett-Packard products for more than 40 years. Hewlett-Packard
stands behind this calculator. We offer worldwide service and exper-
tise to support its use.
Hewlett-Packard Quality
Our calculators are made to excel, to last, and to be easy to use.
B This calculator is designed to withstand the drops, vibrations, pol-
lutants (smog, ozone), temperature extremes, and humidity
variations that it can be exposed to in everyday worklife.
B The calculator and its manual have been designed and tested for
ease of use. We added examples to the manual to highlight the var-
ied uses of this calculator.
B Advanced materials and permanent, molded-in key lettering pro-
vide a long keyboard life and a positive feel to the keyboard.
B CMOS (low-power) electronics and the liquid-crystal display allow
data to be retained even when the calculator is off and let the bat-
teries last a long time.
® The microprocessor has been optimized for fast and reliable com-
putations using 15 digits internally for precise results.
B Extensive research has created a design that has minimized the ad-
verse effects of static electricity (a potential cause of malfunctions
and data loss in calculators).
Welcome to the HP-20S 3

Features
4
Large 12-character display.
Ten data registers and 99 program lines.
One- and two-variable statistics with linear regression.
Probability functions.
Unit and base conversions.
Polar /rectangular conversions.
Hyperbolic functions.
Accurate math, 12-digits with a 10%%% exponent range.
Keystroke programming.
Six built-in programs:
Root finder.
Numerical integration.
Complex number operations.
=
n
u
® 3 X 3 matrix solutions.
® Quadratic equation.
u
Curve fitting.
Welcome to the HP-20S

Contents
1 9 Getting Started
9 Power On and Off
9 Adjusting the Display Contrast
9 Simple Arithmetic Calculations
12 Understanding the Display and Keyboard
12 The Cursor
12 Clearing the Calculator
12 Clearing Memory
13 Annunciators
14 The Shift Keys
14 The INPUT Key
14 The SWAP Key
15 The Alpha Keys
15 Introducing the Math Functions
16 Display Format of Numbers
17 Specifying the Number of Displayed Decimal
Places (FIX)
17 Displaying the Full Precision of Numbers
(ALL)
18 Scientific and Engineering Notation
19 Interchanging the Period and Comma
20 Full Precision of a Number (SHOW)
20 Range of Numbers
21 Messages
2 22 Arithmetic and Storage Registers
22 Chain Calculations
22 Operator Priority and Pending Operations
24 Using Parentheses
25 Reusing the Previous Result (LAST)
26 Exchanging Two Numbers (SWAP)
27 Using Storage Registers
Contents 5

Numeric Functions
30 General and Logarithmic Functions
31 Reciprocal
32 Percent Functions
32 Percent
33 Percent Change
34 Pi ()
34 Trigonometric Modes and Functions
34 Changing the Trigonometric Mode
35 Trigonometric Functions
36 Angle and Hour Conversions
38 Coordinate Conversions
39 Probability Functions
40 Hyperbolic Functions
41 Parts of Numbers
42 Unit Conversions
4 44 Base Conversions and Base Arithmetic
44 Switching Bases
47 Representation of Numbers
47 Range of Hexadecimal, Octal, and Binary Numbers
49 Arithmetic Operations
S 51 Statistical Calculations
51 Entering Statistical Data
53 Clearing Statistical Data
53 Summary of Statistical Calculations
54 Mean, Standard Deviation, and Summation
Statistics
55 Calculating the Population Standard Deviation
57 Linear Regression and Estimation
59 Weighted Mean
60 Statistical Formulas
6 Contents

61 Programming
64 Creating Programs
66 Program Boundaries (LBL and RTN)
67 Entering Programs
68 Positioning the Program Pointer
69 Running Programs
69 Starting Programs With XEQ
70 Starting Programs With GTO and R/S
70 Stopping Programs
71 Clearing Programs
71 Editing Programs
72 Stepping Through Programs
73 Sample Program: Pythagorean Theorem
75 Sample Program: Random Number Generator
76 Subroutines
80 Branching and Conditionals
80 Branching (GTO)
81 Conditional Instructions—Decisions and
Control
85 Keystrokes for Other Conditionals
87 Available Program Memory
87 Nonprogrammable Functions
88 Built-in Program Library
89 Root Finder (root)
91 Numerical Integration (int)
94 Complex Operations (CPL)
97 3 X 3 Matrix Operations (3 bY 3)
102 Quadratic Equation (qQUAd)
105 Curve Fitting (Fit)
Contents
7

Appendix
109 Assistance, Batteries, Memory, and Service
109 Obtaining Help in Operating the Calculator
109 Answers to Common Questions
111 Power and Batteries
111 Low Power Annunciator ]
111 Installing Batteries
113 Resetting the Calculator
114 Erasing Continuous Memory
114 Environmental Limits
114 Determining if the Calculator Requires Service
116 Confirming Calculator Operation—the Self-Test
117 Limited One-Year Warranty
117 What is Covered
117 What is Not Covered
118 Consumer Transactions in the United Kingdom
118 If the Calculator Requires Service
118 Obtaining Service
119 Service Charge
119 Shipping Instructions
120 Warranty on Service
120 Service Agreements
120 Regulatory Information
122 Messages
124 Index
Contents

Getting Started
Power On and Off
To turn on your HP-20S, press (the key above the
“ON” label). To turn the calculator off, press either shift
key ([(#) or (¢*]), then (also written (=] or [¢~]
[OFF]).
Since the calculator has Continuous Memory, turning it off does not affect
the information you’ve stored. To conserve energy, the calculator turns itself
off approximately 10 minutes after you stop using it. The calculator’s three
alkaline batteries last approximately a year. If you see the low-battery
symbol (:3) in the display, replace the batteries as soon as possible.
Refer to the appendix for more information.
Adjusting the Display Contrast
To change the display contrast, hold down and press or [-].
Simple Arithmetic Calculations
If you make a typing mistake while entering a number, press (4] to
erase the incorrect digits.
1: Getting Started 9

Arithmetic Operators. The following examples demonstrate using
the arithmetic operators [(+], (-], (x], (+], and (exponentiation)*.
Keys: Display: Description:
24.715 62.471 (=] 87.1860 Adds 24.715 and
62.471.
When a calculation has been completed (by pressing (=]), pressing a
number key starts a new calculation:
19 12.68 (=] 240.9200 Calculates 19 x 12.68.
is the exponentiation operator:
4.7 3(=) 103.8230 Calculates 4.75.
If you press an operator key after completing a calculation, the cal-
culation is continued:
115.5 115.5_ Continues the
calculation.
(=) 219.3230 Completes the calcula-
tion of 4.73 + 115.5.
You can do chain calculations without using (=] after each step. Calcu-
late 6.9 X 5.35 + 0.918:
6.9 5.35 [+] 36.9150 Pressing [+] displays
the intermediate an-
swer, showing result of
6.9 X 5.35.
918 0.918_ Continues the
calculation.
(=) 40.2124 Completes the
calculation.
*If you press more than one operator, for example (+][=] (+], all are ignored except
the last one.
10 1: Getting Started

Chain calculations are interpreted according to the priority of the op-
erators in the expression. Calculate 4 + (9 X 3):
4[+)9 [
3 (=)
9.0000
31.0000
The addition is de-
layed; has higher
priority than [+].
Calculates
4 + (9 x 3).
Negative Numbers. Enter the number and press [¥].
Calculate —75 + 3:
Keys:
75
=3 (=)
Calculate 0.4 — ¢ 1.1;
4511 B0
(=)
Display:
—75_
—25.0000
—-1.1_
0.3329
0.0671
Description:
Changes the sign of
75.
Calculates the result.
Calculates e~ 11,
Completes the
calculation.
1: Getting Started 11

Understanding the Display and Keyboard
The Cursor
The cursor (—) is visible when you are in the process of entering a
number.
Clearing the Calculator
When the cursor is on, (] erases the last digit you entered. While you are
entering a number, pressing clears it to 0. Otherwise, clears the
display of its current contents and cancels the current calculation.
While you are entering a number, pressing clears it to 0. Other-
wise, clears the display of its current contents and cancels the
current calculation.
Clearing Messages. (¢] and also clear messages. When the
HP-20S is displaying an error message, (4] or clears the message
and restores the original contents of the display.
Clearing Memory
To clear portions of memory:
Keys Description
(H) Clears registers Rg through Rg.
(] Clears statistical registers R4 through Rg.
(] [CLPRGM Clears programs when in Program mode.
12 1: Getting Started

To clear all memory and reset the calculator, press and hold down
(C], then press and hold down both and [Z+]. When you release
them, all memory is cleared. The ALL CLr message is displayed.
Annunciators
Annunciators are symbols in the display that indicate the status of the
calculator.
Annunciator Status
(H) Left shift is active. When you press a key, the function la-
beled in blue above the key is executed (page 14).
(~] Right shift is active. When you press a key, the function
labeled in yellow above the key is executed (page 14).
has been pressed, or two values have been en-
tered or returned (page 14).
PEND An arithmetic operation is pending in addition to what
shows in the display.
1 Battery power is low (page 9).
GRAD The calculator is in Grads mode for trigonometric calcula-
tions (page 35).
RAD The calculator is in Radians mode for trigonometric cal-
culations (page 35).
HEX The calculator is in Hexadecimal mode (page 44).
OCT The calculator is in Octal mode (page 44).
BIN The calculator is in Binary mode (page 44).
PRGM The calculator is in Program mode. (Refer to chapters 6
and 7.)
1: Getting Started 13

The Shift Keys
Most keys have blue or yellow functions printed above the key. The
shift keys access these labeled operations: the blue shift key executes
a blue labeled operation; the yellow shift key executes a yellow la-
beled operation. To perform a shifted operation, press (5] or (] to
turn on the shift annunciator ([%) or (¢>]). Then, press the key that
has the desired label above it.
For example, pressing [4] followed by (also written [q][HEX]) puts
the calculator in Hexadecimal mode. Pressing (4] puts the
calculator in Decimal mode.
To perform consecutive shifted operations, hold down the shift key.
If you accidentally press (] or [¢>], just press it again to turn off the
shift annunciator. If you press the wrong shift key, press the other
one to cancel it and display the correct one.
The INPUT Key
The key is used to separate two numbers when using two-
number functions or two-variable statistics.
The : annunciator is displayed if has been pressed. If a number
is in the display, press to erase the : annunciator and the display.
If the cursor or an error message is visible in the display, press
twice to erase the : annunciator.
The SWAP Key
Pressing [(#y] [SWAP] exchanges:
14 1: Getting Started

® The last two numbers that you entered; for instance, the order of
division or subtraction.
B The results of functions that return two values. The : annunciator
indicates that two results have been returned; press (%] to
see the hidden result.
® The x- and y-values when using statistics.
The Alpha Keys
The A, B, C, D, E, and F labels have several functions. They are used
as program labels and as digits in Hexadecimal mode.
Introducing the Math Functions
One-Number Functions. Math functions involving one
number use the number in the display:
Keys: Display: Description:
89.25 9.4472 Calculates 1/89.25 .
3.57 2.36 0.4237 1/2.36 is calculated
first.
(=] 3.9937 Adds 3.57 and 1/2.36.
180 (] 70.8661 Converts 180 centi-
meters to inches.
1: Getting Started 15

Two-Number Functions. When a function requires two numbers,
the numbers are entered like this: numberl number2. Pressing
evaluates the current expression and displays :. For example,
the following keystrokes calculate the percent change between 17 and
29:
Keys: Display: Description:
17 17.0000 Enters numberl, dis-
plays : annunciator.
29 29 Enters number?2.
(«) 70.5882 Calculates the percent
change.
Calculate the number of combinations of four items taken two at a
time:
4 2 (] 6.0000 Calculates number of
combinations.
If you enter numberl, then press a two-number function key without
pressing (INPUT], the calculator supplies a zero as number2. If you enter a
number, press (INPUT], and then press a two-number function key, the cal-
culator uses the same number for both numberl and number2.
Display Format of Numbers
When you turn on the HP-20S for the first time, numbers are displayed
with four decimal places and a period as the decimal point. The display
format controls how many digits appear in the display.
16 1: Getting Started

Regardless of the current display format, each number is stored as a
signed, 12-digit mantissa with a signed, three-digit exponent. For ex-
ample, pressing [>][x]in FIX 4 (four decimal places) displays 3.1416.
Internally, the number is stored as 3.14159265359 x 10900,
If the result of a calculation is a number containing more significant
digits than can be displayed in the current display format, the dis-
played number is rounded to fit.
Specifying the Number of Displayed Decimal Places
(FIX)
To specify the number of displayed decimal places:
1. Press [¢] [FIX].
2. Enter the number of digits (0 through 9) that you wish
to appear after the decimal point.
Keys: Display: Description:
(«] 3 0.000 Displays three decimal
places.
45.6 [x] .1256 (=) 5.727
(A) 9 5.727360000 Displays nine decimal
places.
(«] 4 5.7274 Restores four decimal
places.
When a number is too large or too small to be displayed in FIX for-
mat, it is automatically displayed in scientific notation.
Displaying the Full Precision of Numbers (ALL)
To set your calculator to display numbers as precisely as
possible, press [>][ALL]. Trailing zeros are not displayed.
1: Getting Started 17

Scientific and Engineering Notation
Scientific and engineering notation express the number as
a mantissa multiplied by a power of 10. The letter E sepa-
rates the exponent from the mantissa.
Scientific Notation (SCI). Scientific notation uses a mantissa with
one digit to the left of the decimal point. For example, this is SCI 6:
Digits after Sign of
decimal point exponent Power of 10
/A/
—1.234567E
-5
e
Sign Mantissa
of
mantissa
To specify scientific notation:
1. Press [¢>] (SCl].
2. Enter the number of digits that you wish to appear after the dec-
imal point.
Engineering Notation (ENG). Engineering notation expresses a
number as a mantissa with one, two, or three digits to the left of the
decimal point, multiplied by 10 raised to a power that is a multiple of
3. For example, this is ENG 4:
Significant
digits after Sign of Power of 10
first digit exponent (multiples of 3)
~
—12.345E—12
—’
Sign Mantissa
of
mantissa
18 1: Getting Started