Texas Instruments TI Programmable 57 User manual

KEY INDEX
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IMPORTANT
Record the serial number from the bottom of the unit and purchase date
in the space below. The serial number is identified by the words “SERIAL NO.”
on the bottom case. Always reference this irformation in any correspondence.
Ti PROGRAMMABLE-57
Mode! No. Serial No. Purchase Date
©Copyright, Texas Instruments, 1977
24
2-16
24
2-16
24
24
2-23
24

Key Index . .
Chapter 1:
Chapter 2 :
Chapter 3 :
Chapter 4 :
Appendix A :
Appendix B :
Appendix C :
Appendix D :
Appendix E :
TABLE OF CONTENTS
056
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Getting
on
Track
A
First
Look
at
the
Tl-Programmable
57.............
&
See
1-1
How
Does
It
Work
?...
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1-6
Firing
Up
!
A
Tour
of
the
Keys
and
Functions
Section
1,
Basic
Keys
and
Functions.
.............0-+.0---00-.
2-2
Section
2,
Advanced
"Slide
Rule”
Keys.........
J.
ge
-
Goa
2-10
Section
3.
Statistical
Functions
and
Keys.................00005
2-22
The
Trackmakers
:
A
Tour
of
the
Programming
Keys
LRN}
—
The
Learn
Key........
IRR
RRP
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See
epider
2
—
The
Resel
Key.....
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Key
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23-3
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—
The
Pause
Key
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to”
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to
a
Step
Number”
Key
sequence
.......
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—
‘Decrement
and
Skip
on
Zero”
Key
sequence.
........
3-6
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and
Skip
if
not
Zero”
...........
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Key
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3-13
Steps
in
Writing
a
Program
.........
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Development
of
Programming
Style
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A-9

A FIRST LOOK AT THE
TI PROGRAMMABLE 57
The
calculator
you're
about
to
begin
using
is
really
straight
out
of
the
“world
of
science
fiction’
of just
a
few
months
ago.
Only
the
most
recent
advancements
in solid-state
technology
have
made it
possible
to
put
such
an
easy
and
fun-to-use
bundle
of
power
right
in
the
palm
of
your
hand.
Easy To Use
A
quick
look
at
your
calculator
will
tell
you
that
it's
packed
with
lots
of
keys
and
features.
Introducing
you,
step-by-step,
to
each
of
these
keys
and
features
is
one
primary
purpose
of
this
book.
Above
and
beyond
all
these
features,
however,
is
one
overriding
characteristic
that
was
designed
into
your
TI
Programmable
57
right
from
the
start:
It's
easy
to
use.
It's
easy
to
make
it
do
many
things
that
can
be
enormously
helpful
in
your
schoolwork,
extremely
powerful
in
your
career,
and
a
lot
of
fun
in
your
everyday
life.
It's
designed
to
be
a
working
tool
that,
working
together
with
the
information
contained
in
this
book,
becomes
a
system
for
problem-solving
and
a
key
to
discovery.
We
hope
you'll
enjoy
using
and
exploring
with
it.
STARTING AT THE ToP
In
learning
about
your
machine,
let's
start
right
off
with
the
nameplate
—
and a brief look at why we called it what we did:
TI — The calculator is built by Texas Instruments Incorporated.
PROGRAMMABLE
—
As
you
wil!
be
seeing
in
a
few
seconds,
it
is
easy
to
“teach”
your
machine
to
help
in
solving
problems,
evaluating
formulas
and
building
“models”
of
your
world.
You
can
lay
down
a
set
of
Tracks’
that
the
machine
will
follow
as
it
solves
a
problem.
A
word,
recognizable
to some
folks,
that
describes
such
a machine
is
already
around:
Programmable”.
This
machine,
however,
is
a
new
thing
—
with
1
whole
new,
easy
approach.
So
if
“programmable”
is
a
word
that
scares
you
—
don't
let
it.
Using
your
57”
is
a
cinch.
57 — This machine is the latest in a growing family of Texas Instruments
programmable calculators, and it's “following in the footsteps" of
another machine, our SR-S6. The 57 is an even easier machine to use —
designed for especially straightforward use.

A FIRST LOOK AT THE
TI PROGRAMMABLE 57
How Does Ir Worx?
Simple!
For
starters,
take
out
the
calculator
and
check
out
the
“heit’’
of
this
little
device.
Light,
isn't
it?
That's
because
most
of
the
important
things
inside
this
calculator
are
handled
with
a
device
that
the folks at TI call a “SOAP” bar.
Now,
turn
it
on!
A
zero
in
the
display
tells
you
that
you're
ready
for
action.
(If
the
zero doesn't
come on,
or
the
display
seems
to
be
doing
‘funny’
things,
don’t
worry.
The
battery
just
needs
charging.
Turn
the
machine
off,
plug
in
your
charger
and
wait
a
few
minutes;
then
you'll
be
set
to
go.)
Let's get right into it with a simple example.
Imagine this situation:
You've just won a rather weird award from a major radio station. You'll
be given 2¢! This money will be doubled every day for three weeks (21
days).
OR
—
you
can
have
$5000
in
cash
immediately.
You
have
two
minutes to make a decision — the announcer is waiting. (This is actually
an “old and classic” problem. Watch how your calculator helps.)
Basically, you can have your machine read out for you just how your
money will ‘grow’. Here's how:
Over on the upper left hand
corner of your machine, one row
down from the top, is a key that
is the real “jewel”:
it's
labelled
ke)
———————>
This is the "learn" key, and when you press it one time, your calculator
begins to learn and remember whatever you put in next. When you press
{RN} again, you're telling the calculator that you've “taught” it everything
you
want
it
to
know
for
now.
The
calculator
stops
learning
at
this
point,
but remembers all the steps you taught it. (The key is like an
ON/OFF" button for teaching your calculator to do things.)
So press [RN], (At this point your display changes to 00 00.) Now, if you
decide to take the “2¢ option’ on the contest, you'll be doubling your
money for 2] days, and you want to watch it grow. To do this, Press
x2 =).
1-2

A FIRST LOOK AT THE
TI PROGRAMMABLE 57
SS
Now
another
“little
jewel’’
—
right
above
the
key
labelled
you'll
see
the
word
Pause”
written
on
the
face
of
the
machine.
Whenever
a
word
or
function
is
printed
above
a
key
—
on
the
face
of
the
machine
instead
of
right
on
the
key
—
that's
called
a
"second
function’.
Second
functions
allow
us
to
pack
all
the
power
we
can
into
your
calculator,
without
loading
it
with
keys.
To
use
a
second
function,
just
push
the
Gad]
key
—
in
the
upper
left
hand
corner,
and
then
the
key
right
below
the
second
function.
In
this
book,
we
will
use
keys
with
a
black
background
Ill
to
indicate
second
functions.
So:
Press:
(20d)
Ml
(You'll
press
@ed)
and
the
key
labelled
“SST”.)
The
MM
key
tells
your
machine:
“Stop
for
a
moment
and
let's
see
what's
going
on”.
One
more
thing
—
we
want
to
keep
doubling
our
money
again
and
again.
To
let
your
machine
know
this,
just
find
the
(reset)
key
(close
to
the
lower
left
corner).
This
key
says,
"go
back
and
do
it
again,
from
the
top’.
PREss:
You
have
taught
your
machine
all
it
needs
to
know
at
this
point,
so
press
again,
and
press
again
to
be
sure
everything
is
back
at
the
beginning.
Now,
to
watch
your
2¢
“grow”
—
first:
Enter
2¢
on
your
calculator:
Press
[*]
(0)
(2\\The
display
should
read
0.02.)
At
this
point,
your
calculator
is
ready
to
“grow
your
money”
—
each
display
readout
will
be
double
the
value
before
it.
You'll
start
things
going
and
count
the
days
as
they
go
by.
You'll
have
0.04
for
the
first
day,
etc.
When
you
reach
21
days,
the
cash
value
in
the
display
is
what
you
will
win.
OK.
—tostart
the
machine,
just
press
the
RUN/STOP
key
—
R)—
the
lower
left
key
on
the
board.
Keep
your
eye
on
the
display,
count
out
21
days,
then
press
the
PA)
key
again
and
hold
it
down
for
a
moment.
On
day
21
you'll
have
won
$41,943.04!
Tell
the
announcer
you'll
take
the
“2¢
option’.
1-3

Se
eee
A
FIRST
LOOK
AT
THE
TI PROGRAMMABLE 57
Se
ConGRATULATIONS!
In
this
little
example,
you
have
already
covered
many
of
the
key
points
that
make
your
programmable
calculator
easy
and
fun
to
use:
¢
The
[RN]
key
lets
you
“teach
the
calculator’.
(You
can
teach
it
up
to
50
steps,
and
there
is
a
lot
it
can
learn
—
any
of
those
“steps”
is
usually
equivalent
to
any
keystroke,
but
some
steps
can
involve
two
or
more
keystrokes.)
*
The
Ist]
key
starts
things
back
at
the
beginning.
*
The
4)
key
allows
you
to
control
the
action
—
stoppingand
starting
where
you
please.
Makinc Tracks
One
way
of
looking
at
how
the
calculator
works
is
to
think
of
it
as
q
little
“railroad”
—
where
you
can
“make
tracks"
for
the
machine
to
follow:
Take the number
in the display
Pause and let's
see the result
2eg 0 hens eeew
Go back and do
it again (reset)
* a s | a iS
The
“train”
on
this
track
has
a
special
name
—
the
"'Pointer’”’
(or,
more
technically,
the
program
pointer),
Each
time
this
train
passes
an
operation,
the
calculator
follows
the
instruction
or
performs
the
operation
listed.
The
calculator
in
effect
pushes
its
own
buttons
for
you
—
in
the
exact
sequence
you
tell
it.
When
you
push
the
@il
key
(or
the
train
comes
to
St)
as-part
of
a
program),
the
train
immediately
goes
back
to
the
beginning
—
to
the
first
step
(step
number
00),
and
starts
over.
To
get
the
“train”
moving,
or
to
stop
it
once
it’s
moving,
you
just
use
the
(‘run/stop")
key.
1-4

A FIRST LOOK AT THE
TI PROGRAMMABLE 57
In
the
example
you
considered
earlier,
when
you
press
RA),
the
machine
simply
pressed
its
own
buttons
and
doubled
the
display
value:
and
would
have
kept
on
doing
this
for
quite
awhile
—
had
you
not
stopped
things
after
21
“go-rounds”
with
the
P&lkey.
(As
you'll
see
later
on,
these
repetitive
go-round”
situations
in
your
calculator
—
and
in
larger
computers
—
are
called
"loops”’.)
At
this
point
you're
already
well
into
many
of
the
features
that
make
your
programmable
calculator
so
special.
Actually,
we've
explained
enough
here
so
that
you
can
now
explore
all
sorts
of
programs
on
your
own.
We'll
naturally
show
you
all
the
ins
and
outs
of
your
machine
with
more
on
how
to
solve
problems
and
run
programs
using
it,
later
in
the
manual.
But
don't
be
afraid
to
explore.
There's
really
nothing
to
it,
and
you
can’t
hurt
the
calculator
by
pressing
any
combination
of
buttons.
Your
calculator
can
be
easily
programmed
to
run
through
any
set
of
keystrokes
(up
to
50
steps)
which
you
could
handle
manually
from
the
keyboard.
Just: Push {tRa)
eEnter your keystrokes
(You'll
need
to
use
RS]
as
your
last
step
if
you
want
things
to
repeat,
or
as
your
last
step
if
you
want
things
to
stop
after
one
time.
Also,
if
you
need
to
enter
a
number
midway
in
a
program,
or
want
to
see
some
intermediate
result,
just
put
an
k#)at
that
point.)
id
¢Press (tRN) again
¢Press
‘
At
this
point
you've
programmed
your
calculator.
To
run
the
program,
just:
eEnter the number(s) you want to work on
ePress
1-5

A PRACTICAL CASE
We'll
be
showing
you
many
ways
to
use
your
programmable
calculator
for
a
variety
of
school,
home
and
recreational
applications.
You'll
see
with
each
example
the
ease
and
power
the
machine
can
bring
to
everyday
mathematics.
Let's
take
a
quick
look
at
a
more
practical
case.
In
this
situation
let's
say
that
you
(or
someone
you
know)
ran
up
a
rather
large
bill
(say
$500)
on
a
credit
card
account.
Credit
cards
are
convenient,
but
they
really
“sock
you”
with
interest
charges
—
typically
1.5%
per
month.
You'd
like
to
weigh
several
alternatives
on
payments
and
get
a
picture
as
to
what
the
best
course
of
action
would
be.
Paying
back
the
cash
right
away
would
be
the
best
way,
of
course,
but
you
might
not
be
able
to
afford
it.
However,
if
you
string
the
payments
out
over
a
long
period,
it
would
cost
quite
a bit.
Your
calculator
can
help
by
speedily
letting
you
calculate
the
alternatives,
For
right
now,
let's
say
you'd
like
to
know
what
your
monthly
payments
would
be
if
you
paid
off
in
3,
6,
9,
or
12
months;
and
how
much
you'd
be
paying
in
interest
in
each
case.
Here's Att You Do:
First,
turn
your
calculator
off
and
on
—
to
clear
everything—
and
then
push
the
following
keys.
(Remember,
we'll
be
covering
all
the
details
later
—
for
now
just
see
what
your
calculator
will
do
for
you!
Push
each
key
carefully.)
(At
this
point
your
display
should
read
27
00.
If
it
doesn’t,
turn
your
calculator
OFF
and
ON,
and
go
back
and
re-key
carefully.)
Now press:
1-6

A PRACTICAL CASE
At this point; all you need to do is store the values you want to try out in
the three memories we've used, and let your calculator do the rest.
Enter the amount you owe and store it in memory one by pressing:
500 1
Enter your monthly interest rate (i= 1.5% =.015) and store it in
memory two.
015 (S19) 2
Enter the first option you'd like to try — equal payments for n=3
months:
3 (30)3
From now on in it's a cinch!
First press 2nd) MI 2 so we'll be reading out dollars and cents
clearly in the calculators display.
Then press &31) RA).
There it is: If you decided to pay back in 3 months, your monthly payment
would be — $171.69.
Press RS) again to see how much you'd be charged for interest — $15.07.
To try the other options:
Enter 6 months, press 6 St) 3
Then press
Your payment: $87.76
Press [RS] again for interest charges: $26.58
Enter 9 months, press 9 [St 3
Then press
Your payment: $59.80
Press RS) again for interest charges: $38.24
Enter 12 months, press 12. 0)3
Then press
Your payment: $45.84
Press R4) again for interest charges: $50.08
1-7

A PRACTICAL CASE
You can now goon and pick a’:payment program very carefully, seeing
exactly
how
much
your
interest'charge
will
be
for
each
alternative.
In
this
example
you've
used
your
calculator
to
handle
a
very
important
and
versatile
business
formula.
The
formula
for
calculating
the
amount
of
(equal
monthly)
payments
on
a
credit card
type
of account
is:
i
Payment
=
PV x
(= al
=|
Where: i=the monthly interest rate (1.5% or .015)
n=number of months
PV =the present value of the balance you owe ($500)
The total interest charge in dollars is calculated as:
Total
Interest
Charge
=
(n
x
payment)
—
PV
In
handling
the
problem
above
the
present
value
of
the
balance
owed
(PV)
was
stored
in
memory
1.
The
monthly,
interest
rate
(1%)
was
stored
in
memory
2,
and
the
number
of
months
you
take
(n)
was
stored
in
memory
3:
From
now
on
in
you
can
“try
out”
any
number
of
months
you'd
like
(for
any
present
value,
or
any
interest
rate)
just
by
changing
what
you've
got
stored
in
one
of
the
three
memories,
Your
calculator
does
all
the
work
at
the
touch
of a
key.

Movinc On
Well,
at
this
point
you've
already
come
quite
a
long
way.
You've
seen
your
calculator
in
action
in
two
program
situations
—
each
of
which
has
a
useful
side
as
well
as.a
fun
side.
What
we
hope
is
that
you'vealso
seen
how
easy
it
is
to
use
and
program
your
calculator.
Let's
make
afew
major
points
about
your
machine
before
we
move,on:
First
of
all,
your
programmable
calculator
is
versatile
and
powerful
—
and
you
can
do
all
sorts
of
manual
calculations
right
off
the
keyboard
anytime.
Secondly,
your
calculator
is
programmable
—
and
all
this
really
means
is
that
it
can
remember
keystroke
instructions
you
give
it,
then
go
back
and
push
its
own
buttons
for
you.
We've
seen
that
programming
the
machine
to
follow
instructions
is
quite
easy.
*
Just
push
¢Enter
your
keystroke
instructions.
¢Push
[RN
again
*Push
(don't
forget
this
one
—
your
program
needs
to
start
at
the
right
place,and
starts
it
back
at
the
first
step.)
*From
then
on
in,
you
just
enter
numbers
you
want
to
work
on
and
press
[R#)
.
This
new
dimension
of
programmability
brings
several
special
benefits
to
you.
Faster
and
more
accurate
calculations
—
particularly
in
repetitive
situations
—
are
now
possible.
You'll
find
it
easier
to
use
your
calculator
as
part
of
decision-making
processes,
in
exploring
relationships
in
math,
and
in
a
host
of
everyday
life
and
career
applications
Thirdly,
and
probably
most
important,
your
programmable‘calculator
should
be
a
lot
of
fun
to
use!
Don't
be
afraid
to
explore
with
it.
1-9

A TOUR OF
KEYS AND FUNCTIONS
Your
calculator
is
a
powerful
problem-solving
device
that's
especially
designed
for
easy
use.
You've
already
seen
some
simple
programs
in
action,
and
we'll
continue
to
discuss
the
programming
side
of
your
calculator's
capability
in
later
chapters.
But
apart
from
its
programmability
—
your
calculator
is
a
versatile
and
powerlul
“slide
rule’
calculator.
It's
always
ready
to
handle
calculations
right
from
the
keyboard.
In
this
chapter
we'll
be
touring
the
direct
problem-solving
keys
on
your
machine
—
the
keys
you
can
use
immediately
to
get
answers.
Then,
in
later
chapters,
we'll
show
you
how
these
basic
keys
can
be
used
with
the
others
on
the
keyboard
to
create
programs.
The
keyboard
of
your
calculator
has
been
organized
and
arranged
in
a
common
sense,
straightforward
way.
You
can
easily
do
simple
things
like
balancing
your
checkbook
or
adding
your
grocery
bill,
as
well
as
complex
technical
problems
-
The
usefulness
of
any
machine
or
tool,
however,
depends
on
the
person
who
operates
it.
You'll
want
to
get
familiar
with
all
of
its
features
—
all
of
what
it
will
(and
will
not)
do
for
you.
To
get
full
use
from
your
calculator,
take
the
few
minutes
necessary
just
to
see
each
key
in
action!
To
make
it
easy
for
you
to
get
acquainted,
this
tour
is
divided
into
three
major
sections:
Basic Keys and Functions
Advanced/'‘'Slide
Rule"
Keys
&
Functions
Statistical Functions & Keys
For
those
of
you
who
have
already
owned
or
are
familiar
with
an
advanced
slide
rule
calculator
—
you
may
want
to
skip
to
Chapter
3
and
get
right
into
programming.
If
there
are
some
keys
on
the
machine
you
don't
know
about,
however,
we'd
advise
that
you
take
this
quick
tour.
Take
out
your
calculator
and
keep
it
handy
as
we
go
through
the
keys
—
relax
—
and
let's
go.

SECTION 1: BASIC
KEYS AND FUNCTIONS
We'll begin with a brief look at the basic ‘‘chassis” on your calculator,
before we go on to check out the ‘extra options’’. These basics are what
allow you to get information into and out of the machine — and let you
handle the arithmetic part of mathematics quickly and accurately.
Tre DispLay
Whenever you first turn on your calculator, you should see a single zero
in the display indicating that all is well, the machine's on, and it’s ready
for action. Just turning the calculator OFF and ON clears everything
inside. To check out your calculator's display, press the [8] key, the
decimal point key [+], the change sign key 4], and then push the [8] key
until the whole display is lit up. You can enter up to 8 digits into your
calculator at any one time, for both positive and negative numbers.
(Entries after the 8th digit are ignored.) For extra accuracy, however,
results of calculations are computed to eleven digits inside your
calculator, and then rounded off to 8 digits in the display. Notice that the
negative sign stays immediately to the left of any negative number in the
display, for easy reading.
To continue the tour press the clear key Gig) in the upper right corner of
keyboard, and read on.
AND [INV]: Tue “Dua. Function” Keys
Your calculator is loaded with functions to make all sorts of calculations
easy and accurate. To allow you access to all of this power, without
loading the machine with keys, many of the calculator keys have more
than one function. The first function of the key is printed right on it. To
use the first function on any key — just press it. The second function of
a key is printed right above it. To use second functions, just press the [2nd]
key, (upper left on the keyboard), and then the key right below the
function you wish to use. (We'll indicate second functions in this book
with a black background key MM. For example, to put a 7 in the display
you'll use the key sequence )
The inverse key — [iN¥) — also provides additional calculator functions
without increasing the number of keys on the keyboard. The [IW] key
“reverses” the purpose or function of certain keys. Note: In cases where
you need to use both the [2d] and [IW) keys — you can use them in either
order and get the same result. If you use the [IN] before a function with
no inverse, it’s simply ignored.

SECTION 1: BASIC
KEYS AND FUNCTIONS
CLEARING THE CALCULATOR
There are several procedures that allow you to clear various parts of your
calculator, or to clear the entire machine — depending on your needs as
you proceed through a problem.
[CE] The [£8] (clear entry) key clears the last number you entered into
the calculator, as long as that number wasn't followed by a
function or operation key. (So if you accidentally hit a [5] instead
of a [Jin the middle of an entry, just hit (c) and try again.) This
key will also stop the display from flashing if you've created an
error condition in your calculator (we'll say more about this later).
The [€€] key, however, doesn't affect pending operations, what's
stored in the memories, or calculated results.
(CLR]_tThe
(Gl
(clear)
key
(upper
right
on
your
machine)
essentially
clears
the
entire machine,
except
for
statistical
data
stored
in the
memories,
settings
made on
the
display
format,
and
program
steps.
—
This
allows
you
to
clear
only
the
“'t’
register
(or
"'t”
memory).
This
capability
is
beneficial
in
programming
and
with
statistical
functions.
We'll
look
at
it
in more
detail
later.
[INV] — This key sequence clears everything in the machine
except program steps and decimal settings. (Technically, this
doesn’t
clear
the
first
two
registers
of
the
math
stack,
but
this
will
seldom be a problem.)
OFF-ON
—
Turning
the
calculator
OFF,
then
ON
again
clears
everything.
In
fact,
it's
one
sure
way
to
quickly
clear
all
your
program
steps,
memories,
display
settings,
everything!

SECTION 1: BASIC
KEYS AND FUNCTIONS
[0 ]-(9 | (+ | [+4] - Dara Ewray Kevs
Your
calculator
operates
with
a
full
floating
decimal
point,
and
numbers
are
entered
into
the
machine
with
the
data
entry
keys
(o]-
1-764).
As
you
enter
any
number,
the
decimal
point
stays
to
the
right
of
your
entry
until
the
decimal
point
key
((=)
is
pressed.
After
pressing
the
decimal
key,
the
fractional
part
of
the
number
is
keyed
in,
and
the
decimal
point
floats
to
the
left
with
it.
To
change
the
sign
of
a
number
in
the
display,
just
push
the
change
sign
key
-Jonce.
(Pressing
F5
again
changes
the
sign
back
again.)
C+ (=) (6) 2] anv [=] - Basic Oreration Keys
Basic
arithmetic
is
handled
with
the
5
basic
operation
keys:
[+]
[=]
[)
(Jand
().
Your
calculator
is
equipped
with
a
simple
and
powerful
entry
system
—
the
AOS™
entry
method.
This
entry
system
makes
problem
solution
exceptionally
easy.
You
just
key
in
the
problem
the
way
it's
written,
press[=],
and
get
your
result.
The
amazing
feature
of
the
AOS
system
is
that
it
automatically
sorts
out
mixed
operations
in
a
problem
for
you,
and
applies
them
in
the
correct
order
as
it
calculates
your
result.
(We'll
say
more
about
the
AOS
entry
system
in
the
next
section.)
When
you
press
the
[=]
key,
all
pending
operations
(things
waiting
to
happen
inside
your
calculator)
are:
completed.
You
get
your
result,
and
the
calculator
is
cleared
—
ready
to
start
on
the
next
problem.
Example: Calculate 15 + 7X31 —4=?
Press Disptay/CoMMENTS
187476031
Ei4e) 228.
Note:
The
AOS
system
of
entry
makes
it
easy
to
get
the
right
answer
in
this
example,
and
not
all
calculators
have
it.

SECTION 1: BASIC
KEYS AND FUNCTIONS
Tue AOS™ Entry Metuop
Mathematics
is
a
science
which
adheres
to
a
variety
of
rules,
One
such
rule
is
that
it
never
permits
two
different
answers
to
the
same
series
of
operations.
Because
of
this
requirement
—
one
solution
for
any
computation
—
mathematicians
have
established
a
set
of
universally
accepted
rules
when
mixed
operations
are
used
in
one
calculation.
For
example,
the
problem:
3+10-2x14+7=?
has
only
one
right
answer!
(Know
what
it
is?
It's
9.)
You
can
key
this
problem
directly,
left
to
right,
into
your
calculator
equipped
with
the
AOS
entry
system
and
you'll
get
the
correct
answer.
The
calculator
sorts
the
operations
you
enter,
applies
them
in
the
correct
order,
and
lets
you
see
what
it's
doing along
the
way.
Your
calculator’s
AOS
entry
system
is
quite
an
organizer!
It
sorts
and
then
performs
operations
it
receives
from
you
in
the
following
universally
accepted
order:
1)
Special
Single
Variable
function
keys
(
[#4]
(¥]
etc.)
—
act
on
the
displayed
number
immediately
—
as
soon
as
you
push
the
key.
(We'll
talk
more
about
each
of
these
keys
later
in
the
‘tour’
—
but
they
include
all
the
keys
for
the
trig
and
log
functions
and
their
inverses,
as
well
as
square
root,
and
reciprocal
keys.)
2)
Exponential
calculations
B=)
and
[iN]
(or
¥/y)
are
done
next
(we'll
discuss
these
further
in
a following
section).
3)
Multiplications
and
divisions
are
completed
next,
in
order
from
left
to
right,
followed
by
4)
Additions
and
subtractions,
in
order
from
left
to
right.
Finally,
the
equals
key
=)
completes
all
operations.
When
you
were
in
elementary
school
you
may
have
heard
the
memory
aid
“My
Dear
Aunt
Sally’
(MDAS)
applied
to
help
you
remember
the
last
part
of
this
hierarchy:
Multiplications
and
Divisions
first,
in
order
left
to
right
—
then
Additions
and
Subtractions
in
the
same
way.
Ina
calculator
equipped
with
the
AOS
entry
system
—
all
of
this
is
remembered
for
you.
There
are
cases
in
problem-solving
where
you
may
want
to
exactly
specify
the
order
in
which
an
expression
is
evaluated,
or
the
way
in
which
a
problem
is
completed.
In
these
cases
you
can
control
the
order
with
the
parentheses
keys
(C1)
(1discussed
in
the
next
section.
Parentheses
demand
a
special
first
level
of
attention
in
mathematics
—
and
they're
treated
that
way
by
your
calculator.
2-5

nT
ee
SECTION
1:
BASIC
KEYS
AND
FUNCTIONS
EE
eee
CC)
(1
J-
Pasentneses
Keys
Ina
variety
of
problems
you
may
need
to
specify
the
exact
order
in
which
expressions
are
evaluated,
or
the
way
in
which
numbers
are
grouped,
as
a
problem
is
solved.
Parentheses
give
you
a
way
to
“cluster”
numbers
and
operations.
By
putting
a
series
of
numbers
and
operations
in
parentheses
you
tell
the
calculator:
“Evaluate
this
little
problem
first
—
down
to
a
single
number
result,
then
use
this
result
for
the
rest
of
the
calculation.”
Within
each
set
of
parentheses
your
calculator
will
operate
according
to
the
rules
of
algebraic
hierarchy.
You
should
use
parentheses
if
you
have
any
doubts
in
your
mind
about
how
the
calculator
will
handle
an
expression.
There
is
a
limit
to
the
number
of
parentheses
that
can
be
opened
at
one
time,
and
how
many
“pending”
operations
can
be
handled.
Your
calculator
allows
you
to
open
nine
parentheses
at
one
time,
with
up
to
four
operations
pending
—
exceeding
these
limits
results
in
a
flashing
display.
(You'll
rarely
encounter
this
as
a
problem.)
Note
an
important
point
when
using
parentheses.
You
may
often
see
equations
or
expressions
written
with
parentheses
to
indicate
implied
multiplication:
(2+1)
(8+2)=
15.
Your
calculator
will
not
recognize
implied
multiplications.
You
must
key
in
the
operation
between
the
parentheses:
Cem
mbw34)201
Es.
Here's
an
example
on
using
parentheses:
(8
x
4)
+
(9
x
—
19)
_
(8+10+7)
x
2
Solution:
In
problems
of
this
type
—
you
want
the
calculator
to
evaluate
the
entire
numerator,
then
divide
by
the
entire
denominator.
You
can
be
sure
of
this
taking
place
by
placing
an
extra
set
of
parentheses
around
the
numerator
and
denominator
as
you
key
the
problem
in.
Evaluate
Press
DispLay/COMMENTS
lomso404
92.
(8x4)
displayed
cosGa19e4
OI
OO
-—199.
The
value
of
the
numerator
(O03
G@I10G)7
060205
8.8571429
Value
of
denominator
3)
—15.693548
The
final
result.
2-6

SECTION
1:
BASIC
KEYS
AND
FUNCTIONS
Memory
Keys
There
are
8
muljti-purpose
memories
available
for
you
to
use
in
your
calculator.
These
memories
are
special
locations
in
the
machine
where
you
can
store
numbers
you
may
need
to
use
later
on.
The
memories
are
a
real
bonus
—
and
in
many
ways
give
you
“'several
calculators”
in
one,
since
you
can
store,
recall
or
perform
arithmetic
on
the
numbers
in
the
memories
without
affecting
calculations
you
have
in
progress
in
the
“main
machine”,
The
[6]
and
(A)
keys
will
not
affect
what's
in
the
memories
—
but
you
can
use
the
[INV]
[2nd]
I
key
Sequence
to
clear
them
all
out
if
you
need
to.
(Turning
the
calculator
OFF
and
ON
does
this,
too.)
Since
you
have
8
memories
you
need
to
tell
the
machine
which
one
you
want
to
work
with
at
any
given
time.
Every
time
you
push
a
memory
key
you
need
to
follow
it
immediately
with
the
number
of
the
memory
you
are
using
(n=
0,
1,
2/3,
4,
5,6,
or
7).
This
tells
the
machine
which
one
of
the
8
memories
you're
referring
to
at
the
moment.
The
operations
of
the
memory
keys
is
pretty
much
“common
sense"
as
shown
below.
[STO]
n
—
Tue
Store
Key
This
key
just
“stores”
the
displayed
number
in
the
memory
you
specify
with
n.
(n=0,1,2,...7).
(Any
number
previously
stored
in
memory
n
is
automatically
cleared
out
first.)
n
—
Tue
Recat
Key
Any
time
you
press
[RéiJn,
the
number
stored
in
memory
n
appears
in
the
display
and
can
be
used
in
operations
and
calculations.
The
number
remains
in
the
memory
after
you
press
[R@)n,
and
you
can
recall
the
value
from
any
memory
as
many
times
as
you
need
to
in
any
calculation.
A
stored
number
remains
in
memory
until
you
alter
it
with
another
memory
operation,
the
[INV)
(2na)
[iy
clearing
operation,
or
by
turning
the
calculator
off.