Q.Write the Boolean expression for the carry of half adder.

Adders are the combinational circuits that carry out binary addition and form the arithmetic heart of every digital system.

A half adder adds two single bits, A and B, and produces two outputs: the sum and the carry. The sum is 1 when the inputs differ and the carry is 1 only when both inputs are 1, giving $\text{Sum} = A \oplus B$ and $\text{Carry} = A \cdot B$. It is called a half adder because it has no provision for a carry coming in from a previous stage, so it cannot by itself add multi-bit numbers. …