Residue Number Systems

Residue Number Systems

RNSs are extremely good for applications such as digital signal processing, communications engineering, computer security (cryptography), image processing, speech processing, and transforms, all of which are extremely important in computing ...

Author: Amos R. Omondi

Publisher: World Scientific

ISBN: 9781860948664

Category: Technology & Engineering

Page: 296

View: 775

Residue number systems (RNSs) and arithmetic are useful for several reasons. First, a great deal of computing now takes place in embedded processors, such as those found in mobile devices, for which high speed and low-power consumption are critical; the absence of carry propagation facilitates the realization of high-speed, low-power arithmetic. Second, computer chips are now getting to be so dense that full testing will no longer be possible; so fault tolerance and the general area of computational integrity have become more important. RNSs are extremely good for applications such as digital signal processing, communications engineering, computer security (cryptography), image processing, speech processing, and transforms, all of which are extremely important in computing today.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.
Categories: Technology & Engineering

Residue Number Systems

Residue Number Systems

[Hung4] C.Y. Hung and B. Parhami, An approximate sign detection algorithm method for residue numbers and its ... 1156-1158, Sept.1988 [Jenk77] W.K. Jenkins and B.J. Leon, The use of residue number systems in the design of Finite impulse ...

Author: P.V. Ananda Mohan

Publisher: Springer Science & Business Media

ISBN: 9781461509974

Category: Technology & Engineering

Page: 253

View: 970

There has been continuing interest in the improvement of the speed of Digital Signal processing. The use of Residue Number Systems for the design of DSP systems has been extensively researched in literature. Szabo and Tanaka have popularized this approach through their book published in 1967. Subsequently, Jenkins and Leon have rekindled the interest of researchers in this area in 1978, from which time there have been several efforts to use RNS in practical system implementation. An IEEE Press book has been published in 1986 which was a collection of Papers. It is very interesting to note that in the recent past since 1988, the research activity has received a new thrust with emphasis on VLSI design using non ROM based designs as well as ROM based designs as evidenced by the increased publications in this area. The main advantage in using RNS is that several small word-length Processors are used to perform operations such as addition, multiplication and accumulation, subtraction, thus needing less instruction execution time than that needed in conventional 16 bitl32 bit DSPs. However, the disadvantages of RNS have b. een the difficulty of detection of overflow, sign detection, comparison of two numbers, scaling, and division by arbitrary number, RNS to Binary conversion and Binary to RNS conversion. These operations, unfortunately, are computationally intensive and are time consuming.
Categories: Technology & Engineering

Embedded Systems Design with Special Arithmetic and Number Systems

Embedded Systems Design with Special Arithmetic and Number Systems

M. Etzel, W.K. Jenkins, Redundant residue number systems for error detection and correction in digital filters. IEEE Trans. Acoust., Speech, Signal Process. 28(5), 538–545 (1980) V.T. Goh, M.U. Siddiqi, Multiple error detection and ...

Author: Amir Sabbagh Molahosseini

Publisher: Springer

ISBN: 9783319497426

Category: Technology & Engineering

Page: 389

View: 923

This book introduces readers to alternative approaches to designing efficient embedded systems using unconventional number systems. The authors describe various systems that can be used for designing efficient embedded and application-specific processors, such as Residue Number System, Logarithmic Number System, Redundant Binary Number System Double-Base Number System, Decimal Floating Point Number System and Continuous Valued Number System. Readers will learn the strategies and trade-offs of using unconventional number systems in application-specific processors and be able to apply and design appropriate arithmetic operations from these number systems to boost the performance of digital systems.
Categories: Technology & Engineering

Arithmetic and Logic in Computer Systems

Arithmetic and Logic in Computer Systems

D. K. Banerji, T. Y. Cheung and V. Ganesan, “A High-Speed Division Method in Residue Arithmetic,” in 5th IEEE Symp. on Comp. Arith., 1981, pp. 158-164. . W. A. Chren Jr., “A New Residue Number System Division Algorithm,” Computers Math.

Author: Mi Lu

Publisher: John Wiley & Sons

ISBN: 9780471726210

Category: Computers

Page: 246

View: 879

Arithmetic and Logic in Computer Systems provides a useful guide to a fundamental subject of computer science and engineering. Algorithms for performing operations like addition, subtraction, multiplication, and division in digital computer systems are presented, with the goal of explaining the concepts behind the algorithms, rather than addressing any direct applications. Alternative methods are examined, and explanations are supplied of the fundamental materials and reasoning behind theories and examples. No other current books deal with this subject, and the author is a leading authority in the field of computer arithmetic. The text introduces the Conventional Radix Number System and the Signed-Digit Number System, as well as Residue Number System and Logarithmic Number System. This book serves as an essential, up-to-date guide for students of electrical engineering and computer and mathematical sciences, as well as practicing engineers and computer scientists involved in the design, application, and development of computer arithmetic units.
Categories: Computers

Finite Precision Number Systems and Arithmetic

Finite Precision Number Systems and Arithmetic

Design of residue generators and multioperand modular adders using carry-save adders. IEEE Trans. Computers, C-43:68–77, Jan. 1994. [PP95] K. C. Posch and R. Posch. RNS-modulo reduction in residue number systems. IEEE Trans.

Author: Peter Kornerup

Publisher: Cambridge University Press

ISBN: 9780521761352

Category: Mathematics

Page: 699

View: 542

This comprehensive reference volume, suitable for graduate teaching, includes problems, exercises, solutions and an extensive bibliography.
Categories: Mathematics

RESIDUE NUMBER SYSTEMS FOR COMPUTERS

RESIDUE NUMBER SYSTEMS FOR COMPUTERS

of residue classes , permits addition and multiplication to be performed without the existence of carries . The main advantage to be gained from the residue number system follows from the fact that it should be possible to execute ...

Author: H. L Garner, R. F. Arnold, E. C. Benson, C. G. Brockus, R. J. Gonzalez, D. P. Rosenberg

Publisher:

ISBN: UOMDLP:bac2784:0001.001

Category:

Page:

View: 855

Categories:

Advances in Computers

Advances in Computers

Residue Number Systems The concept of residue classes is very ancient as evidenced by the existence of the Chinese remainder theorem. Recently residue number systems have been studied extensively to determine whether such systems can be ...

Author:

Publisher: Academic Press

ISBN: 0080566383

Category: Computers

Page: 309

View: 487

Volume 6 reflects the editors’ conviction that application of digital computers to areas akin to human thinking—machine-aided cognition, to borrow a term from another environment—is one of the most active frontiers of development in our time. Articles in this volume deal with two such areas: information retrieval and what is called “ultraintelligent machines.
Categories: Computers

The Electrical Engineering Handbook

The Electrical Engineering Handbook

This may be achieved through the use of one of the many available versions of the residue number system (RNS) (Szabo and Tanaka, 1967). RNS arithmetic faces difficulties with sign detection, division, and magnitude comparison.

Author: Wai Kai Chen

Publisher: Elsevier

ISBN: 0080477488

Category: Technology & Engineering

Page: 1018

View: 857

The Electrical Engineer's Handbook is an invaluable reference source for all practicing electrical engineers and students. Encompassing 79 chapters, this book is intended to enlighten and refresh knowledge of the practicing engineer or to help educate engineering students. This text will most likely be the engineer’s first choice in looking for a solution; extensive, complete references to other sources are provided throughout. No other book has the breadth and depth of coverage available here. This is a must-have for all practitioners and students! The Electrical Engineer's Handbook provides the most up-to-date information in: Circuits and Networks, Electric Power Systems, Electronics, Computer-Aided Design and Optimization, VLSI Systems, Signal Processing, Digital Systems and Computer Engineering, Digital Communication and Communication Networks, Electromagnetics and Control and Systems. About the Editor-in-Chief... Wai-Kai Chen is Professor and Head Emeritus of the Department of Electrical Engineering and Computer Science at the University of Illinois at Chicago. He has extensive experience in education and industry and is very active professionally in the fields of circuits and systems. He was Editor-in-Chief of the IEEE Transactions on Circuits and Systems, Series I and II, President of the IEEE Circuits and Systems Society and is the Founding Editor and Editor-in-Chief of the Journal of Circuits, Systems and Computers. He is the recipient of the Golden Jubilee Medal, the Education Award, and the Meritorious Service Award from the IEEE Circuits and Systems Society, and the Third Millennium Medal from the IEEE. Professor Chen is a fellow of the IEEE and the American Association for the Advancement of Science. * 77 chapters encompass the entire field of electrical engineering. * THOUSANDS of valuable figures, tables, formulas, and definitions. * Extensive bibliographic references.
Categories: Technology & Engineering