Adder is one of the important combinational circuit to perform the Arithmetic Logical operations.
A half adder is used to add two single digit binary number. First step in designing the Half Adder circuit is to have truth table. Before that let see the binary addition rules.
Using the k-map, we can get the optimised Boolean expression for sum and carry.
Boolean expression for sum
Boolean expression for carry
From above equations , the Half adder circuit implemented as below