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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

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5 Author(s)
Molahosseini, A.S. ; Dept. of Comput. Eng., Islamic Azad Univ., Tehran, Iran ; Navi, K. ; Dadkhah, C. ; Kavehei, O.
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In this paper, we introduce two new 4-moduli sets {2n-1, 2n, 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 5 n-bit DR moduli set {2n-1, 2n, 2n+1, 2n-1-1, 2n+1-1}. Also, New CRT-I is used to achieve a high-performance reverse converter for the moduli set {2n-1, 2n+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} .

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Circuits and Systems I: Regular Papers, IEEE Transactions on  (Volume:57 ,  Issue: 4 )