We have seen that a full adder is a combinational circuit that forms the arithmetic sum of three input bits. It consists of three inputs and two outputs. Two of the input variables,
K-map simplification for carry and sum
The Boolean function for sum can be further simplified as follows :
With this simplified Boolean function circuit for full-adder can be implemented as shown in the Fig. 3.17.
A full-adder can also be implemented with two half-adders and one OR gate, as shown in the Fig. 3.18. The sum output from the second half-adder is the exclusive-OR of Cin and the output of the first half-adder, giving