Design of Efficient Reversible Logic Based Binary and BCD Adder Circuits

TL;DR

This paper introduces new, optimized reversible binary and BCD adder circuits that minimize quantum cost, delay, and ancilla inputs, advancing the design of efficient reversible computing components.

Contribution

The paper presents novel reversible ripple carry adder designs with reduced quantum cost and delay, and four new reversible BCD adder designs based on binary addition and correction methods.

Findings

Reduced quantum cost and delay in ripple carry adders

Four new reversible BCD adder designs

Designs applicable in digital signal processing

Abstract

In this work, we present a class of new designs for reversible binary and BCD adder circuits. The proposed designs are primarily optimized for the number of ancilla inputs and the number of garbage outputs and are designed for possible best values for the quantum cost and delay. First, we propose two new designs for the reversible ripple carry adder: (i) one with no input carry $c_0$ and no ancilla input bits, and (ii) one with input carry $c_0$ and no ancilla input bits. The proposed reversible ripple carry adder designs with no ancilla input bits have less quantum cost and logic depth (delay) compared to their existing counterparts in the literature. In these designs, the quantum cost and delay are reduced by deriving designs based on the reversible Peres gate and the TR gate. Next, four new designs for the reversible BCD adder are presented based on the following two approaches: (i) the addition is performed in binary mode and correction is applied to convert to BCD when required through detection and correction, and (ii) the addition is performed in binary mode and the result is always converted using a binary to BCD converter. The proposed reversible binary and BCD adders can be applied in a wide variety of digital signal processing applications and constitute important design components of reversible computing.