Quasar HHC User manual

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Copyright © 1982 by Matsushita Electric Industrial Co., Ltd.
All Rights Reserved. HHCTM is a Trademark of Matsushita
Electric Industrial Co., Ltd.
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TABLE OF CONTENTS
SECTION 1. INTRODUCTION TO THE
SCIENTIFIC CALCULATOR
SCIENTIFIC CALCULATOR FEATURES .......... 1·1
REQUIREMENTS FOR OPERATION ............. 1·2
HOW TO USE THIS MANUAL ................... 1·2
SECTION 2. GETTING STARTED
GETTING SET UP ............................. 2-1
BECOMING ACQUAINTED WITH THE STACK . , ... 2·1
INPUTTING NUMBERS ........................ 2·3
CONTROLLING THE OUTPUT FORMAT
.......... 2·5
USING MEMORY
............................. 2·6
ERRORS
AND WARNINGS ..................... 2-7
SECTION 3. USING THE
OPERATION KEYS
CONTROLOPERATIONS ....................... 3·1
Memory Control ............................ 3·1
Stack Control .............................. 3·3
OPERATIONAL
CONTROL ..................... 3·5
Inputting Numbers ......................... 3-7
ELEMENTARY OPERATIONS
.................. 3-7
MATHEMATICAL FUNCTIONS ................ 3-10
Trigometric, Inverse Trigometric, Hyperbolic,
Inverse Hyperbolic ....................... 3-10
Power,
Logarithm, and Root Functions ....... 3-11
STATISTICAL FUNCTIONS ................... 3-12
PROGRAMMABLE KEYS
..................... 3-13
SECTION 4. PROBLEM·SOLVING
EXAMPLES
TRIGONOMETRIC FUNCTIONS ................ 4-1
LOGARITHMIC FUNCTIONS ................... 4-2
ENGINEERING FUNCTIONS
................... 4-3
FIX and FRAC
............................. 4·3
Modulo (y mod x) ........................... 4-4
Degrees/Radians
........................... 4·5
Percentages and ConVersion Factors .......... 4-6
Factorials ................................. 4-6
4;-

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ST ATISTICAL FUNCTIONS .................... 4-7
Summations ............................... 4-7
Arithmetic Mean ..................... . .... 4-9
Harmonic Mean ............................ 4-9
Standard Deviation ........................ 4·10
Means and Sums of Squares ................ 4·11
An Investment Problem .................... 4·14
SECTION 5. FLOATING·POINT NUMBERS
AND ALGORITHMS
FLOATING·POINT NUMBERS AND ALGORITHMS. 5-1
MATHEMATICAL FUNCTIONS ................. 5·3
GENERATION OF RANDOM DEViATES
.......... 5·3
Uniform Psedo-random Deviates .............. 5·3
Normal Psedo·random Deviates .......... . .. 5-4
SECTION 6. MACHINE PARAMETERS
SECTION
7. OPERA nON KEY
PARAMETERS
GENERALINFORMATION ..................... 7·1
SyMBOLS ................................... 7·2
FLOATING·POINT ERRORS
.................... 7·2
ARITHMETIC FUNCTIONS
..................... 7·3
TRIGONOMETRIC FUNCTIONS
................ 7·3
HYPERBOLIC FUNCTIONS . .
................ 7·5
LOGARITHMS AND EXPONENTIALS
............ 7·6
ROOTS AN D POWERS
........................ 7·7
RANDOM NUMBER GENERATORS
............. 7·8
ADDITIONAL FUNCTIONS
..................... 7·9
MEMORY REGISTER HANDLING
.............. 7-10
STACK MANIPULATION AND CONTROL ........ 7·10
CONSTANTS
............................... 7-12
OPERATIONALCONTROL
.................... 7·12
INPUT AND EDITING
......................... 7·13
PROGRAMMING KEYS
....................... 7·13
SECTION 8. ERROR MESSAGES
SECTION 9.
HHC AND SCIENTIFIC
CALCULATOR SYMBOLS
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APPENDIX A. REFERENCES
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APPENDiX B. USING PERIPHERALS
,i) THE SCIENTIFIC CALCULATOR
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APPENDIX C. USING
THE SCIENTIFIC
CALCULATOR AS A LIBRARY CAPSU
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FOR OTHER PROGRAMS
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APPENDIX
D. HHC OVERLAY
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SECTION 1. INTRODUCTION TO
THE SCIENTIFIC CALCULATOR
The Scientific Calculator capsule satisfies a broad spectrum
of needs from hand calculations requiring extreme ver-
satility and accuracy to the support, as a function library, for
programs you
may write using other HHC capsules.
SCIENTiFIC CALCULATOR FEATURES
The Scientific Calculator is a read-only-memory (ROM) cap-
sule containing 4096 bytes of program for the HHC. It pro-
vides a set of abilities based on
an arithmetic architecture
that previously was available only in much larger and more
costly computing systems.
• A complete floating-point arithmetic system for numbers
from 101024 to +101024, It includes the basic operations
add, subtract, multiply, and divide as well as the math-
ematical functions listed below. A minimum of ten deci-
mal digits of accuracy is maintained, with most
calculations achieving twelve digits.
III A complete set of mathematical functions built upon this
floating-point system that provides accurate approxima-
tions and precise error control: sine/cosine/tangent/co-
tangent, arcsine/arccosine/arctangentlarctangent
(y/x) ,
logarithm and exponentiation for three bases (2, e, 10),
the hyperbolics sinh/coshl tanh/arctanh, and four ver-
sions of the power function
(XY, yx, nth root, and square
as well as Ix
I, x2, and 1Ix.
til Optional standard or scientific notation for input and out-
put. Either kind of input is always allowed. However, for
large numbers (Le., IxI> 105
), outputis always in scientif-
ic notation, which allows entry, display, and calculation of
numbers in the full range of
-10
1024 to
+10
1024•
Ii User-selectable memory for saving intermediate results
and frequently used constants.
$ Completeerrorcontrol, with error messages displayed on
HHC.
@ The ability to function as a library for use by other HHC
programs.
1,,1

I» Innut/oLJtnut ability that allows selection of printer or dis-
recording calculations.
• Continuous memory that allows the retention of results
for latercalculations. Memory is lost, however, when you
go out of the calculator to use another HHC application.
II) Three HHC user-definable function keys that allow you to
program sequences of up to 15 keystrokes on each that
will execute when the programmed key is pressed.
This manual will guide both the casual user who needs the
calculatoroccasionally and the userwho needs to define the
preciseness
of results in some larger calculations. Full infor-
is given
in Sections 6 through 8 on the accuracy of
calculations performed by this capsule.
REQUIREMENTS FOR OPERATION
The capsule requires 96 free bytes of HHC internal RAM. If
the
1/0 menu shows less than this amount, you must delete
a file or detach a peripheral before entering the calculator
program.
HOW TO USE THIS MANUAL
Read Section 2to becomefamiliar with the keyboard and the
stack concept. Section 3 gives you an explanation of how
each key functions. Later you will want to examine Section
4, which leads you through examples of varying complexity.
Section 5 explains the algorithms used
in the mathematical
and statistical areas; they are designed to
provide accurate
resuIts over the large argument domains.
Finally, Sections 6 through 8 give complete specification on
the boundaries and parameters associated with the Scientif-
ic Calculator's floating-point number system, argument do-
mains and result ranges for' each function, and error
messages that are displayed when appropriate.
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SECTION 2$
STARTED
GETTING SET UP
To get started, turn the HHC OFF, then plug the Scientific
Calculator capsule into the back
of the HHC, but do not yet
put the keyboard overlay
in place. Press ON and then press
the CLEAR key once or twice. The primary programs menu
will
be displayed; press the number of SCIENTIFIC CAL-
CULATOR. Notice the momentary display confirming that
you have selected the desired capsule. Now you can put the
keyboard overlay in place and use the calculator.
ACQUAINTED THE STACK
The stack is baSic to the Scientific Calculator. It is a section
of memory that can contain up to ten standard
or floating-
pOint numbers. The first number (top of the stack) is dis-
played at all appropriate times. The STACK is under user
control through the operation keys.
Reverse Polish Notation is used to enter arguments for cal-
culations. This concise "programming" notation is used in
many computers and calculators, particularly those that are
stack-oriented.
As an example, use your calculator to follow the calculation
of adding 4 to 6. A standard statement would be 6 + 4
10. However, using the Scientific Calculator and Reverse
POlish Notation, you press
6 ENTER 4 ADD; 10 is displayed as the an-
swer.
In this example, keys affect the stack as follows (assuming
that only stack levels 1 and 2 have numbers in them).
Stack
Key in
Level Value Display
6 ENTER 1: 6 8
4ADD
i.
4 6 is displayed I •
2: 6 ADD is pressed,
the addition
occurs yielding the
next condition)
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1: 10
10
2:
(note that level 2
is now empty.)
Now press DROP to remove the one remaining stack entry
and trv a more complex example.
Calculate the square root of 1 - x2. Let x be 0.6. Note that
PUSH and ENTER are the same key. The term PUSH is the
more "stack-oriented", but we use both interchangeably.
Key in Stack
1 PUSH 1:
.6 PUSH
1: .6
2: 1
SHIFT
X2
1: .36
2: 1
SUB 1: .64
V-
1: .8
In the Scientific Calculator, all one-operand operations
(keys such as X2) use the first stack entry (the top) as the
argument, and replace that entry with the result. Thus, to
both save and use an argument, you should first store it
in
memoryorduplicate it (DUP) on the stacksothat it is on both
level 1 and level
2. Then you can perform the operation and
still retain the original number.
Two-operand operations like addition (ADD) combine the
two numbers nearest the top of the stack, placing the result
at level
1, eliminating level 2 and shifting levels 3,4,...n up
one level each.
NOTE: Keying in a numberdoes notput it
on thestack
automatically. For tv-va-operand operations, if the first
numberis keyed in, it mustbe PUSHed ontothe stack.
If the first numberisthe result of a preceding operation
or if it has been recalled from memory, it will be on the
top of the stack already and need not be PUSHed.
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There are also no-operand keys; forexample, generation of
a random number adds a resultto the top ofthe stack. There
are
control keys that give precise control of the stack. All
this, as well as what happens in case of an out-of-bounds
result,
is discussed in detail in Section 3 and in Section 7.
Sometimes you may want to view the current contents of the
stack. If you are not in the middle of an operation, you may
do so by pressing the DISP key. The first use of this key
results in a display of the quantity of items on the stack.
HEIGHT=5
After this, each time you press any key except CLEAR or
CANCEL, the next level of the stack will be displayed, start-
ing with level
1.
1: 2.56E9
After the fast item is shown, the calculator returns to key-
board input mode, displaying the value on the top of the
stack. To leave the display mode while it is cycling , press
CANCEL; this will return you to keyboard mode so that you
can continue normal operations.
To try out this display feature, press DISP now. Then press
CANCEL to return to keyboard mode and DROP the .8 put
in level 1 at the end of the example above. Work your way
through this example, using DISP
to view the stack after
each step. You should be able to verify the stack level and
contents as they are shown. Remember to press CANCEL
to return to keyboard mode.
INPUTTING NUMBERS
The number displayed on the LCD (liquid crystal display) is
usually the number on the top of the stack. When you key
in another number, it will become the new top entry as soon
as you press PUSH. The number you enter may contain as
many as seven components.
1. a sign
2. a string of integers
3. a decimal point
4, a fractional part
5.
an exponent symbol
6. a sign for the exponent
7. an integer for the
exponent
Keys Example
+/
0,1,...9 12
O,i 34
ENT EXP E
+/-
0,1, ... ,9
56
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This example yields the number 12.34 x
10 - 56; the cal-
culator stores this internally as 1.234 x
10-
55.
of acceptable numeric entries
are:
Integers such as:
0
1
650
-442
+17
Decimal values:
0.0
.00096
.2
+643.33333333333
12.00
Values
with exponents:
Examples
6E20
(=6 x 10
20)
4.12E-1
(=4.12x 10-
1
.412)
1.0009E 6 (
-1.0009 x 10-
6 )
4E+16 ( 4x
10
16)
The overall sign and the exponent's sign may be omitted with
positive or zero values. You should use the
key to enter
a negative
sign (do not use the SUB key). The + key can be
usedfor correcting improper minus signs during input and for
indicating sign
on a printed output.
The magnitude of
the mantissa (e.g., 12.34 above) need not
contain
all three components, but must include at least one
numeric digit. For example, 12, 12., and 012.0 all yield the
same result. Although thirteen significant digits of accuracy
are retained, more digits may be entered,
exponent (e.g., E
56 above) may be omitted for num-
bers that can be represented by no more than twenty-six
characters without
an exponent. If the ENT EXP key is used,
then at least one digit must appear for the exponent's inte-
geL
This integer cannot contain more than four digits; within
this constraint, leading zeros are allowed.
The number input
is limited to twenty-six characters and
cannot exceed the range of numbers the calculator can
store.
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Before the PUSH key is pressed, the number may be com-
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pletely reedited. Use the left- and right-arrow keys to place
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the cursor for editing; there is no space bar. After a number
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has been entered with the PUSH key, it cannot be changed.
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CONTROLUNG THE OUTPUT FORMAT
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The SCI and DIG keys control calculator output format (the
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is not affected). Their default values are fixed-
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point notation (SCI key toggled off) and display of 10 signifi-
cant digits (DIG).
e ':;) To have your results presented
in scientific notation, press
e
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the
SCI key once to turn it on; the DELETE blip shows on
e
the display to indicate that SCI is active. Key in the following
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e demonstration.
.,
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.,
Key
in
Display
~'
.,
123456
PUSH 123458
till;
SCI DUP 1.23458E5
...
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.,.
To return to standard notation, press SCI again to turn it off;
II!!
the DELETE blip disappears:
fl
@~
,Ill!!
Key in Display
~
@
SCI DUP
123458
~ ..
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The DIG key controls the number of significant digits
~
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presented
on the display. The default value for this function
§l) is
10 digits; however,the maximum value of 12 digits allows
you to take full advantage of the Scientific Calculator's 13-
II') digit arithmetic. Calculations use
all the digits entered (up to
e,.
13), and results will be rounded to the number of significant
e ? digits
you have chosen. Continuing with the example above:
? Key
in
")
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?
DIG
3 ENTER
'),
DUP
. ~'~
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295 ADD
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Display
123458
TYPE NUMBER (1-12):
TYPE NUMBER (1-12): 3
123000
124000
(123456 + 295 ;: 123751,
which
is rounded to
3 significant digits.)
To verify that all digits entered have been used in the calcula-
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tion and put onto the stack, reset DIG to a larger number and
k
~
then DUP to see the top of the stack.
~.
It· ?!'i

Key in Display
DIG 7 ENTER
124000
DUP 123751 (= 123456 + 295)
The DIG setting will remain until changed deliberatelyoruntil
the CLEAR key
is pressed, which causes the setting to revert
to default. Turning the calculator off does not affect the set-
ting.
USING MEMORY
Everynumber used in a calculation is put on the stack auto-
matically, and the stack must emptied when it becomes full.
However, numbers must be specificallystored
in one of the
12 memory locations and they stay there until specifically
cleared with either
ClM, which clears all memory locations,
or CLS, which clears a specified memory storage location.
Contents of memory can
be recalled at any time either by
you
or by a program that you have entered in the f1 , f2, and
f3, user-definable function keys.
Data stored
in memory is not affected by turning off the HHC
or by pressing CLEAR once. However, pressing CLEAR
twice to access the HHC primary menu and other HHC
applications will destroy the contents of
all 12 memory loca-
tions.
To familiarize yourself with the storage function,
run through
the following example. Either key
in a new number to store
or use the number
on top of the stack that is displayed.
Key
in
Display
4 4
~ 3.141592854
MUl 12.58837081
SHIFT STO TYPE NUMBER (1-12):
6 TYPE NUMBER (1-12):8
ENTER 12.58837081
To verify entry, recall the number from storage:
Key in
Display
TYPE NUMBER (1-12)
6 ENTER 12.58837081
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ERRORS AND WARNINGS
.~
Attempting calculations with invalid parameters will result in
.~
error messages. These can occur in the following two situa-
tions.
e;,.
/IIegal operation-if you violate the constraints of the float-
e ~
ing-point system in your calculations or if you use math-
(f .,
ematical functions with incorrect arguments. For example,
raising 2 to the power 10000 is prohibited, because 10000
is too large
an argument, and the result exceeds the max-
imum machine-representable number (Section
6). Similarly,
~
tf •
e .~
division by zero is not toleiated.
e ~
Accuracy Bound -jf
an argument presented to a routine
f!; ~
results
in a function value considered to be too inaccurate.
For example, sine routine arguments should be less than
~ ~
102942 radians in absolute value. This is because n times
~ ...
~ is used to reduce the argument; if the argument is large,
~ ,.
it is nearly n times
~ (being identical to it to a number of
significant digits). Then, in subtraction, these identical digits
~ " are lost. The sine approximation
is tailored for arguments in
~. fA)
the (OJ~/2) range, so that the reduced argument will be less
.... fIJi
significant than was the original argument by too large
an
~ I)
amount; the result cannot be as accurate as desired, since
the argument was slightly altered during reduction. The
~ IIiJI bounds
on the argument domains presented in Section 7
@ ...
were chosen so that the floating-point arithmetic system
@ II') could be fully exploited by the algorithms used. Users are
~. '!It
protected from results which may
be "less than accurate"
~
because of arguments that are too large to be accurately
~
reduced.
e' ~~
In both overflow and accuracy bound,
''''J,
e:
• an "ERROR n" message is displayed. Tables 7 and 8
e ~
discuss the meanings for the various values of n. Usethe
e: ~
CANCEL key to remove the message from the LCD;
e "')
• the same number of inputs
is dropped from the stack as
? would be appropriate if the operation succeeded;
?
II the resultant top stack entry (an invalid-floating point
~
number)
is automatically dropped; and
~
• other stack entries and user memory are unchanged.
~
..... ~
There are other situations in which warning messages are
given. Forexample,
an attempt to execute an instruction that
~4'.
would underflowthe stack causes abeep; neitherthe display
,4\ nor the stack is changed. When the maximum stack height
of 10
is reached, the HEIGHT WARNING message Is dis-
•
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2·7

~
~
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played. No more stack entries will be accepted. You can use
the DISP key to display stack entries and can diminish the
stack by using a combination of the ROLL and DROP keys.
You can also press CLEAR once; however, this will cause
the DIG and SCI keys to revert to their default values.
2·11
.~
fJ
SECTION 3. USING THE
t;, ~
OPERATION KEYS
e
~
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This section discusses the operation of each key you may
•
~
use while operating the Scientific Calculator. Simple
exam~
pies are given that include key strokes, stack contents, and
Cf
• the HHC display for each step where this information will be
Cjl
• helpful. The HHC will BEEP when you enter an illegal
keys~
~,
troke.
e,
. ~
The discussion is organized by category: control operations,
~
e elementary operations, mathematical functions, statistical
e
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functions, and programmable keys. The more complex
func~
tions are explained with problem-solving examples in Sec-
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tion IV.
~
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NOTE: When
two functions are assigned to one key,
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f"
the upper function printed on the keyboard overlay
is
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accessed by pressing and releasing the SHIFT key
..
fIJ
before using thefunction key. If you changeyour mind
after pressing SHIFT, press SHIFT again to cancel
it.
..
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~ CAUTION: All the HHC keys are still functional when
II) you are using the ScientificCalculator. Therefore, you
@:
must be careful not to press the HHC 2nd SFT key.
@:
,~
If it is used with an HHC alphabetic key that has a
second shift value, the calculator will BEEP; if used
f!' ~
III!lI
with an alphabetic key without a second shift value,
the calculator will treat the keystroke as CANCEL.
~
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CONTROL OPERATIONS
e
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e Memory Controi
'~
Memory contents are not affected by turning the HHC off or
e by pressing the CLEAR key once. However, pressing
.?
CLEAR twice to return to the HHC primary menu will destroy
e
""AI
the contents of locations 1 through 12.
'.;;\
(;;
411 STO (Store Memory), This key allows you to store any
~~
valid HHC number (one you enter for this purpose
or one
~
already on the top of the stack)
in a storage location 1
through i 2. The iocation number is entered afterthe prompt
~:
~...,.
asking for one appears on the display. Location 12 is used
to store the seed for
Xu and Xn in statistical calculations; it
is the only location that can have its contents altered by the
lIP'"
.'"
1t',
capsule without an explicit request from the user.
..
III
'1. 'i

~
'::1
•
'-. To verify the subtraction, you can recall from memory:
Key in Display
~;
'"
t,,:
~
Display
1234 1234 Key
in
SHIFT
STO
TYPE NUMBER (1-12):
9
TYPE NUMBER (1-12):9
ENTER 1234
The number entered into memory is also put on the top of
the stack.
s REC (Recall Memory). Use this key to recall to the display
the contents of any storage location 1 through 12; the num-
ber recalled is also put on the top of the stack.
Key in Display
REC
TYPE NUMBER (1-12):
9
TYPE NUMBER (1-12):8
ENTER 1234
When a number has been recalled and is shown on the
display,
it can be used in 1- and 2-operand calculations
because it has been puton the top of the stack automatically,
pushing the preceding entry down to level
2.
@ ClM (Clear Memory to zero). Pressing this key clears all
memory storage locations to zero.
III ClS (Clear Storage location n). The prompt asks for the
number of the memory storage location to clear.
e M -, M+ (Memory subtract and add). These two keys
operate on the contents of a specified memory location 1
through 12. The number on the top of the stack is used; this
can be the result of the preceding operation
or a numberthat
have iust keyed in.
Key in Display
(assume that the contents of 9 are 68)
24 24
M- TYPE NUMBER (1-12):
9 TYPE NUMBER (1-12):8
ENTER 24
t;;; ~
REC
t;
~
• 9
If;;:
ENTER
ill
t;:,
~
~
(.:'
Stack Control
•
e,
~
Every number that you key in must be pushed onto the
:i
~:
, of the stack by you or by an operation key. A
f!; message will be displayed when the stack
is
.,
no new numbers will be accepted. If you receive this warning
~
..
message, you can store your last entry in a memory storage
~,
~
location, then use DROP or a combination of
ROll and
111)
DROP to remove numbers from the stack to continue oper-
~
ation. You can also press CLEAR once.
..
CAUTION: If you press the CLEAR key for any rea-
.'
.,
son, stack contents are destroyed (and the
SCI and
.. ~
~
DIG keys are turned off, returning to their default val-
II),
~
ues).
~
~.:
., PUSH. The ENTER,PUSH,DUP key is used to put your
."
~,
keyboard entry on the top of the stack. Used several times
')
~~
in succession, it will put the same entry on several levels.
tI)
@:
• DROP,C/E. This key is used to delete the entry on the top
I',) ofstackand displaythe nextlevel as the newtop level.
">
the stack
is empty, the cursor is displayed. You must be in
")
keyboard mode to do this; the key will not operate while you
':')
are cycling through the stack display (press CANCEL to
abort the DISP cycle).
'.::II
":':I!
Key in
e:
?
e ?I.
e
~
~
DROP
:?-
TYPE NUMBER (1-12) =
TYPE NUMBER (1-12):8
ilL! ( = 68 -24) The number keyed
in
is subtracted from the contents
of the memory location specified.
Stack
1:
2:
3:
4:
8.3E2
4.683E
3.1415
6
9
1:
2:
3:
4.683E
3.1415
6
9
The DROP,C/E key is also used to CLEAR ENTRYfrom the
,
,~
~~
'V")

3
~. ¥
t;.; ~
display before it has been PUSHed onto the stack. In this
use, the entry on top of the stack
is not dropped.
• SWAP. Use this key to exchange the top two entries
on
the stack. Neither number is destroyed.
Key in Stack Display
1: 789 789
2:476
SWAP 1: 476
478
2: 789
It ROLL. This key will remove the numberfrom the specified
stack level and push it onto the top of the stack. The prompt
requests the number of the stack level containing the num-
ber you want moved.
Key in Stack Display
1: 9 9
2: 8
3:7
ROLL TYPE NUMBER
<1-3) :
TYPE NUMBER
(1-3):3
ENTER 1: 7 7
2:9
3:8
Note that the number 7 is no longer in its original relative
position
in the stack.
It PICK. This I<ey operates like ROLL except that the num-
ber at the specified stack level is left in its original place as
well as being placed on the top of the stack. Press PICK.
Afterthe prompt, key in the level number and press ENTER.
The duplicate is pushed onto the top of the stack; the original
retains its initial relative position
in the stack sequence, but
is
one level lower.
II\lI DISP. Use this key to see how many entries there are on
the stack and what their values are. The first time you press
the key, the display will tell you the height of the stack for
example
HEIGHT::: 1I
If you pressagain, the first levelofthestackwill be displayed.
1 : 3.58ElI
~. ~
Press again to see level 2, and so on. When all levels have
f; ~
been displayed, the calculator returns to keyboard input
e ;,
mode, displaying the value on the top of the stack. To stop
ti, ~
the cycle at any paint and return to keyboard input mode,
;, press CANCEL.
~
G • DISP will not show a number that has not been PUSHed.
~. ~
t;
~
OPERATIONAL CONTROL
f;. ~
II ENTER. The ENTER,PUSH,DUPkey is used to complete
e ~
the entering of data requested by a prompt on the display,
e. !;
such as for a number of digits
or memory storage number.
e ~
• CANCEL. Use this key to cancel operations that ask for
~ ~
a response (such as REC, STO, and DIG) if you decide not
~ ~
to activate the operation, to return to input mode when the
~ Il) DISP key
is active, and to cancel an error message so that
you can continue operation.
~ ~
~. 'J;
Ell DIG. This key is used to control the numberof significant
digits in the numbers displayed. The key is effective until
~ ~
pressed again and the setting is changed. Pressing CLEAR
~ ~
for any reason, however, will release the setting and will
~ ~
return to the defaultvalue of ten digits. Although the number
is displayed rounded to the specified number
of digits. it is
~ ~
in memoryas entered and can be recalled in its original form
e l1li;,
by respecifying a larger number of digits.
~ ~
e ")
Key in Stack Display
e ~
DIG
TYPE NUMBER
e .~
(1-12):
e' ~.
2
TYPE NUMBER
(1-12):2
e .,.
ENTER
e ? 123
123
e ? PUSH 1:123
123
":.'l
456 458
¢ ADD 1:579
580 (note the
c; ~+'
effect
of round-
e ~
in the display)
~+
Up to here all calculations have been displayed rounded to
"4'
2 significant digits. Now, if you specify more digits you can
# obtain the result of the calculation unrounded unless your
was more than 12 digits.
A~
:-:1.1;

~ ~
Key in Stack
DIG
4
ENTER
DISP 1:579
Display
TYPE NUMBER
(1-12':
TYPE NUMBER
(1-12):4
579 ( 123 +
456)
Note that although a large number of digits may be input and
thirteen are retained, twelve digits of accuracy at most will
be displayed.
Ii SCI. This key operates as an on-off switch; the ON mode
is disabled when CLEAR is pressed; default value is stan-
dard, fixed- point notation. The SCI key ON will cause all
numbers to be displayed
in scientific notation, the number
ofdigits being controlled by the DIG key (default is ten digits).
The DELETE blip is displayed when the SCI key is active.
III DEG/RAD.lnthe ScientificCalculator, trigonometricfunc-
lions can be used with angles specified in either decimal
degrees orradians. The DEG/RAD key
is atoggleswitchthat
must be setto match the mode of your inputs; its default
value
is radian mode. Press the key to cause the mode (but
not the data currently
on the display) to change to degree
mode. Press the key again to revert to radian mode. The
currentmode is indicated by the INSERTblip-blip showing
means degrees, blip not showing means radians.
The DEG/RAD key does not convert previous calculations.
You can use the following conversions to do this. If it is a
frequent calculation, program one of the
f1 ,f2,f3 keys to do
it for you.
n degrees
on stack: enter
11" 180 DIV
(n degrees x 1T/180 radians equivalent)
n radians on stack: enter
180 1T DIV MULT
radians x i
80i1T == degrees equivalent)
Angles
in degrees, minutes, seconds must be converted to
decimal format before entry. Section 4 shows you how to
program the calculator to do this.
::I.A
Itt ~
Inputting Numbers
.; ~
1111 ±. Use this key to enter a sign for a number or an
f!. ~
exponent. This is not a function key and will not add or
t;, ~
subtract.
~
• 0,1, ... ,9. The numeral keys are used to enter the numbers
e ~
for your calculations or
in response to prompts from the
(;, .,
display. Press the ENTER, PUSH,DUP key to complete the
entry. To cancel
an entry rather than entering it, press
(jr ~
DROP,C/E to clear argument entries and press CANCEL to
~ ..
clear the response to a prompt for storage location, number
e. ~
of digits, etc.
,!. ~
• .(Declmal). This key is used to enter the decimal ooint in
f!;
!)
numbers.
~ 5 • ENT EXP (Enter Exponent). Use this key to enter an
~. .,
exponent with your number. For example. 123E 5 PUSH
~; .,
stores 1.23 x 10-
3 (.00123
in standard notation) on the top
of the stack; pressing the ENT EXP key after the 3 key
......
causes
"E" to be displayed.
~ . • .,
II +-,~. Use these arrow keys to space the cursor forward
and backward to change a numberbefore you have PUSHed
@- 'l
or ENTERed it. Note, however, that you cannot correct an
error in the f1, f2, f3 keys this way; you must start over.
@t. ~
~
~
I;)
ELEMENTARY OPERATIONS
4!.
~
• 11" and 'Y. Keying in either ofthese constants automatically
~
" pushes your previous entryto stack level two. Use the proce-
dure below to find the circumference ofa circle with a radius
~.
of 2.6 feet (or meters).
e .,
e ?
?
e
Key in
?
e 2
e ?
1T
~~
MULT
e .~,j!>
2.6
c
~
e .
(11" = 3.14159265359)
('Y = 0.5772156649)
Display
2
3.14159285359
8.28318530718
2.8
18.33828 ft (Ifll
~...,
(I) ADD, SUB, MUL T, DIV. These functions require two argu-
mentson thestack. Pressing theoperation key automatically
~i
pushesthe second argumentontothe stack if it hasjust been
~I
I keyed in; then it performs the operation, deleting both argu-
I
;,
...
ments and putting the result on the top of the stack.
·.~It·' i
• c+'
,$'
3·7
~;

Key in Stack Display
360 PUSH 1:360
380
2 1:720 720
Any numbers within the HHC range can be used for these
two-number operations. However, because the HHC trun-
cates
at the thirteenth digit, adding or subtracting numbers
whose exponents differ by more than 12will result in display
of an answer identical, except possibly in sign, to the input
number that is the larger
in magnitude. As an example,
consider trying
to add 1.E13 and 2.
10000000000000
+ 2
10000000000002
t_ Truncation at the thirteenth digit.
If an out-of-bounds result is produced, an error message is
given, and the result is automatically dropped. As an exam-
ple, enter
9E1023 PUSH DUP MULT
The displaywill show the message ERROR 2 (floating-point
overflow). Press CANCELto cancel the error message, then
press DISP. Note that none of the above calculation is
present on the stack.
Any number less than
10-
1024
is considered to be 0 and
could result
in a zero-divide error.
., 1/X, X2, These two functions operate on the number on
the top of the stack or a number just keyed in. 1/X will give
the reciprocal of any number
in the HHC maximum range;
X2 will give the square of any number no larger than the
square root of the plus-or-minus maximum HHC number
(see Section 6).
Key in Display Key in Display
25
25
25
25
SHIFT
X
2
825
1/x
.04
@) FRAC. Used to obtain the fractional part of the number
on
the top of the stack and to drop the integer. Answers will
be in the range> 1 to <+ 1. The fraction is placed on the
top
of the stack with the original number being destroyed.
3·8
.e, .,
• Key in Display Key in Display
f.:, ~
f.;, ';.
123.456
123.458
123.456
-123.456
SHIFT SHIFT
It; " FRAC
4.S8E-l
FRAC -4.S8E-1
e; ~
or • a58
or t 458
~, ~
• FIX. The opposite of FRAC; the fractional part of the
Cf ill number is dropped and the integer is placed on top of the
.,
stack and on the display.
G: ;;,
Key in Display
e ~
e ::.
-123.456 -123.458
e , FIX
-123
e: J) NOTE: Rounding can seriously affect FIX and FRAC,
as shown by the following example. Assume that DIG
~ .t) has been set to 3.
(II! '~
~ ~
Key in Stack Display
@i .,
9.999
10
~ fIj FIX 9 8
~
~' ~
Key in Stack Display
~ "'11
@> .~
9.999 10
FRAC .999
.888
~ ~
e ~
or worse,
~
9.9995
10
e ~
FRAC .9995 1
if: ~
8 IXI[ABS(X)]. This key will change the number on the top
if: ,~
of the stack to its absolute value.
e; ~
.~~
Key in Display
~.
-12.4
-12.4
~~
SHIFT
~. ~~
IXI
12.4
,,-~
$ CHS. This key changes the sign of the number being
~;:.
displayed (mantissa only, exponent is not affected). If the
"'~,
number being changed is already on the top of the stack, it
will be replaced with the changed value. If the number has
Iii
"~4'
not yet been PUSHed onto the stack, pressing CHS will
!Ii
.A
Iii"
".~
3·9

~.'V
cause stack contents to be pushed down one level, and the
changed number to be put on top.
Key in Stack Display
25E-8
CHS
-2.5E8 -2.5EB
CHS 2.5ES
2.5E8
MATHEMATICAL FUNCTIONS
Note that for functions using two stacked arguments, x
denotes the item
on top ofthe stack at level 1 and y denotes
the item at stack level
2.
Trigometric, Inverse Trigometric, Hyperbolic,
Inverse Hyperbolic
The Scientific Calculator is initialized to expect angles to be
entered
in radians. If you are using degrees, press the DEG/
RAD key to set degree mode. The INSERT blip will show
when degrees mode is active.
• SIN, COS, TAN, COT; ASIN, ACOS, ATAN, ACOT; SINH,
COSH, TANH, ATANH, and ATAN2 automatically control
over- and underflow. Examples are given in Section 4; de-
tailed parameter information is contained
in Sections 6 and
7.
Exceptfor the ATAN2 function, all ofthese functions operate
on the value on the top of the stack. ATAN2, the two-argu-
ment arctangent computes [tan-j
(y/x)J, x being the value at
stack level 1 and y the value at stack level
2.
• Find the angle whose tangent is 36.75:
Key in Display
36.75
38.75
SHIFT
ATAN 1
.54358-radians
II Two-argument arctangent: x "" 14.57; y = 36.4
Key in Display
36.4 PUSH 38.4
14.57
ATAN2
1.18005
t;, -., Cosine of 36.75 degrees:
,-
e ,. Key
in
Display
re ,..
DEG/RAD (INSERT blip goes on for degree
f; ,.
,.
mode)
36.75
38.75
(f ,.
COS
.801254
(f ,.
Power, logarithm, and Root Functions
~ ..
Most of these keys operate on the value at the top of the
e • stack. However, several require twoarguments. Forthe one-
e
~
operand functions, justkey
in avalue, then pressthefunction
key. The result
of the calculation will be displayed.
e ~
'!>
Ii XV, yx. These keys allow you to raise any number to any
e
')
power, keeping within the Scientific Calculator range. Y is
~
the value at stack level 2 and X is the value at stack level
1.
!;
@
@ ~ Key
in Stack Key
in Stack
~ 3 PUSH
1: 3 3 PUSH 1: 3
@
~
@
'"
~
2 1: 2 2
1: 2
@Ii,
~ 2: 3
2: 3
8')
~
SHIFT
@:
$I)
XY
1: 8
yx
1: 9
~
(2
3)
(3
2)
~
,,,),
@ •
2'1., ex, 10X. These keys allow you to raise these three
@. ~
constants to any power, keeping within the Scientific Cal-
culatorrange. x is the value
on the top ofthe stack. The value
e. ~
of e is 2.71828182846. Key
in the value of x, then press one
~
e of the power keys. The result appears
on the display and is
e ~ automatically put onto the top of the stack.
e ... ~
• Log2• Loge' Log
1o
' These keys compute the log of x, the
C: '41
value on the top of the stack, to base 2, base e
"?, (2.71828182846), and base 10, respectively.
x, the value on
~~,
thetop of the stack, is replaced by the result ofthe operation.
0) • Gives the square root of the value on the top of the
t;, -:;"
stack.
c: ""*
111\ V. This key will give you the nth root of the value on
~, ':'".4:\
top of the stack. When you press this key (SHIFT first), the
~4
display will ask you for the value
of n -- an integer from 1
to 50. Key in the number and press ENTER.
"!';
3-10
4"
3·11

Key in Stack
10,3
SHIFT
.y--
3 ENTER 1: 2.176
STATISTICAL FUNCTIONS
Display
10.3
TYPE NUMBER
(1-50l:
2.178
(the cube root of
10.3)
II X, Xu' These keys are used to generate pseudo-random
n
normal oruniform deviates, respectively. Storage location 12
is used to store the seed forcalculations. If no seed is placed
there, a specific seed will be chosen by the generator. For
a given seed, the pseudo-random numbers are always gen-
erated in the same sequence; therefore, if you restart with
the same seed, you can duplicate yourcalculations. The use
of these keys is demonstrated in Section 4 in An Investment
Problem; parameters are given in Section
7. A detailed ex-
planation of the algorithms used is given in Section 5.
The uniform deviate, Xu' has a uniform built·in distribution
preference and can generally be represented by a straight
line (the range
of results is from zero to one). You are as
likely to get
.001 as a result as .799; this is analogous to
picking numbers out
of a hat, replacing each number after
picking it. More correctly, the deviate is distributed uniformly
on the (0,1) line. I
I
I
I
I
!
u
The normal deviate, has a built·in distribution that can be
represented by a normal curve (the "bell" curve).
I
I
I
I
~
I
I
I
!
u
In a normal distribution your result is more likely to be t
than u (because the curve is higher at t
), whereas in
a uniform distribution t and u are equally probable.
3-12
w
w Normal distributions occur very often in real-life situations:
It;. '.w
IQ-.-most people have an 10 between 85 and 115; far
,f;, w fewer have an
10 below 60 or above 140.
~ .,
•
.,
dice-throwing two dice, you are more to throw 7
than 2 or 12.
t.I: • PROGRAMMABLE KEYS
t:. • These are the three user-definable keys (f1,f2,f3) described
c. ., in the HHC user manual, INSTRUCTIONS FOR USE. You
can define each key to represent a sequence
of up to 15
e· ., keystrokes that will be executed when you press the defined
e ~
key. For instance, you can program them to function as a
~
constant recurring value
or to execute a series of calcula-
tions.
~ !)
~. ~
To enter a program, press HELP, then the desired program
key (e.g., f1). Enter the required keystrokes, then finish the
.. 8.)
programming by pressing the same f key again. (When 15
~. ~
keystrokes are entered, the program terminates automat-
. .,
ically.) Mistakes can not be edited; you must cancel the
program
by pressing the f key and then starting the proce-
~ ",
dure again from the beginning.
~ ....
The use
of these keys is demonstrated extensively in Sec-
~: ~
tion 4. Section 9 shows the correlation between the Scientific
@' ";'II
Calculator keyboard and the HHC characters that appearon
e ~
the display when you are programming one
of these keys.
@' J"),
e· ?
Ii!' ""
e ";;!,
e
~
e
':",;1\
';l;
II!:
e ~
e
~
e ,4'
C'<!,.
~
~.,;.
s;
,~,
,~
3·13

v
V
to, ~
SECTION 4. PROBLEM .. SOL VING
~
EXAMPLES
,.
e,. ~
Nowthat we have seen the operation of the individual keys,
..
we can begin combining the various elements available in
(f. .,
the Scientific Calculator to solve problems.
..
..
TRIGONOMETRIC FUNCTIONS
e .-
The following trigonometric exampies assume that the stack
e ;;" is initiallyempty and that the SCI (standard, fixed-point nota-
tion), DIG (10 digits), and DEG/RAD (radians) keys are at
It :>
their default values.
e '!)
" Calculate the sine of 0.5 radians.
~
1. Select the desired number of output digits, say 9:
@ '"
~
Key in Stack Display
~ ~
f' .,
DIG TYPE NUMBER
(1-12):
~
9 ENTER TYPE NUMBER
4! .~
(1-12):9
@ lIP)
2. Enter 0.5 and execute SIN
~ #).
t!!' ",
0.5 1: .5
I) • 5 (in this case,
,II)
PUSH is optional)
SIN
1:.479425539
.478425538
e ? Ifyou want to enter degree arguments, press the DEG/RAD
e "!)
.,
key before you start entering them. Thus, the calculator
e assumes that arguments for the trigonometric functions are
e: ? being given
in degrees, and results of inverse trigonometric
J,?>
functions will be presented
in degrees. Pressing the key
again will cause the calculatorto revert to radians mode, but
~ "?
will not convert data already entered.
e ~
" Calculate the arctangent of 1 .01 1.0. This operation
~1t
places the result in the proper quadrant
~.
?
~. ?
Key in
Stack Display
;~$
1 PUSH
1: 1
s;. ~
:..:>
DUP 1: 1 1
2: 1 1
7i~
Ci"
4·1

CHS
1: -1
-1
2: 1 1
ATAN2 1: 2.35619449 2.35819449
LOGARITHMIC FUNCTIONS
.. Calculate the logarithm with base 5 of 25.
Several formulas can
be used -note that the Scientific
Calculator allows logarithm calculations to bases
2, e, and
10.
We select
10
95(25) loge(25)/loge
(5)
Key in Stack Display
25 1: 25
25
LOGe
1: 1n(25) 3.218875825
5 1: 5 5
2: 1n(25)
LOGe
1: 1n(5) 1.809437912
2: 1n(25)
DIV 1: 2 2
[= log5(25)]
For retention ofthat result for later calculations, you can call
on user storage (STO), or can use the higher levels of the
stack and then use PICK or ROLL. Say that subsequent
calculation results
in the stack arrangement below,
Level
1: result
Level
2:
intermediate result
Level
3: intermediate result
Level
4:
log5(25)
and
we wished to multiply the ·result by log5(25). PICK 4
ENTER would result in a stack of
Level
1:
log5(25)
Level
2:
result
Level
3: intermediate result
Level
4: intermediate result
Level
5:
log5(25)
tl.?
..
~
ij
~
~
(ROLL 4 would have deleted the laststack leveL) Now when
you press MULT, stack levels 1and 2 are multiplied, and the
.~
...
product of [result] x [log5(25)]
is placed on top of the stack.
(;
• Other values move up one level.
c;.
~
,.,
Level 1: [result) (log5(25)]
~
• Level
2:
intermediate result
Level
3:
intermediate result
iii Level
4:
log5(25)
,.
f#
ENGINEERING FUNCTIONS
~
"""
~
When programming the user-defineable keys, you must pay
e
~
attention to the stack during each step to be sure that the
~
e program will use the proper value in its calculations. Always
~ press HELP, then begin and end the program by pressing
e
13
the f key you are using. When you are calculating, the pro-
~
gram will execute each time you press that f key again.
~
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CAUTION: When using an f key during calculations,
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press the PUSH key before keying in f1, f2, or f3 if the
~
~
programmed sequence starts with a number. This
is
~
necessary to put the new number just keyed in onto
~
~
the top of the stack. For instance, if the program se-
~
quence in f1 starts with 3 and you key in "12 f1", the
~
,~
3 will
be appended to the 12, resulting in 123 and
~
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causing
an erroneous answer. "12 PUSH f1" will give
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the correct answer. Ifyou don't remember exactly how
your programmed sequence starts, press PUSH be-
~
~ fore the f key just to be sure of correct operation.
e
~
Also remember to check stack levels. If a function
tl!I
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key's program uses three stack levels, it won't work
if
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you start with eight levels on the stack already.
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FIX and FRAC
e
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• Calculate x [xl (find the value of a number less the
II! largest integer in that number). Let x
=: 5.2345.
~
f/!:
.. ",
e Key in Stack Display
e
~
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5.2345 PUSH 1: 5.2345
5.2345
C
~~
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DUP 1: 5.2345
5.2345
2: 5.2345
:::<1'
Il;;
:-:~
FIX 1: 5 5
2: 5.2345
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SUB 1: .2345 .2345
Or, better,
5.2345
1: 5.2345 5.2345
FRAC
1: .2345
.2345
NOTE: See DIG in Section 3 for an explanation of
that takes place
in the Scientific Calculator.
Modulo (y mod x)
Enter the y value first, then the xvalue. y is divided by x and
the remainder is multiplied by xand put on top of the stack,
replacing xand
y.
Key in
Stack Display
(y) 275 PUSH
1: 275
275 (y value)
(x) 3 DIV 1: 91.66666667
81.66666667
(x value)
SHIFT FRAC
1: .6666666667 .6666666667
(x) 3 MULT 1: 2 2 (reenter the x
value=
3)
You can program this routine
an f key as
HELP f3
SWAP
PICK 2 ENTER
DIV
SHIFT FRAC
MULT
f3
Brings y value to top of stack.
Duplicates x
on top of stack so
that x at level 1 can be used
to
divide y at level 2, and x at
level 3
will move up with each
calculation
and be available for
multiplication at the end of the
calculation.
Divides y by
x.
Drops integer and displays
remainder.
Multiplies the remainder by the
x value.
To usethe program, key in:
yvalue PUSH xvalue f3
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Degrees/Radians
• Convert degrees to radians: n degrees x
ans
Program: HELP
f1 'IT 180 DIV
It Convert radians to degrees: n radians{1
Program: HELP f2 180
11' DIV
80) = radi-
f1
= degrees
f2
Example: Convert 20 degreesto radians equivalent and then
convert back to degrees.
Key in Display
20 PUSH f1 .3490858504 (radians equivalent)
f2 20 (converted back to degrees)
Ii Convert degrees or hours, minutes, seconds to decimal
format.
In this oxample, f1 and f2 are programmed to calcu-
late the decimal equivalent:
1 minute = .01666667 degree
1 second = .00027778 degree
Program:
HELP
f1 .01666667 MULT ADD f1
(converts minutes and adds to degrees already en-
tered)
HELP f2 .00027778 MULT ADD
f2
(converts seconds and adds to degrees and minutes)
Example: Convert 3 16'25" to decimal format.
Key in
Stack
3 PUSH
16 PUSH f1
1: 3
1: 3.2666656
25 PUSH
f2 1: 3.2736081
Display
3
3.2668656
(deg+min)
3.2738081
(deg+min+sec)
NOTE: If there are no degrees, key
in "0 PUSH"
fore using
11 or 12.
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A..A

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C. w
tjli)
1 SUB Decrease number of factors by 1.
Percentages and Conversion Factors
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SHIFT STO Store new total for recall.
(ill Compute a sales tax of 6'% and add to total purchase.
el~
ENTER
Program:
HELP
.06
ADD M
f1 DUP
ULT
f1
Amount of purchase must be
duplicated
Calculates 6% sales tax
and adds to subtotal for
grand total
The
va.lue you key in must be duplicated on the stack by the
program so that it will be available for both MULT and ADD.
Example: Calculatetotal bill for purchases of $25.96 and 6%
sales tax.
Key in Display
25.96
25.86
PUSH f1 27.5176
• Convert from liters to quarts. The conversion factor can
be stored
in a memory location from 1 to 12, but, if it is a
frequently used conversion, itis more convenient to program
it into
an f key along with the multiplication.
Example: Convert 25 liters
to the quarts equivalent. Conver-
sion factor
is 0.946.
Program: HELP f3 .946 MULT f3
Key in
Display
25 PUSH f3 23 + 65 (equivalent of
25 liters)
Factorials
" Find how many ways seven symbols can be arranged on
a straight line.
Program:
HELP
f1
REC 1 ENTER Recalis the totai number of
factors stored here when
starting calculation.
MULT
f1 Multiplies stack levels 1 and 2.
i&1~
C.I~
Key In to Use Stack
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c,:,..
7 SHIFT STO
1 ENTER 1: 7 (Store total number of
fi,. I 'Ii
factors)
c,iii
f1 1: 42 (7 x 6)
t..I.~
f1 1:210 (42 x 5)
I
f1 1: 840 (210 x4)
el;'
f1 1: 2520 (840 x3)
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f1 1: 5040 (2520 x 2)
el'!')
f1 1: 5040 (5040 x 1)
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You can press REC 1 ENTER to see which factor you
~! .~
have just multiplied by. If you do this during calculation, be
sureto press DROP after recalling the factor; ifyou don't, the
~
next multiplication will be wrong because the wrong number
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will be on the top of the,stack.
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STATISTICAL FUNCTIONS
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III)
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Summations
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In the following example, pairs of numbers are entered. The
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f1 and f2 keys are programmed to accumulate in memory
locations 1 through 6 the values x, x2, y, y2, xy, and the
,;II!)
number of paired entries. Several examples follow that are
based on these values.
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e Location Value
e:
~
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1
::Ex
2
::E X2
>? 3
::Ey
e :"? 4
::E y2
~
5
::Exy
t;; 6 number of pairs calculated
t;::,
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4-7