In electronics, an adder is a digital circuit that performs addition of numbers. In many computers and other kinds of processors, adders are used not only in the arithmetic logic units, but also in other parts of the processor, where they are used to calculate addresses, table indices, and etc.
Half Adder
A half adder adds two one-bit binary numbers X and Y. It has two outputs, S and C (the value theoretically carried on to the next addition); the final sum is 2C + S.
The Firgure below is shown simplest half-adder design, incorporates an XOR gate for S and an AND gate for C. Half adders cannot be used compositely, given their incapacity for a carry-in bit.
Full adder diagram

Truth Table of half Adder