A Reverse Converter and Sign Detectors for an Extended RNS Five-Moduli Set

This paper deals with the extended five moduli set <inline-formula> <tex-math notation="LaTeX">$ \left({{2^{2n+p}, 2^{n}-1, 2^{n}+1, 2^{n}-2^{\frac {n+1}{2}}+1, 2^{n}+2^{\frac {n+1}{2}}+1}}\right)$ </tex-math></inline-formula> where <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> is a positive odd integer and <inline-formula> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> is nonnegative integer such that <inline-formula> <tex-math notation="LaTeX">$p\leq \frac {n-5}{2}$ </tex-math></inline-formula>. The paper proposes an efficient residue-to-binary converter along with a converter-based sign detector for this extended set. The paper also presents a residue-to-residue transformer that transforms the same five-moduli set to the three-moduli set <inline-formula> <tex-math notation="LaTeX">$(2^{2n+p}, 2^{2n}-1, 2^{2n}+1)$ </tex-math></inline-formula>. Such a transformer enables the five-moduli set to utilize components that are (or will be) designed for the three-moduli set such as sign detectors.

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