Residue Number Systems

Residue Number Systems PDF

Author: Amos R. Omondi

Publisher: World Scientific

Published: 2007

Total Pages: 311

ISBN-13: 1860948669

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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.

Residue Number Systems

Residue Number Systems PDF

Author: P.V. Ananda Mohan

Publisher: Birkhäuser

Published: 2016-10-14

Total Pages: 353

ISBN-13: 3319413856

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This new and expanded monograph improves upon Mohan's earlier book, Residue Number Systems (Springer, 2002) with a state of the art treatment of the subject. Replete with detailed illustrations and helpful examples, this book covers a host of cutting edge topics such as the core function, the quotient function, new Chinese Remainder theorems, and large integer operations. It also features many significant applications to practical communication systems and cryptography such as FIR filters and elliptic curve cryptography. Starting with a comprehensive introduction to the basics and leading up to current research trends that are not yet widely distributed in other publications, this book will be of interest to both researchers and students alike.

Residue Number Systems: Theory And Implementation

Residue Number Systems: Theory And Implementation PDF

Author: Amos R Omondi

Publisher: World Scientific

Published: 2007-09-10

Total Pages: 311

ISBN-13: 1908979119

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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./a

Residue Number Systems

Residue Number Systems PDF

Author: P.V. Ananda Mohan

Publisher: Springer Science & Business Media

Published: 2002-04-30

Total Pages: 272

ISBN-13: 9781402070310

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This text is an excellent reference for both professional and academic researchers in the field of VLSI using residue number systems. It is also of interest to those working in the general fields of VLSI design, DSP design, and cryptography. Topics covered include choice of moduli; architectures for conversion from binary to RNS; RNS to binary conversion techniques; quadratic RNS; and applications. Numerous examples illustrate the ideas developed. The area and computational requirements are highlighted for all designs, so the selection of a particular architecture is facilitated. Some of the topics covered have application in cryptography. The book includes a comprehensive bibliography in this area.Residue Number Systems: Algorithms and Architectures is also suitable for a graduate-level course as part of a VLSI curriculum.

Embedded Systems Design with Special Arithmetic and Number Systems

Embedded Systems Design with Special Arithmetic and Number Systems PDF

Author: Amir Sabbagh Molahosseini

Publisher: Springer

Published: 2017-03-20

Total Pages: 390

ISBN-13: 3319497421

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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.

Arithmetic and Algebraic Circuits

Arithmetic and Algebraic Circuits PDF

Author: Antonio Lloris Ruiz

Publisher: Springer Nature

Published: 2021-03-27

Total Pages: 682

ISBN-13: 3030672662

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This book presents a complete and accurate study of arithmetic and algebraic circuits. The first part offers a review of all important basic concepts: it describes simple circuits for the implementation of some basic arithmetic operations; it introduces theoretical basis for residue number systems; and describes some fundamental circuits for implementing the main modular operations that will be used in the text. Moreover, the book discusses floating-point representation of real numbers and the IEEE 754 standard. The second and core part of the book offers a deep study of arithmetic circuits and specific algorithms for their implementation. It covers the CORDIC algorithm, and optimized arithmetic circuits recently developed by the authors for adders and subtractors, as well as multipliers, dividers and special functions. It describes the implementation of basic algebraic circuits, such as LFSRs and cellular automata. Finally, it offers a complete study of Galois fields, showing some exemplary applications and discussing the advantages in comparison to other methods. This dense, self-contained text provides students, researchers and engineers, with extensive knowledge on and a deep understanding of arithmetic and algebraic circuits and their implementation.

Current Problems in Applied Mathematics and Computer Science and Systems

Current Problems in Applied Mathematics and Computer Science and Systems PDF

Author: Anatoly Alikhanov

Publisher: Springer Nature

Published: 2023-06-05

Total Pages: 528

ISBN-13: 3031341279

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This book is based on the best papers accepted for presentation during the International Conference on Actual Problems of Applied Mathematics and Computer Systems (APAMCS-2022), Russia. The book includes research materials on modern mathematical problems, solutions in the field of scientific computing, data analysis and modular computing. The scope of numerical methods in scientific computing presents original research, including mathematical models and software implementations, related to the following topics: numerical methods in scientific computing; solving optimization problems; methods for approximating functions, etc. The studies in data analysis and modular computing include contributions in the field of deep learning, neural networks, mathematical statistics, machine learning methods, residue number system and artificial intelligence. Finally, the book gives insights into the fundamental problems in mathematics education. The book intends for readership specializing in the field of scientific computing, parallel computing, computer technology, machine learning, information security and mathematical education.

Advances in Intelligent Systems and Computing V

Advances in Intelligent Systems and Computing V PDF

Author: Natalya Shakhovska

Publisher: Springer Nature

Published: 2020-12-22

Total Pages: 1190

ISBN-13: 3030632709

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This book reports on new theories and applications in the field of intelligent systems and computing. It covers cutting-edge computational and artificial intelligence methods, advances in computer vision, big data, cloud computing, and computation linguistics, as well as cyber-physical and intelligent information management systems. The respective chapters are based on selected papers presented at the workshop on intelligent systems and computing, held during the International Conference on Computer Science and Information Technologies, CSIT 2020, which was jointly organized on September 23-26, 2020, by the Lviv Polytechnic National University, Ukraine, the Kharkiv National University of Radio Electronics, Ukraine, and the Technical University of Lodz, Poland, under patronage of Ministry of Education and Science of Ukraine. Given its breadth of coverage, the book provides academics and professionals with extensive information and a timely snapshot of the field of intelligent systems, and is sure to foster new discussions and collaborations among different groups.

Inventive Communication and Computational Technologies

Inventive Communication and Computational Technologies PDF

Author: G. Ranganathan

Publisher: Springer Nature

Published: 2022-11-13

Total Pages: 940

ISBN-13: 9811949603

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This book gathers selected papers presented at the Inventive Communication and Computational Technologies Conference (ICICCT 2022), held on May 12–13, 2022, at Gnanamani College of Technology, Tamil Nadu, India. The book covers the topics such as Internet of Things, social networks, mobile communications, big data analytics, bio-inspired computing, and cloud computing. The book is exclusively intended for academics and practitioners working to resolve practical issues in this area.

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