On Design of Parity Preserving Reversible Adder Circuits

In this paper novel parity preserving reversible logic blocks are presented and verified. Then, we present cost-effective parity preserving reversible implementations of Full Adder, 4:2 Compressor, Binary to BCD converter, and BCD adder using these blocks. The proposed parity preserving reversible BCD adder is designed by cascading the presented 4-digit parity preserving reversible Full Adder and a parity preserving reversible Binary to BCD Converter. In this design, instead of realizing the detection and correction unit, we design a Binary to BCD converter that its inputs are the output of parity preserving binary adder, and its output is a parity preserving BCD digit. In addition, several theorems on the numbers of garbage outputs, constant inputs, quantum cost and delay of the designs have been presented to show its optimality. In the presented circuits, the delay and the quantum cost are reduced by deriving designs based on the proposed parity preserving reversible blocks. The advantages of the proposed designs over the existing ones are quantitatively described and analysed. All the scales are in the Nano-metric area.