Question

Show how a half adder can be constructed using fewer gates than are used in Figure \(8\) of Section \(12.3\) when \(XOR\) gates can be used in addition to \(OR\) gates, \(AND\) gates, and inverters.

Short answer

Need only two gates to form the half adder if you allow an \(XOR\) gate and an \(AND\) gate when using half adder and input will be \(OR\) gate.

Step-by-step solution

Definition

A half adder is an electronic circuit that used to addition of numbers.

Sum bit

The sum bit is the exclusive \(OR\) of the inputs, and the carry bit is their product.

Therefore, need only two gates to form the half adder if you allow an \(XOR\) gate and an \(AND\) gate.