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RNS to Binary Conversion

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Residue Number Systems

Abstract

This important topic has received extensive attention in literature. The choice of the moduli set in RNS is decided by the speed of RNS to binary conversion for performing efficiently operations such as comparison, scaling, sign detection and error correction. Both ROM-based and non-ROM-based designs will be of interest. The number of moduli to be chosen is decided by the desired dynamic range, word length of the moduli and ease of RNS to binary conversion. There are two basic classical approaches to converting a number from RNS to binary form. These are based on Chinese Remainder Theorem (CRT) and Mixed Radix Conversion (MRC) [1]. Several new techniques have been introduced recently such as New CRT-I, New CRT-II, Mixed-Radix CRT, quotient function, core function and diagonal function. All these will be presented in some detail.

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Further Reading

  • R.E. Altschul, D.D. Miller, Residue to binary conversion using the core function, in 22nd Asilomar Conference on Signals, Systems and Computers, pp. 735–737 (1988)

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  • F. Pourbigharaz, H.M. Yassine, A signed digit architecture for residue to binary transformation. IEEE Trans. Comput. 46, 1146–1150 (1997)

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  • W. Zhang, P. Siy, An efficient FPGA design of RNS core function extractor, in Proceedings of 2005 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS), pp. 722–724 (2005)

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    P. V. Ananda Mohan

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Ananda Mohan, P.V. (2016). RNS to Binary Conversion. In: Residue Number Systems. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-41385-3_5

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