Towards efficient modular adders based on reversible circuits

Reversible logic is a computing paradigm that has attracted significant attention in recent years due to its properties that lead to ultra-low power and reliable circuits. Reversible circuits are fundamental, for example, for quantum computing. Since addition is a fundamental operation, designing efficient adders is a cornerstone in the research of reversible circuits. Residue Number Systems (RNS) has been as a powerful tool to provide parallel and fault-tolerant implementations of computations where additions and multiplications are dominant. In this paper, for the first time in the literature, we propose the combination of RNS and reversible logic. The parallelism of RNS is leveraged to increase the performance of reversible computational circuits. Being the most fundamental part in any RNS, in this work we propose the implementation of modular adders, namely modulo 2 n -1 adders, using reversible logic. Analysis and comparison with traditional logic show that modulo adders can be designed using reversible gates with minimum overhead in comparison to regular reversible adders.