Discrete Mathematics

86 DISCRETE MATHEMATIC..._

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The

way

to

add

is

to

work

one

column at a time, and adding the carry out

it

to

the

column

to

our

left.

Now, in principle,

we

could work

on

all columns at

the

same time, provided the carry

out

was accounted for

that is, we could

add

6 and 9 in the

ls

column, 7

and

8

in

the lOs

column

as

well as 1

and

I in the

lOOs

column.

We

need

to

account for the carries,

but

it looks as

if

we

could use three adders for the

job.

-

~

I

I I

J

I I I I

X y

X y

X y

-

cout

FA

cin

cout

FA

cin

-

cout

FA

I

sum

sum

sum

I

I

I

Fig.

1.11:

A

3-bit

adder, constructed from 2 full adders and a half adder

Well, this ...