This paper presents the design methods of residue-to-binary (reverse) converters for the new flexible balanced five-moduli set {2k,2n-1,2n+1,\documentclass[12pt]{minimal}
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\begin{document}$$\{ 2^k, 2^n-1, 2^n+1,$$\end{document}2n+1-1,2n-1-1}\documentclass[12pt]{minimal}
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\begin{document}$$2^{n+1}-1, 2^{n-1}-1 \}$$\end{document} for the pairs of positive integers n≥4\documentclass[12pt]{minimal}
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\begin{document}$${n \ge 4}$$\end{document} (even) and any k>0\documentclass[12pt]{minimal}
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\begin{document}$${k>0}$$\end{document}, which can provide the exact required dynamic range of the residue number system. This modulus set is the generalisation of the five-moduli set {2n,2n-1,2n+1,2n+1-1,2n-1-1}\documentclass[12pt]{minimal}
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\begin{document}$$\{ 2^n, 2^n-1, 2^n+1, 2^{n+1}-1, 2^{n-1}-1 \}$$\end{document} (n even) with only a single parameter, n. The reverse converter for the new modulus set is the first ever proposed. Synthesis results obtained for the 65 nm technology for all dynamic ranges from 19 to 88 bits have shown that the state-of-the-art converters available for the five-modulus sets with a single parameter n{2n,2n-1,2n+1,2n+1-1,2n-1-1}\documentclass[12pt]{minimal}
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\begin{document}$${\{ 2^n, 2^n-1, 2^n+1, 2^{n+1}-1, 2^{n-1}-1 \}}$$\end{document} (n even) and {2n-1,2n,2n+1,2n+1+1,2n-1+1}\documentclass[12pt]{minimal}
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\begin{document}$${\{ 2^n-1, 2^n, 2^n+1, 2^{n+1}+1, 2^{n-1}+1 \} }$$\end{document} (n odd) not only introduce from 28 to 40% larger delay but also still consume more area and power than the converters proposed here.
