Energy-Efficient Residue-to-Binary Conversion Based on a Modulo-Adder-Free Architecture

This paper proposes a novel residue-to-binary converter for residue number system (RNS) based on the moduli set $\{2^{n+\mathrm{k}},\ 2^{2_{n}+1}-1,2^{n}+1,2^{n}-1\}$. By adopting the new Chinese Remainder Theorem II (CRT II) and the properties of modulo 2
^k
-1 arithmetic, the research herein presented shows the possibility of designing RNS residue-to-binary converters free of modular adders. By using exclusively regular binary adders, one can leverage the design of efficient residue-to-binary converters based on the large range of optimizations proposed to those regular arithmetic units. Experimental results show over 37% energy-improvement in comparison to conventional designs, which make use of modulo adders.