IBM 7090 - Page 71

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Fixed-Point

Binary

(4)

000100

(11) 001001

Floating

Point

.1

x 2 011

.1001

x 2

100

Because

the

7090

works

in

binary,

all

floating-point

numbers

will

be

to

the

base

2.

Therefore,

to

represent

a

float

ing-point

number

in

the

computer,

there

is

no

need

to

carry

the

base

along

with

the

number.

This

cuts

our

need

to

representing

the

fraction

and

the

exponent.

The

exponent

is

represented

in

positions

(1-8) of

the

word

and

is

now

called

the

characteristic.

The

fraction

is

contained

in

positions

(9-35).

The

binary

point

is

to

the

left

of

the

9

bit.

The

sign

position

is

used

to

sign

the

fraction.

Word

layout

takes

this

format:

S 1

-----------

8

.9---------------------35

Characteristic

Fraction

The

value

of

the

number

in

the

characteristic

field

signifies

the

exponent

and

its

sign.

The

characteristic

is

derived

by

adding

200

8

to

the

exponent.

If

the

character-

istic

is

200

8

the

exponent

is

zero.

If

the

number

is

201

to

377,

the

exponent

is

posi-

tive.

If

it

is

0

to

177,

the

exponent

is

negative.

The

following

chart

gives

examples

of

exponential

numbers

and

their

floating

point

representation:

Exponential

Floating

Point

Binary

S 1 - 8 9 -

35

+

.1

x 2

011

+ 10000011

10000----0

-.01

x 2

001

10000001

0100-----0

+ • 1 x

2-

011

+ 01111101

1000-----0

Normal

and

Unnormal

Forms

A

floating-point

number

is

said

to

be

in

normal

form

when

the

digit

immediately

to

the

right

of

the

point

is

a

significant

bit

(1).

If

the

number

is

a

zero,

it

is

said

to

be

in

unnormal

form.

The

exception

to

this

rule

is

a

normal

zero:

a

normal

zero

is

a

floating-point

number

whose

characteristic

and

fraction

are

both

zero.

To

go

along

with

the

two

types

of

numbers,

the

instructions

are

also

divided

into

two

categories,

normal

and

unnormal.

The

difference

in

computer

operation

is

that

the

normal

instructions

always

attempt

to

produce

a

normal

answer

and

the

unnormal

in-

structions

do

not.

Arithmetic

of

Floating

Point

Addition

of

floating-point

numbers

is

done

by

adding

the

fractions

of

floating-point

numbers

which

have

equal

characteristics.

The

characteristics

are

set

equal

pre-

ceding

the

addition

by

placing

the

number

with

the

smallest

characteristic

in

the

AC.

The

fraction

is

then

shifted

right,

and

for

each

right

shift

one

is

added

to

the

character-

istic.

When

the

characteristic

of

the

AC

equals

the

characteristic

of

the

SR,

shifting

stops,

and

the

fractions

of

the

AC

and

SR

are

added.

Bits

shifted

out

of

AC(35)

enter

MQ(9).

The

sum

appears

in

the

AC

and

forms

the

most

significant

part

of

the

answer.

The

least

significant

part

is

the

bits

that

were

shifted

into

the

MQ.

The

MQ

character-

istic

is

set

2710

less

than

the

AC

characteristic

to

complete

an

unnormalized

floating

70

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