Digital Logic Structures: Chapter 3

Digital Logic Structures: Chapter 3

COMP 2610Dr. James Money

COMP 2610

1

Full Adder

In order to implement a full adder circuit, let’s

consider our method for adding binary

numbers

Recall that this is done in a similar way to

long addition for decimal numbers

Full Adder

Carry: 100110000

110011010

+ 011011100

001110110

Full Adder

Note that for each column of bits, we need

three values:

– Bit from value 1 - ai

– Bit from value 2 - bi

– Carry Bit – carryi

Full Adder

The two outputs of the add are:

– The result of the add is stored in si

– The carry value is stored in carryi+1

When can now formally turn this into a truth

table for adding one bit

Full Adder

ai bi carryi carryi+1 si

0 0 0 0 0

0 0 1 0 1

0 1 0 0 1

0 1 1 1 0

1 0 0 0 1

1 0 1 1 0

1 1 0 1 0

1 1 1 1 1

Full Adder

Full Adder

Figure 3.15 is on the previous slide

PLAs

A Programmable Logic Array (PLA) is a

common building block for building logical

functions

It consists of an array of AND gates, an array

of OR gates, and some way to connect these

outputs

PLAs

PLAs

For a PLA, we consider a truth table with n

inputs and m outputs

You will need 2n AND gates and m OR gates

We then program the connections between

the AND and OR gates

The full adder is an example of this

Logical Completeness

There is an important property to notice before

we leave logic circuits called logical

completeness

We’ve shown that we only need AND, OR,

NOT to form a logic circuit using PLAs

We say {AND, OR, NOT} is logically complete

because of this