Enhancing Computational Efficiency in Intensive Domains via Redundant Residue Number Systems

In computation-intensive domains such as digital signal processing, encryption, and neural networks, the performance of arithmetic units, including adders and multipliers, is pivotal. Conventional numerical systems often fall short of meeting the efficiency requirements of these applications concerning area, time, and power consumption. Innovative approaches like residue number systems (RNS) and redundant number systems have been introduced to surmount this challenge, markedly elevating computational efficiency. This paper examines from multiple perspectives how the fusion of redundant number systems with RNS (termed R-RNS) can diminish latency and enhance circuit implementation, yielding substantial benefits in practical scenarios. We conduct a comparative analysis of four systems - RNS, redundant number system, Binary Number System (BNS), and Signed-Digit Redundant Residue Number System (SD-RNS)-and appraise SD-RNS through an advanced Deep Neural Network (DNN) utilizing the CIFAR-10 dataset. Our findings are encouraging, demonstrating that SD-RNS attains computational speedups of 1.27 times and 2.25 times over RNS and BNS, respectively, and reduces energy consumption by 60% compared to BNS during sequential addition and multiplication tasks.