9.1 ADDER

An adder is a digital circuit that performs addition of digital inputs.

A simple addition of two binary bits can cause any one of four possible elementary operations, namely 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10. The first three operations produce a sum whose length is one bit. The fourth operation produces a sum whose length is 1 bit and a carry whose length is 1 bit. A higher order bit which is a result of addition is called a carry.

An adder circuit that performs the addition of two bits is called a half-adder. An adder circuit that performs the addition of three bits is called a full-adder.

Half-Adder

Inputs	Output
x	y	Carry	Sum
0	0	0	0
0	1	0	1
1	0	0	1
1	1	1	0

Writing Boolean expressions for carry and sum outputs, after simplification using the K-map technique, is simple. The final expression for carry and sum may be derived as follows:

Sum ( S)= x ? y + xy ?

Carry ( C)= xy.

Implementation for the two outputs are done separately. As a final step, the inputs x and y are combined.

Figure 9.1: Half-adder circuit.

Note	The simplification of a Boolean expression may be done in different ways and there can be other ways of implementing a half-adder circuit.