A Residue-to-Binary Converter for the Extended Four-Moduli Set $\{2^{n}-1, 2^{n}+1, 2^{2n}+1, 2^{2n+p}\} $

This brief presents a residue-to-binary converter for the moduli set <inline-formula> <tex-math notation="LaTeX">$\{2^{n}-1, 2^{n}+1, 2^{2n}+1, 2^{2n+p}\} $ </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> is a positive integer and <inline-formula> <tex-math notation="LaTeX">$0\leq p \leq n-2 $ </tex-math></inline-formula>. The converter consists of three simplified <inline-formula> <tex-math notation="LaTeX">$4n$ </tex-math></inline-formula>-bit carry-save adders (CSAs) along with a modulo <inline-formula> <tex-math notation="LaTeX">$(2^{4n}-1) $ </tex-math></inline-formula> adder. The main contribution of this brief is reducing the requirements of the proposed CSA network, which has impacted the area, delay, power and energy. Compared with four-moduli and five-moduli sets that have the dynamic range <inline-formula> <tex-math notation="LaTeX">$2^{v}(2^{4n}-1) $ </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">$ v=n {~\mbox {or }} 2n$ </tex-math></inline-formula>, the proposed converter resulted in the average area, delay, power, and energy reductions of 22.7%, 9.2%, 17.8%, and 24.5%, respectively. Moreover, the throughput rate per unit area has been improved by an average of 48.7%.

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