Implement of Half adder
Adders
Digital computers perform a variety of information processing tasks. Among the basic tasks encountered are the various arithmatic operartions. The most basic arithmatic operation is the additon of two binary digits.
A combinational circuit that performs the addition of two bits is called a half adder. Again the combinational circuit that performs addition of three bits (Two significant bits and a previous carry) is called Full adder.
Half Adder
A half adder is a combinational circuit with two binary inputs (augend and addend bits) and two binary outputs (sum and carry bits). It adds two inputs (A and B) and produces the sum (S) and the carry (C) bits. It is an arithmatic circuit used to perform the arithmatic operaton of addition of two single bit words.
| Inputs | Outputs | ||
|---|---|---|---|
| A | B | C | S |
| 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 0 |
The characteristic equation of a Half Adder is expressed as:
Sum = AB̅ + A̅B = A⨁B
Cout = AB
When any of the inputs A and B is equal to 1, the Sum is 1. Otherwise, it is 0. Carry Cout is 1 only when both the inputs are 1.
Full Adder
The combinational circuit that performs addition of three bits (Two significant bits and a previous carry) is called Full adder.
| Inputs | Outputs | |||
|---|---|---|---|---|
| A | B | Cin | Cout | S |
| 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 |
The characteristic equation of a Full Adder is expressed as:
Sum = A̅B̅Cin+A̅BCin+AB̅C̅in+ABCin = (AB̅+A̅B)C̅in+(AB+A̅B̅)Cin = (A⨁B)C̅in+(¯(A⨁B))Cin = A⨁B⨁Cin
Cout = A̅BCin+AB̅Cin+ABC̅in+ABCin = AB+(A⨁B)Cin = AB+ACin+BCin
The Sum is High i.e. 1 only when odd number of the inputs are High. Carry Cout is High i.e. 1 only when more than one input are High.