High-speed residue number system reverse converter based on new Chinese remainder theorem with fractional values

Abstract

This article proposes a novel high-speed reverse converter from the Residue Number System (RNS) to a positional number system. The proposed method is designed for arbitrary RNS moduli sets that include a power-of-two modulus and is based on a Chinese Remainder Theorem with fractional values conversion technique. Hardware simulations demonstrate that our converter outperforms the state-of-the-art designs by 34.70% to 86.11% in terms of speed, at the cost of increased silicon area and power consumption, making it particularly suitable for latency-critical applications. This performance gain makes it directly applicable to demanding RNS-based domains such as cryptography, digital signal processing, and image processing for neural networks. Furthermore, the proposed conversion method provides a foundation for efficiently implementing other complex RNS operations, including division, sign detection, and magnitude comparison.