Adder based residue to binary number converters for (2n-1, 2n, 2n+1)

Based on an algorithm derived from the new Chinese remainder theorem I, we present three new residue-to-binary converters for the residue number system (2/sup n/-1, 2/sup n/, 2/sup n/+1) designed using 2n-bit or n-bit adders with improvements on speed, area, or dynamic range compared with various previous converters. The 2n-bit adder based converter is faster and requires about half the hardware required by previous methods. For n-bit adder-based implementations, one new converter is twice as fast as the previous method using a similar amount of hardware, whereas another new converter achieves improvement in either speed, area, or dynamic range compared with previous converters.

[1]  Yuke Wang.  Residue-to-binary converters based on new Chinese remainder theorems , 2000 .

[2]  Amar Aggoun,et al.  Novel RNS structures for the moduli set (2 n −1, 2 n , 2 n +1) , 1995 .

[3]  B. Vinnakota,et al.  Fast conversion techniques for binary-residue number systems , 1994 .

[4]  Michael A. Soderstrand,et al.  Residue number system arithmetic: modern applications in digital signal processing , 1986 .

[5]  M. K. Ibrahim,et al.  Novel RNS structures for the moduli set (2n - 1, 2n, 2n + 1) and their application to digital filter implementation , 1995, Signal Process..

[6]  Richard Conway,et al.  Fast Converter for 3 Moduli RNS Using New Property of CRT , 1999, IEEE Trans. Computers.

[7]  S. Andraos,et al.  A new efficient memoryless residue to binary converter , 1988 .

[8]  Yuke Wang.  New Chinese remainder theorems , 1998, Conference Record of Thirty-Second Asilomar Conference on Signals, Systems and Computers (Cat. No.98CH36284).

[9]  Richard I. Tanaka,et al.  Residue arithmetic and its applications to computer technology , 1967 .

[10]  Salam N. Saloum,et al.  An efficient residue to binary converter design , 1988 .

[11]  F. Petry,et al.  The digit parallel method for fast RNS to weighted number system conversion for specific moduli (2/sup k/-1,2/sup k/,2/sup k/+1) , 1997 .

[12]  Kai Hwang,et al.  Computer arithmetic: Principles, architecture, and design , 1979 .

[13]  Yuke Wang,et al.  A new algorithm for RNS decoding , 1996 .

[14]  A. Dhurkadas.  Comments on "An efficient residue to binary converter design" by K.M. Ibrahim and S.N. Saloum , 1990 .

[15]  T. Srikanthan,et al.  Breaking the 2n-bit carry propagationbarrier in residue to binary conversion for the [2n-1. 2n, 2n + 1] modula set , 1998 .

[16]  T. Srikanthan,et al.  Breaking the 2n-bit carry propagation barrier in residue to binary conversion for the [2/sup n/-1, 2/sup n/, 2/sup n/+1] modula set , 1998 .

[17]  Fred J. Taylor,et al.  An efficient residue-to-decimal converter , 1981 .

[18]  W. Kenneth Jenkins,et al.  Techniques for residue-to-analog conversion for residue-encoded digital filters , 1978 .

[19]  S. Piestrak.  A high-speed realization of a residue to binary number system converter , 1995 .

[20]  Harvey L. Garner,et al.  RESIDUE NUMBER SYSTEM ENHANCEMENTS FOR PROGRAMMABLE PROCESSORS , 2008 .