Efficient reverse converter designs for the new 4-moduli sets {2(n)-1, 2(n), 2(n)+1, 2(2n+1)-1} and {2(n)-1, 2(n)+1, 2(2n), 2(2n)+1} based on new CRTs

Molahosseini, A.Navi, K.Dadkhah, C.Kavehei, O.Timarchi, S.2010-08-252010-08-252010IEEE Transactions on Circuits and Systems Part 1: Regular Papers, 2010; 57(4):823-8351549-83281558-0806http://hdl.handle.net/2440/60041In this paper, we introduce two new 4-moduli sets {2n-1, 2 n, 2n +1, 22n + 1-1} and {2n-1, 2n +1, 22n, 22n +1} for developing efficient large dynamic range (DR) residue number systems (RNS). These moduli sets consist of simple and well-formed moduli which can result in efficient implementation of the reverse converter as well as internal RNS arithmetic circuits. The moduli set {2n-1, 2n, 2n +1, 22n + 1-1} has 5n-bit DR and it can result in a fast RNS arithmetic unit, while the 6n-bit DR moduli set {2n-1, 2n +1, 22n, 22n +1} is a conversion friendly moduli set which can lead to a high-speed and low-cost reverse converter design. Next, efficient reverse converters for the proposed moduli sets based on new Chinese remainder theorems (New CRTs) are presented. The converter for the moduli set {2n-1, 2n, 2n +1, 22n + 1-1} is derived by New CRT-II with better performance compared to the reverse converter for the latest introduced 5n-bit DR moduli set {2n-1, 2n, 2n+1, 2 n-1}-1, 2n + 1-1}. Also, New CRT-I is used to achieve a high-performance reverse converter for the moduli set {2n-1, 2 n+1, 22n, 22n+1}. This converter has less conversion delay and lower hardware requirements than the reverse converter for a recently suggested 6n-bit DR moduli set {2n-1, 2n +1, 22n-2, 22n + 1-3}. © 2006 IEEE.en© 2010 IEEEComputer arithmeticnew Chinese remainder theorems (New CRTs)residue arithmeticreverse converterresidue number system (RNS)Efficient reverse converter designs for the new 4-moduli sets {2(n)-1, 2(n), 2(n)+1, 2(2n+1)-1} and {2(n)-1, 2(n)+1, 2(2n), 2(2n)+1} based on new CRTsJournal article002009658210.1109/TCSI.2009.20266810002765352000092-s2.0-7795102549334971