Efficient Reverse Converters for 4-Moduli Sets {22n-1-1, 2n, 2n+1, 2n-1} and {22n-1, 22n-1-1, 2n+1, 2n-1} Based on CRTs Algorithm

• Published in: Circuits, systems, and signal processing Vol. 33; no. 10; pp. 3145 - 3163
• Main Authors: Noorimehr, Mohammad Reza, Hosseinzadeh, Mehdi, Navi, Keivan
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.10.2014; Springer Nature B.V
• Subjects: Algorithms; Circuits; Circuits and Systems; Converters; Delay; Dynamic range; Electrical Engineering; Electronics and Microelectronics; Engineering; Hardware; Instrumentation; Residue number systems; Signal,Image and Speech Processing; Texts; Residue number system (RNS); Computer arithmetic; Reverse converter; Chinese Remainder Theorem (CRT)
• ISSN: 0278-081X; 1531-5878
• DOI: 10.1007/s00034-014-9798-1

Speed and complexity of a reverse converter are two important factors that affect the performance of a residue number system. In this paper, two efficient reverse converters are proposed for the 4-moduli sets {2 2 n - 1 - 1 , 2 n , 2 n + 1 , 2 n - 1 } and {2 2 n - 1 , 2 2 n - 1 - 1 , 2 n + 1 , 2 n - 1 } with 5 n -bit and 6 n -bit dynamic range, respectively. The proposed reverse converter for moduli set {2 2 n - 1 - 1 , 2 n , 2 n + 1 , 2 n - 1 } has been designed based on CRT and New CRT-I algorithms and in two-level structure. Also, an efficient reverse converter for moduli set {2 2 n - 1 , 2 2 n - 1 - 1 , 2 n + 1 , 2 n - 1 } has been designed by applying New CRT-I algorithm. The proposed reverse converters are based on adders and hence can be simply implemented by VLSI circuit technology. The proposed reverse converters offer less delay and hardware cost when compared with the recently introduced reverse converters for the moduli sets {2 n + 1 , 2 n - 1 ,2 n , 2 2 n + 1 - 1 } and {2 n + 1 , 2 n - 1 , 2 2 n , 2 2 n + 1 - 1 }.