HP-15C
Owner’s Handbook
Legal Notice
Introduction
Contents
Part I: HP-15CFundamentals
Section 5: The Display and Continuous Memory
Part II: HP-15CProgramming
Section 6: Programming Basics
Section 6: Programming Basics
Section 7: Program Editing
Section 8: Program Branching and Controls
Section 9: Subroutines
Part III: HP-15CAdvanced Functions
Section 14: Numerical Integration
Appendix A: Error Conditions
Appendix C: Memory Allocation
Appendix D: A Detailed Look at
Appendix E: A Detailed Look at f
Appendix F: Batteries
Function Summary and Index
Programming Summary and Index
Subject Index
The HP-15C:
A Problem Solver
To Compute
Keystrokes
Display
531,441.0000
Example:
Writing the Program
Loading the Program
KeystrokesDisplay
001-42,21,11
PRGM
Running the Program
Page
Page
Getting Started
"^ • G f > i O m ´ | P I l F T s ? t H b
´ CLEAR u
CLEAR u
(change sign)
Keying in Exponents
The “CLEAR” Keys
Clearing Sequence
Effect
Display Clearing: `and −
12,345
1,234
912,349
Keystrokes Display
Two-NumberFunctions and
Terminating Digit Entry
Chain Calculations
[(5.4 × 0.8) ÷ (12.5 − 0.72 )]
Numeric Functions
|K“|‘
General Functions
Reciprocal
Factorial and Gamma
Square Root
Trigonometric Operations
Trigonometric Modes
RAD
GRAD
Trigonometric Functions
Degrees/Radians Conversions
Logarithmic Functions
Natural Logarithm
Natural Antilogarithm
Common Logarithm
Common Antilogarithm
The Power Function
To Calculate
Percentages
Percent
30 Section 2: Numeric Functions
For example, to find the sales tax at 3% and total cost of a $15.76 item:
Enters the base number (the price)
3 |k
Calculates 3% of $15.76 (the tax)
Rectangular Conversion
The Automatic Memory Stack
LAST X, and Data Storage
Stack Lift
No Stack Lift or Drop
Stack Drop
x + y
Page
The LAST X Register and K
before execution of a numeric operation
(LAST X)
12.9 +
Oops! The wrong divisor
36 Section 3: The Memory Stack, LAST X, and Data Storage
*287.0000 Reverses the function that produced the wrong answer
13.9 +
The correct answer
Calculator Functions and the Stack
Order of Entry and the vKey
Nested Calculations
Arithmetic Calculations With Constants
LAST
Page
Loading the Stack with a Constant
1,000
42 Section 3: The Memory Stack, LAST X, and Data Storage
*1,150.0000 Population at the end of day
1,322.5000
Day
1,520.8750
Turn the calculator off. Next day, turn it back on again
For storage arithmetic
Recall Arithmetic
For recall arithmetic
x
8.33(4 − 5.2) ÷ [(8.33 − 7.46)0.32]
4.3 (3.15 − 2.75) − (1.71)(2.01)
Page
Statistics Functions
48 Section 4: Statistics Functions
How many different four-cardhands can be dealt from a deck of 52 cards
Fifty-two(y) cards dealt four
(x) at a time
270,725.0000
statistics
registers
Register
Contents
1,415.00
-value
drops to four
52 Section 4: Statistics Functions
Correcting Accumulated Statistics
x, y
Mean
Example:
Average kg of nitrogen, x, for all cases
®6.40 Average tons of rice, y, for all cases
Standard Deviation
Linear Regression
Linear Estimation and Correlation Coefficient
Linear Estimation
Correlation Coefficient
The
The Display
and Continuous Memory
Scientific Notation Display
(scientific)
undisplayed
With the previous number still in the display:
´i6
Mantissa Display
Round-OffError
Annunciators
Digit Separators
12,345.67
12,345.6700
Error Display
Overflow
Low-PowerIndication
Status
Resetting Continuous Memory
Page
Page
Programming Basics
Location in Program Memory
Program Begin
Recording a Program
one
Executing a Program
running
300.51300.51 ´A
Restarting a Program
User Mode
Direct entry
Program Memory
Example
Radius, r
Height, h
Base Area
Volume
Surface Area
007-44,40,1
011-44,40
019–
020–44,40,3
021– 43
¦254.4690
Program Instructions
Instruction Coding
Instruction
Code
Keycode 25: second row, fifth key
Memory Configuration
76 Section 6: Programming Basics
60 ´m%
R60 and below allocated to data
storage; five (R61 to R65) remain
for programming
1 ´m%
19 ´m%
lm%
Displays the current highest data register
The m and W (memory status) functions are described in detail in appendix C
Unexpected Program Stops
Pressing Any Key
Error Stops
Abbreviated Key Sequences
User Mode
USER
Polynomial Expressions and Horner's Method
001-42,21,12
12,691.0000
Nonprogrammable Functions
Page
Program Editing
The Back Step
Instruction
Deleting Program Lines
Inserting Program Lines
Deletions:
84 Section 7: Program Editing
Program mode. (Assumes
position is at line 000.)
t“020
020-44,40,3
011-44,40,2
007-44,40
Single-StepOperations
Single-Step
Program Execution
001−42,21,11
Â002− 44 0 t0
2.5000 Result
003−
004−
Insertions and Deletions
Initializing Calculator Status
´b.1 001-42,21,.1
002-42,7
Interest
Page
Program Branching
and Controls
conditional test
Tn
1.Direct: |£and |
2.Indirect: |Tn
Test
Page
Example: Branching and Looping
010-45,20,1
013-43,30,9
016-44,40,0
Example: Flags
002-43,5
004-42,21,15
005-43,4
006-42,21
016-45,10,1
10,698.3049
(Repeat stack entries.)
10,645.0795
Set to Run mode. Monthly payment
Payment periods (4 years × 12 months)
Looping
Conditional Branching
Tests
The System Flags: Flags 8 and
Flag
Page
Subroutines
Subroutine Limits
MAIN PROGRAM
001- ´b9
002- |R
003- O0
004- ®
xample: Nesting
The Subroutine Return
Nested Subroutines
The Index Register
and Loop Control
Direct Versus Indirect Data Storage With the Index Register
Indirect Program Control With the Index Register
Program Loop Control
Index Register Storage and Recall
Direct
Indirect
Index Register Arithmetic
Exchanging the X-Register
Indirect Branching With
To Labels
To Line numbers
Indirect Flag Control With
Indirect Display Format Control With
Loop Control With Counters: Iand e
nnnnnx x x y y
Start count at zero
Count by twos
Count up to
nnnnn
For
Iterations
Examples: Register Operations
Storing and Recalling
Exchanging the X-Register
Storage Register Arithmetic
Example: Loop Control with e
−−011- 42
012-42,5
15 “ O
Example: Display Format Control
Value in R
value in display
To display fixed point notation for all possible decimal places on the HP-15C:
´B 9.000000000 8.00000000 7.0000000 6.000000 5.00000 4.0000 3.000 2.00
Display at ´©instruction
Display when program halts
Index Register Contents
116 Section 10: The Index Register and Loop Control
Iand e
must be specified as a
cannot be zero
the value for
Page
Page
Page
Calculating With
Complex Numbers
real
RAD
GRAD
Deactivating Complex Mode
Entering Complex Numbers
Page
Page
Stack Lift in Complex Mode
Manipulating the Real and Imaginary Stacks
real exchange imaginary
Clearing a Complex Number
Clearing the Real
X-Register
Clearing the Imaginary
Entering Complex Numbers with −. The clearing functions − and
(−)(0.0000)
Entering a Real Number
Entering a Pure Imaginary Number
130 Section 11: Calculating With Complex Numbers
Storing and Recalling Complex Numbers
X-register
only;
a + ib
¤xNo∕@'a:;
Two-NumberFunctions
+-*÷y
®) ( v K
Example: Complex Arithmetic
Complex Results from Real Numbers
and without disturbing the stack contents
normally would result in an Error 0. complex value arc sin 2.404 can be
|F8
´% (hold)
Page
+3.1434 |:
Page
Page
Calculating With Matrices
´>12.0000
1,1
X = A-1B
running
C –
C 1,1
Dimensioning a Matrix
´ m
Key the number of rows
2.Key the number of columns (x) into the X-register
3.Press ´ m followed by a letter key, A through E
Displaying Matrix Dimensions
Keystrokes l>B
Changing Matrix Dimensions
Storing and Recalling All Elements in Order
null
A 1,1
Checking and Changing Matrix Elements Individually
Using R
and R
2,3
Using the Stack
Storing a Number in All Elements of a Matrix
Matrix Descriptors
148 Section 12: Calculating with Matrices
LU factorization
The Result Matrix
result matrix
maximum
Copying a Matrix
One-MatrixOperations
150 Section 12: Calculating with Matrices
One-MatrixOperations:
Sign Change, Inverse, Transpose, Norms, Determinant
Result in
Effect on Matrix
Scalar Operations
Elements of Result Matrix
Operation
Matrix in Y-Register
Scalar in Y-Register
Scalar in X-Register
Arithmetic Operations
Calculates
Y +
Y
C = B - A
154 Section 12: Calculating with Matrices
Calculates B - A and stores
values in redimensioned result
The result is
Matrix Multiplication
C = AT B
Keystrokes Display l> A A
17⎦
156 Section 12: Calculating with Matrices
Solving the Equation AX = B
The ÷function is useful for solving
matrix equations of the form AX = B
where A is the coefficient matrix, B is
Week
Total Weight (kg)
Total Value
Solution:
AD = B
158 Section 12: Calculating with Matrices
274OB
233OB
331OB 120.32 OB 112.96 OB 151.36 OB ´<Á
Stores b11
Cabbage (kg)
Broccoli (kg)
Calculating the Residual
R–YX
B – AC
Using Matrices in LU Form
then Z can be represented in the calculator by
Into
⎡4 +
Z = ⎢
⎣1 +
The Complex Transformations Between ZP and Z
Inverting a Complex Matrix
Multiplying Complex Matrices
Keystrokes l>A l>B
C4 C 1,1
–2.8500 –10
–4.0000 –111.0000 1.0000 –113.8000 –101.0000 –11
–1.0500 –10
Solving the Complex Equation AX = B
AX = B
–200.0000
Transforms AP into Ã
Designates matrix C as
Calculates XP and stores
in C
Transforms XP into XC
Page
Using a Matrix Element With Register Operations
O*l
O{+, -, *, ÷} l{+, -, *, ÷}
Using Matrix Descriptors in the Index Register
If the Index register contains a matrix descriptor:
Conditional Tests on Matrix Descriptors
Page
Page
Results
Page
Keystroke(s) Results
Finding the Roots
of an Equation
Page
182 Section 13: Finding the Roots of an Equation
´b0
001–42,21,0
Begin with binstruction
Subroutine assumes stack
–10
–2.0000
G G r
Keystrokes |¥
000–
001–42,21,11
009–
010–
011–
012–
013–
001–42,21,1
Page
Page
001–42,21,3
Page
Page
Page
Page
Numerical Integration
|¥ 000–
Page
001-42,21,1
Page
Find Si(2)
Key in the following subroutine to evaluate the function f(x) = (sin x) / x
´b.2
001–42,21
Begin subroutine with a b
200 Section 14: Numerical Integration
no more
You'll recall that the HP-15Cprovides three types of display formatting:
´ • V
i V
approximates
´i2
3.1400 Set display format to
1.300 Integral approximated in
® 1.8 - Uncertainty of
202 Section 14: Numerical Integration
Set display format to
Roll down stack until upper
limit appears in X-register
Integral approximated in
´CLEAR u
Page
Error Conditions
Error 1: Improper Matrix Operation
Error 2: Improper Statistics Operation
Error 3: Improper Register Number or Matrix Element
Error 4: Improper Line Number or Label Call
Error 5: Subroutine Level Too Deep
Error 6: Improper Flag Number
Error 7: Recursive _or f
Pr Error (Power Error)
Pr Error
Stack Lift and
the LAST X Register
Disabling Operations
Stack Lift
Imaginary
Enabling Operations
Appendix B: Stack Lift and the LAST X Register
Stack
enabled
when the next number is keyed or recalled into the display
Neutral Operations
212 Appendix B: Stack Lift and the LAST X Register
The following operations save x in the LAST X register:
-x H\ k
+[ H] ∆
*\ h :
Memory Allocation
Total allocatable memory:
Memory Status (W)
To view the current memory configuration of the calculator, press |
W(memory), holding W to retain the display.* The display will be four numbers
dduu pp-b
dd= the number of the highest-numbered register in the data storage
216 Appendix C: Memory Allocation
Place
, the
available for programming) will be (65 –
2.Press ´m%
Automatic Program Memory Reallocation
Two-ByteProgram Instructions
Function
Registers Needed
´ V, ´ }
"8 is executed
until you dimension it
A Detailed Look at
Page
Page
Page
001–42,21,12
010–43,30,7
012–43,30,0
226 Appendix D: A Detailed Look at
Execute _again:
´vB
Value of modified f(t) at root
Page
001–42,21,2
019–42,21,9
022–
1,000.0000
Page
´b.0 001–42,21,.0
10.0000 Error 8 455.335 48,026,721.85 1.0000 455.4335 Error 8 48,026,721.85
1.0000 Error 8 2.1213 2.1471 0.3788 2.1213 Error 8 2.1213
1.0000 –20
´_.0
–20
–16
Another x-value.Previous value. Same function value
x = a
001-42,21,2
023–
024–
025–
026–
027–
028–
029–
030–
031–
032–
–208.4999
–1.0929 –07
035–
037–
038–
Page
Counting Iterations
Specifying a Tolerance
A Detailed Look at f
by just one
Page
Keystrokes ´i3
–03
7.786 –03
1.448 –04
Page
Page
–04
=0.5×10−n+m( x)
relative
absolute
Page
Page
Page
001-42,21
“002- 1
Page
Page
Page
Page
Page
Page
Page
Batteries
Page
1.L 2.C 3.H
Function Summary and Index
(page 19)
(page 22)
Display Control
(page 58)
(page 59)
(page 19)
Hyperbolic
(page 28)
Index Register
Control
(page 29)
Mathematics
(page 25)
(page 24)
(page 180)
152-155)
(pages 152- 155)
to ZP (page164)
to XT (page 150)
X (page 154)
Percentage
Probability
(page 47)
Stack
Manipulation
(page 21)
(page21)
Statistics
(page 49)
(page 52)
Trigonometry
26)
(page 26)
26)
(page 26)
Programming Summary and Index
(page 101)
(page 68)
G(page 101)
(page 92)
(page 91)
Subject Index
Page
D
E
F
G
H
I
K
L
M
Page
N
O
P
66
Q
R
184-186
S
Page
T
U
V
W
X
Y
Z
Product Regulatory &
Environment Information
Canadian Notice
Avis Canadien
European Union Regulatory Notice
Japanese Notice
Korean Notice
Chemical Substances
Perchlorate Material - special handling may apply