Recall laws of binary addition,
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10
Half adder is a logical circuit that is used to perform this operation. It accepts two binary digits as input and produces two binary digits, a sum and a carry, in its output. The logic symbol of a half adder is given below.
The truth table of a half adder is given below.
| A | B | ∑ | Cout |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
The expressions for Sum and Carry can be generated from the following K-Maps.
Observe that the value of Cout is 1 only when both inputs A and B are 1. Therefore Cout can be implemented as AND of two variables.
Cout = AB
Now notice that the value of Sum (∑) is 1 only when inputs A and B are not equal. Therefore the Sum can be expressed as XOR of two variables.
∑ = A⊕B
From these equations, we can implement the logic circuit required for a half adder. The Sum is generated with an XOR gate with two inputs A and B, and the Carry is generated with an AND gate.
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