A Comprehensive Approach and Analysis of Reverse Converters for a Class of Moduli Sets

The reverse conversion is one of the hardest inter-modular operations in Residue Number Systems (RNS). Conse-quently, a significant amount of research in RNS has focused on developing efficient reverse converters for different moduli sets. This paper introduces a comprehensive approach to designing RNS reverse converters for a class of extended moduli sets. The proposed approach unifies the solutions in the related state-of-the-art using mathematical operators that are easily mapped to regular hardware structures. Additionally, a new set is added to the considered class of moduli sets, illustrating how the presented approach can be applied in practice. The results show that the proposed reverse converters outperform the related state-of-the-art with reductions up to 13.61 %, 20.74%, and 21.39% in delay, circuit area, and power consumption, respectively.