HALF ADDER
Arithmetical operations are often an essential function of logic circuits. This truth table describes the simplest possible operation, adding two 1-bit binary numbers A and B:
The half adder circuit generally needs two outputs, these inputs are sum (S) and the carry-out (Co). The logic of each of these inputs is normally determined separately. Comparing the output values in the S column with those in the truth tables tells us that the operation for summing is equivalent to exclusive-OR. The operation for producing the carry-out digit is AND. The complete half adder needs only two gates. If required, the half adder can be built entirely from NAND gates by using an exclusive-OR circuit to produce S. The exclusive-OR circuit
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