Titlebook: Residue Number Systems; Algorithms and Archi P. V. Ananda Mohan Book 2002 Springer Science+Business Media New York 2002 VLSI.algorithm.algo

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Introduction,i of the Ming dynasty (1368AD–1643AD). Later, Euler presented a proof for the Chinese Remainder Theorem (CRT) in 1734. In the twentieth Century, Lehmer, Svoboda and Valach built hardware using RNS and much work was done at various laboratories during 1950’s and 1960’s. The text books by Szabo and Ta

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Forward and Reverse Converters for The Moduli Set {2k-1, 2k, 2k+1},forward and reverse conversion, scaling and other operations [Anan00b]. In this Chapter, VLSI architectures for forward and reverse conversion are discussed in detail. Related moduli sets {2.-1, 2., 2.-1}, {2n, 2n+1, 2n-1} and {2n, 2n+1, 2n+2} also will be considered.

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Multipliers For RNS,hey have application in other areas such as Cryptography as well. The realization of multipliers could be using ROMs or could be without ROMs. Both these approaches will be studied in detail in this Chapter.

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Error Detection and Correction in RNS,e some faults may occur which may be corrected by reconfiguring or bypassing the faulty device using additional residues corresponding to additional moduli. These additional moduli are termed as redundant moduli. The errors evidently can occur in the residues or redundant residues. These redundant r

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Quadratic Residue Number Systems,n etc. However, under certain special cases of choice of moduli, the complete decoupling of computation of real and imaginary parts of the result is feasible. Nussbaumer [Nuss76] suggested that Fermat primes of the type 4k+l have this property. Later, this advantage has been extended to any primes o

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Quadratic Residue Number Systems,RNS is the restriction on the type of moduli. Another technique which allows any modulus but with increase in number of multiplications has also been found known as Modified Quadratic Residue Number System (MQRNS) [Sode84b]. This will also be discussed in detail in this Chapter.

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