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Computer Arithmetic

Author: Behrooz Parhami
Publisher: Oxford University Press, USA
ISBN: 9780195328486
Size: 35.73 MB
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Ideal for graduate and senior undergraduate courses in computer arithmetic and advanced digital design, Computer Arithmetic: Algorithms and Hardware Designs, Second Edition, provides a balanced, comprehensive treatment of computer arithmetic. It covers topics in arithmetic unit design and circuit implementation that complement the architectural and algorithmic speedup techniques used in high-performance computer architecture and parallel processing. Using a unified and consistent framework, the text begins with number representation and proceeds through basic arithmetic operations, floating-point arithmetic, and function evaluation methods. Later chapters cover broad design and implementation topics-including techniques for high-throughput, low-power, fault-tolerant, and reconfigurable arithmetic. An appendix provides a historical view of the field and speculates on its future. An indispensable resource for instruction, professional development, and research, Computer Arithmetic: Algorithms and Hardware Designs, Second Edition, combines broad coverage of the underlying theories of computer arithmetic with numerous examples of practical designs, worked-out examples, and a large collection of meaningful problems. This second edition includes a new chapter on reconfigurable arithmetic, in order to address the fact that arithmetic functions are increasingly being implemented on field-programmable gate arrays (FPGAs) and FPGA-like configurable devices. Updated and thoroughly revised, the book offers new and expanded coverage of saturating adders and multipliers, truncated multipliers, fused multiply-add units, overlapped quotient digit selection, bipartite and multipartite tables, reversible logic, dot notation, modular arithmetic, Montgomery modular reduction, division by constants, IEEE floating-point standard formats, and interval arithmetic. Features: * Divided into 28 lecture-size chapters * Emphasizes both the underlying theories of computer arithmetic and actual hardware designs * Carefully links computer arithmetic to other subfields of computer engineering * Includes 717 end-of-chapter problems ranging in complexity from simple exercises to mini-projects * Incorporates many examples of practical designs * Uses consistent standardized notation throughout * Instructor's manual includes solutions to text problems * An author-maintained website http://www.ece.ucsb.edu/~parhami/text_comp_arit.htm contains instructor resources, including complete lecture slides

Computer Arithmetic

Author: Mircea Vlăduţiu
Publisher: Springer Science & Business Media
ISBN: 364218314X
Size: 17.52 MB
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The subject of this book is the analysis and design of digital devices that implement computer arithmetic. The book's presentation of high-level detail, descriptions, formalisms and design principles means that it can support many research activities in this field, with an emphasis on bridging the gap between algorithm optimization and hardware implementation. The author provides a unified view linking the domains of digital design and arithmetic algorithms, based on original formalisms and hardware description languages. A feature of the book is the large number of examples and the implementation details provided. While the author does not avoid high-level details, providing for example gate-level designs for all matrix/combinational arithmetic structures. The book is suitable for researchers and students engaged with hardware design in computer science and engineering. A feature of the book is the large number of examples and the implementation details provided. While the author does not avoid high-level details, providing for example gate-level designs for all matrix/combinational arithmetic structures. The book is suitable for researchers and students engaged with hardware design in computer science and engineering.

Computer Arithmetic And Verilog Hdl Fundamentals

Author: Joseph Cavanagh
Publisher: CRC Press
ISBN: 1351834118
Size: 43.99 MB
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Verilog Hardware Description Language (HDL) is the state-of-the-art method for designing digital and computer systems. Ideally suited to describe both combinational and clocked sequential arithmetic circuits, Verilog facilitates a clear relationship between the language syntax and the physical hardware. It provides a very easy-to-learn and practical means to model a digital system at many levels of abstraction. Computer Arithmetic and Verilog HDL Fundamentals details the steps needed to master computer arithmetic for fixed-point, decimal, and floating-point number representations for all primary operations. Silvaco International’s SILOS, the Verilog simulator used in these pages, is simple to understand, yet powerful enough for any application. It encourages users to quickly prototype and de-bug any logic function and enables single-stepping through the Verilog source code. It also presents drag-and-drop abilities. Introducing the three main modeling methods—dataflow, behavioral, and structural—this self-contained tutorial— Covers the number systems of different radices, such as octal, decimal, hexadecimal, and binary-coded variations Reviews logic design fundamentals, including Boolean algebra and minimization techniques for switching functions Presents basic methods for fixed-point addition, subtraction, multiplication, and division, including the use of decimals in all four operations Addresses floating-point addition and subtraction with several numerical examples and flowcharts that graphically illustrate steps required for true addition and subtraction for floating-point operands Demonstrates floating-point division, including the generation of a zero-biased exponent Designed for electrical and computer engineers and computer scientists, this book leaves nothing unfinished, carrying design examples through to completion. The goal is practical proficiency. To this end, each chapter includes problems of varying complexity to be designed by the reader.

Computer Arithmetic Algorithms Second Edition

Author: Israel Koren
Publisher: A K Peters/CRC Press
ISBN: 9781568811604
Size: 50.17 MB
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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.

Advanced Computer Arithmetic Design

Author: Michael J. Flynn
Publisher: Wiley-Interscience
ISBN: 9780471412090
Size: 41.17 MB
Format: PDF, Mobi
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Innovative techniques and cutting-edge research in computer arithmetic design Computer arithmetic is a fundamental discipline that drives many modern digital technologies. High-performance VLSI implementations of 3-D graphics, encryption, streaming digital audio and video, and signal processing all require fast and efficient computer arithmetic algorithms. The demand for these fast implementations has led to a wealth of new research in innovative techniques and designs. Advanced Computer Arithmetic Design is the result of ten years of effort at Stanford University under the Sub-Nanosecond Arithmetic Processor (SNAP) project, which author Michael Flynn directs. Written with computer designers and researchers in mind, this volume focuses on design, rather than on other aspects of computer arithmetic such as number systems, representation, or precision. Each chapter begins with a review of conventional design approaches, analyzes the possibilities for improvement, and presents new research that advances the state of the art. The authors present new data in these vital areas: * Addition and the Ling adder * Improvements to floating-point addition * Encoding to reduce execution times for multiplication * The effects of technology scaling on multiplication * Techniques for floating-point division * Approximation techniques for high-level functions such as square root, logarithms, and trigonometric functions * Assessing cost performance of arithmetic units * Clocking to increase computer operation frequency * New implementation of continued fractions to the approximation of functions This volume presents the results of a decade's research in innovative and progressive design techniques. Covering all the most important research topics in the field, Advanced Computer Arithmetic Design is the most up-to-date and comprehensive treatment of new research currently available.

Digital Arithmetic

Author: Miloš D. Ercegovac
Publisher: Elsevier
ISBN: 1558607986
Size: 39.49 MB
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The authoritative reference on the theory and design practice of computer arithmetic.

Algorithms And Design Methods For Digital Computer Arithmetic

Author: Behrooz Parhami
Publisher:
ISBN: 9780199766932
Size: 68.22 MB
Format: PDF, Docs
View: 2134
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Ideal for graduate and senior undergraduate courses in computer arithmetic and advanced digital design, Computer Arithmetic: Algorithms and Hardware Designs, Second Edition, provides a balanced, comprehensive treatment of computer arithmetic. It covers topics in arithmetic unit design and circuit implementation that complement the architectural and algorithmic speedup techniques used in high-performance computer architecture and parallel processing. Using a unified and consistent framework, the text begins with number representation and proceeds through basic arithmetic operations, floating-point arithmetic, and function evaluation methods. Later chapters cover broad design and implementation topics-including techniques for high-throughput, low-power, fault-tolerant, and reconfigurable arithmetic. An appendix provides a historical view of the field and speculates on its future.An indispensable resource for instruction, professional development, and research, Computer Arithmetic: Algorithms and Hardware Designs, Second Edition, combines broad coverage of the underlying theories of computer arithmetic with numerous examples of practical designs, worked-out examples, and a large collection of meaningful problems. This second edition includes a new chapter on reconfigurable arithmetic, in order to address the fact that arithmetic functions are increasingly being implemented on field-programmable gate arrays (FPGAs) and FPGA-like configurable devices. Updated and thoroughly revised, the book offers new and expanded coverage of saturating adders and multipliers, truncated multipliers, fused multiply-add units, overlapped quotient digit selection, bipartite and multipartite tables, reversible logic, dot notation, modular arithmetic, Montgomery modular reduction, division by constants, IEEE floating-point standard formats, and interval arithmetic.Readership: Graduate and senior undergraduate courses in computer arithmetic and advanced digital design.

Hardware Implementation Of Finite Field Arithmetic

Author: Jean-Pierre Deschamps
Publisher: McGraw Hill Professional
ISBN: 0071545824
Size: 52.27 MB
Format: PDF, ePub, Mobi
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Implement Finite-Field Arithmetic in Specific Hardware (FPGA and ASIC) Master cutting-edge electronic circuit synthesis and design with help from this detailed guide. Hardware Implementation of Finite-Field Arithmetic describes algorithms and circuits for executing finite-field operations, including addition, subtraction, multiplication, squaring, exponentiation, and division. This comprehensive resource begins with an overview of mathematics, covering algebra, number theory, finite fields, and cryptography. The book then presents algorithms which can be executed and verified with actual input data. Logic schemes and VHDL models are described in such a way that the corresponding circuits can be easily simulated and synthesized. The book concludes with a real-world example of a finite-field application--elliptic-curve cryptography. This is an essential guide for hardware engineers involved in the development of embedded systems. Get detailed coverage of: Modulo m reduction Modulo m addition, subtraction, multiplication, and exponentiation Operations over GF(p) and GF(pm) Operations over the commutative ring Zp[x]/f(x) Operations over the binary field GF(2m) using normal, polynomial, dual, and triangular

Numerical Methods

Author: Anne Greenbaum
Publisher: Princeton University Press
ISBN: 1400842670
Size: 37.27 MB
Format: PDF, Kindle
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Numerical Methods provides a clear and concise exploration of standard numerical analysis topics, as well as nontraditional ones, including mathematical modeling, Monte Carlo methods, Markov chains, and fractals. Filled with appealing examples that will motivate students, the textbook considers modern application areas, such as information retrieval and animation, and classical topics from physics and engineering. Exercises use MATLAB and promote understanding of computational results. The book gives instructors the flexibility to emphasize different aspects--design, analysis, or computer implementation--of numerical algorithms, depending on the background and interests of students. Designed for upper-division undergraduates in mathematics or computer science classes, the textbook assumes that students have prior knowledge of linear algebra and calculus, although these topics are reviewed in the text. Short discussions of the history of numerical methods are interspersed throughout the chapters. The book also includes polynomial interpolation at Chebyshev points, use of the MATLAB package Chebfun, and a section on the fast Fourier transform. Supplementary materials are available online. Clear and concise exposition of standard numerical analysis topics Explores nontraditional topics, such as mathematical modeling and Monte Carlo methods Covers modern applications, including information retrieval and animation, and classical applications from physics and engineering Promotes understanding of computational results through MATLAB exercises Provides flexibility so instructors can emphasize mathematical or applied/computational aspects of numerical methods or a combination Includes recent results on polynomial interpolation at Chebyshev points and use of the MATLAB package Chebfun Short discussions of the history of numerical methods interspersed throughout Supplementary materials available online