Half-adder is used to add two bits. Therefore, half-adder has two
inputs and two outputs, with SUM and CARRY. Figure shows the truth table of a half-adder. The Boolean expressions for SUM and CARRY are,
SUM = AB’+A’B
CARRY = AB
These expressions shows`that, SUM output is EX-OR gate and the CARRY output is AND gate. Figure shows the be implementation of half-adder with all the combinations including the implementation using NAND gates only.
