Synthesis of full-adder circuit using reversible logic

A reversible gate has the equal number of inputs and outputs and one-to-one mappings between input vectors and output vectors; so that, the input vector states can be always uniquely reconstructed from the output vector states. This correspondence introduces a reversible full-adder circuit that requires only three reversible gates and produces least number of "garbage outputs ", that is two. After that, a theorem has been proposed that proves the optimality of the propounded circuit in terms of number of garbage outputs. An efficient algorithm is also introduced in this paper that leads to construct a reversible circuit.