A combinational circuit that performs the arithmetic sum of three input bits is called full adder. It consist of three input bits that are to be added and two output bits that are sum and carry.
The truth table for half adder is:
Here x and y are the two significant bits to be added and z is the carry from the previous lower significant position.
We can derive simplified boolean function for full adder with the above truth table as :
S = x'y'z+x'yz'+xy'z'+xyz = (x⊕y)⊕z
C = xy+xz+yz
The full adder can be implemented using two half adder and one OR gate.The logic diagram for this implementation is as below: