halfadders

A half adder is a simple combinational logic circuit that adds two single-bit binary numbers, producing a sum bit and a carry bit. It does not include a carry-in input, so it cannot perform multi-bit addition by itself.

The sum output equals A XOR B, and the carry output equals A AND B. For the input pairs (A,B): (0,0) -> sum 0, carry 0; (0,1) -> sum 1, carry 0; (1,0) -> sum 1, carry 0; (1,1) -> sum 0, carry 1.

Implementation: typically with one XOR gate and one AND gate. To add multi-bit numbers, a half adder is commonly used together with another half adder and an OR gate to form a full adder, which includes a carry-in input.

Applications and limitations: half adders are used in digital arithmetic circuits, such as arithmetic logic units and microprocessors, as well as in educational materials to illustrate binary addition. Their main limitation is the absence of a carry-in input, requiring composition with other adders for larger operands. See also full adder and ripple-carry adder for related concepts.