Residue Number System Arithmetic
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Residue Number Systems
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Author : P.V. Ananda Mohan
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-04-30
Residue Number Systems written by P.V. Ananda Mohan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-04-30 with Computers categories.
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.
Residue Number Systems
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Author : P.V. Ananda Mohan
language : en
Publisher: Birkhäuser
Release Date : 2016-10-14
Residue Number Systems written by P.V. Ananda Mohan and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-14 with Mathematics categories.
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
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Author : Amos R. Omondi
language : en
Publisher: Imperial College Press
Release Date : 2007
Residue Number Systems written by Amos R. Omondi and has been published by Imperial College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Technology & Engineering categories.
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. Sample Chapter(s). Chapter 1: Introduction (301 KB). Contents: Introduction; Mathematical Fundamentals; Forward Conversion; Addition; Multiplication; Comparison, Overflow-Detection, Sign-Determination, Scaling, and Division; Reverse Conversion; Applications. Readership: Graduate students, academics and researchers in computer engineering and electrical & electronic engineering.
Residue Number System Arithmetic
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Author :
language : en
Publisher:
Release Date : 1986
Residue Number System Arithmetic written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Modular arithmetic categories.
Residue Number Systems
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Author : P.V. Ananda Mohan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Residue Number Systems written by P.V. Ananda Mohan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
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.
Computer Arithmetic Algorithms
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Author : Israel Koren
language : en
Publisher: CRC Press
Release Date : 2018-10-08
Computer Arithmetic Algorithms written by Israel Koren and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-08 with Computers categories.
This text explains the fundamental principles of algorithms available for performing arithmetic operations on digital computers. These include basic arithmetic operations like addition, subtraction, multiplication, and division in fixed-point and floating-point number systems as well as more complex operations such as square root extraction and evaluation of exponential, logarithmic, and trigonometric functions. The algorithms described are independent of the particular technology employed for their implementation.
Finite Precision Number Systems And Arithmetic
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Author : Peter Kornerup
language : en
Publisher: Cambridge University Press
Release Date : 2010-09-30
Finite Precision Number Systems And Arithmetic written by Peter Kornerup and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-30 with Mathematics categories.
Fundamental arithmetic operations support virtually all of the engineering, scientific, and financial computations required for practical applications, from cryptography, to financial planning, to rocket science. This comprehensive reference provides researchers with the thorough understanding of number representations that is a necessary foundation for designing efficient arithmetic algorithms. Using the elementary foundations of radix number systems as a basis for arithmetic, the authors develop and compare alternative algorithms for the fundamental operations of addition, multiplication, division, and square root with precisely defined roundings. Various finite precision number systems are investigated, with the focus on comparative analysis of practically efficient algorithms for closed arithmetic operations over these systems. Each chapter begins with an introduction to its contents and ends with bibliographic notes and an extensive bibliography. The book may also be used for graduate teaching: problems and exercises are scattered throughout the text and a solutions manual is available for instructors.
Arithmetic And Algebraic Circuits
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Author : Antonio Lloris Ruiz
language : en
Publisher: Springer Nature
Release Date : 2021-02-23
Arithmetic And Algebraic Circuits written by Antonio Lloris Ruiz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-23 with Technology & Engineering categories.
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.
Arithmetic And Logic In Computer Systems
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Author : Mi Lu
language : en
Publisher: John Wiley & Sons
Release Date : 2005-03-04
Arithmetic And Logic In Computer Systems written by Mi Lu and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-03-04 with Computers categories.
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.
Cryptography Arithmetic
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Author : Amos R. Omondi
language : en
Publisher: Springer Nature
Release Date : 2020-01-30
Cryptography Arithmetic written by Amos R. Omondi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-30 with Computers categories.
Modern cryptosystems, used in numerous applications that require secrecy or privacy - electronic mail, financial transactions, medical-record keeping, government affairs, social media etc. - are based on sophisticated mathematics and algorithms that in implementation involve much computer arithmetic. And for speed it is necessary that the arithmetic be realized at the hardware (chip) level. This book is an introduction to the implementation of cryptosystems at that level. The aforementioned arithmetic is mostly the arithmetic of finite fields, and the book is essentially one on the arithmetic of prime fields and binary fields in the context of cryptography. The book has three main parts. The first part is on generic algorithms and hardware architectures for the basic arithmetic operations: addition, subtraction, multiplication, and division. The second part is on the arithmetic of prime fields. And the third part is on the arithmetic of binary fields. The mathematical fundamentals necessary for the latter two parts are included, as are descriptions of various types of cryptosystems, to provide appropriate context. This book is intended for advanced-level students in Computer Science, Computer Engineering, and Electrical and Electronic Engineering. Practitioners too will find it useful, as will those with a general interest in "hard" applications of mathematics.