A full adder accepts two input bits and an input carry and generates a sum and a carry, in its output. The logic symbol of a full adder is,
Truth table of a full adder is given below,
Expression for Sum and Carry can be derived using the following K-Map.
A full adder should add Cout with other input bits A and B. We have used XOR operation to perform addition of two bits A and B. To add input carry, Cin, with the input bits, it must be XOR-ed with A⊕B. Logic expression for sum and carry can be derived from the truth table.
The expression for Cout can be simplified into
This means two XOR gates are used to implement full adder sum function. The first will generate A⊕B and the second will add this output with an input carry Cin. The complete logic circuit of a full adder will be,
Implementation of Full Adder using Half Adders
A full adder can also be implemented using two half adder as follows.