Topic
Residue number system
About: Residue number system is a research topic. Over the lifetime, 1482 publications have been published within this topic receiving 18824 citations.
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Book•
01 Aug 1986
626 citations
Book•
11 Sep 2007
TL;DR: This book provides an up-to-date account of RNSs and arithmetic and covers the underlying mathematical concepts of R NSs; the conversion between conventional number systems and RNSS; the implementation of arithmetic operations; various related applications are introduced.
Abstract: This book provides an up-to-date account of RNSs and arithmetic. It covers the underlying mathematical concepts of RNSs; the conversion between conventional number systems and RNSs; the implementation of arithmetic operations; various related applications are also introduced. In addition, numerous detailed examples and analysis of different implementations are provided.
423 citations
03 Mar 1959
TL;DR: The residue code is probably of little utility for general-purpose computation, but the code has many characteristics which recommend its use for special-purpose computations.
Abstract: In this paper we develop and investigate the properrties of a novel system, called the residue code or residue number system. The residue number system is of particular interest because the arithmetic operations of addition and multiplication may be executed in the same time as required for an addition operation. The main difficulty of the residue code relative to arithmetic operations is the determination of the relative magnitude of two numbers expressed in the residue code. The residue code is probably of little utility for general-purpose computation, but the code has many characteristics which recommend its use for special-purpose computations.
377 citations
TL;DR: In this paper, a technique for implementing a finite impulse response (FIR) digital filter in a residue number system (RNS) is presented, and a new hardware implementation of the Chinese Remainder Theorem is proposed for an efficient translation of residue coded outputs into natural numbers.
Abstract: A technique is presented for implementing a finite impulse response (FIR) digital filter in a residue number system (RNS). For many years residue number coding has been recognized as a system which provides a capability for the implementation of high speed multiplication and addition. The advantages of residue coding for the design of high speed FIR filters result from the fact that an FIR requires only the high speed residue operations, i.e., addition and multiplication, while not requiring the slower RNS operations of division or sign detection. A new hardware implementation of the Chinese Remainder Theorem is proposed for an efficient translation of residue coded outputs into natural numbers. A numerical example illustrates the principles of residue encoding, residue arithmetic, and residue decoding for FIR filters. An RNS implementation of a 64th-order dual bandpass filter is compared with several alternative filter structures to illustrate tradeoffs between speed and hardware complexity.
294 citations