Residue-to-Binary Converter for the New RNS Moduli Set $\{2^{2n}-2, \ 2^{n}-1, \ 2^{n}+1\}$

Even moduli of the $2^{n}-2$ form have been recently proposed in the design of various digital systems that utilize the Residue Number System (RNS), as an alternative to the dominating modulo channel of $2^{n}$. Although efficient arithmetic units and residue generators have been proposed for the $2^{n}-2$ channel, the residue-to-binary conversion for moduli sets that incorporate this channel still remains a challenging task. In this work, we propose a reverse converter for the novel 3-moduli set $\{2^{2n}-2,2^{n}-1,2^{n}+1\}$ that can be easily derived based on the well-known New Chinese Remainder Theorem-I (New CRT-I). Performance evaluation based on experimental CMOS VLSI results for various bit-lengths reveals a significant reduction in conversion delay and integration area of up to 49% and 27% respectively, when compared with reverse converters of similar moduli sets.