A Reverse Converter for the Enhanced Moduli Set {2n-1, 2n+1, 22n, 22n+1-1} Using CRT and MRC

Author

Molahosseini, Amir Sabbagh ; Navi, Keivan

Author_Institution

Dept. of Comput. Eng., Islamic Azad Univ., Kerman, Iran

fYear

2010

fDate

5-7 July 2010

Firstpage

456

Lastpage

457

Abstract

The moduli set {2ⁿ-1, 2ⁿ, 2ⁿ+1, 2²ⁿ⁺¹-1} has been newly introduced for residue number system (RNS) as an arithmetic-friendly large dynamic range moduli set which can lead to a fast RNS arithmetic unit. In this paper, we present a reverse converter for the moduli set {2ⁿ-1, 2ⁿ+1, 2²ⁿ, 2²ⁿ⁺¹-1} which is derived from the moduli set {2ⁿ-1, 2ⁿ, 2ⁿ+1, 2²ⁿ⁺¹-1} by enhancing modulo 2ⁿ to 2²ⁿ. With this enhancement the DR increased to 6n+1 bits, while the speed of moduli set for arithmetic unit is not changed. The reverse converter for the moduli set {2ⁿ-1, 2ⁿ, 2ⁿ+1, 2²ⁿ⁺¹-1} is obtained by considering an existing Chinese remainder theorem (CRT)-based design of reverse converter for the subset {2²ⁿ, 2ⁿ-1, 2ⁿ+1} along with a two-channel mixed-radix conversion (MRC) algorithm for the composite set {2²ⁿ (2²ⁿ-1), 2²ⁿ⁺¹-1}.

Keywords

residue number systems; set theory; CRT; Chinese remainder theorem; MRC; RNS arithmetic unit; enhanced moduli set; residue number system; reverse converter; two-channel mixed-radix conversion; Adders; Cathode ray tubes; Computers; Converters; Delay; Hardware; Logic gates; Digital Arithmetic; Residue Number System (RNS); Reverse Converter; VLSI architecture;

fLanguage

English

Publisher

ieee

Conference_Titel

VLSI (ISVLSI), 2010 IEEE Computer Society Annual Symposium on

Conference_Location

Lixouri, Kefalonia

Print_ISBN

978-1-4244-7321-2

Type

conf

DOI

10.1109/ISVLSI.2010.105

Filename

5572741