A half-adder is a combinational circuit that adds two single-bit binary numbers and produces the sum and carry as output. The half-adder has two inputs and two outputs, one for the sum (S) and one for the carry (C). It can be implemented using basic logic gates such as AND, XOR, and NOT gates.

The truth table for a half-adder is shown below:

The implementation of a half-adder using AND and XOR gates is shown below:

In this circuit, the two input bits A and B are connected to an XOR gate and an AND gate. The XOR gate produces the sum bit (S) and the AND gate produces the carry bit (C).

The XOR gate produces a high output (1) when one input is high (1) and the other input is low (0), which gives the sum bit. The AND gate produces a high output (1) when both inputs are high (1), which gives the carry bit.

The half-adder is the building block of many more complex digital circuits such as full-adders and multi-bit adders.