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Author : Norman Ross Scott
Publisher : Prentice Hall
Page : 288 pages
File Size : 53,8 Mb
Release : 1985
Category : Mathematics
ISBN : UOM:39015010640475
Author : Ronald T. Kneusel
Publisher : Springer
Page : 346 pages
File Size : 49,6 Mb
Release : 2017-02-09
Category : Computers
ISBN : 9783319505084
This is a book about numbers and how those numbers are represented in and operated on by computers. It is crucial that developers understand this area because the numerical operations allowed by computers, and the limitations of those operations, especially in the area of floating point math, affect virtually everything people try to do with computers. This book aims to fill this gap by exploring, in sufficient but not overwhelming detail, just what it is that computers do with numbers. Divided into two parts, the first deals with standard representations of integers and floating point numbers, while the second examines several other number representations. Details are explained thoroughly, with clarity and specificity. Each chapter ends with a summary, recommendations, carefully selected references, and exercises to review the key points. Topics covered include interval arithmetic, fixed-point numbers, big integers and rational arithmetic. This new edition has three new chapters: Pitfalls of Floating-Point Numbers (and How to Avoid Them), Arbitrary Precision Floating Point, and Other Number Systems. This book is for anyone who develops software including software engineers, scientists, computer science students, engineering students and anyone who programs for fun.
Author : Ulrich Kulisch
Publisher : Walter de Gruyter
Page : 456 pages
File Size : 42,9 Mb
Release : 2013-04-30
Category : Mathematics
ISBN : 9783110301793
This is the revised and extended second edition of the successful basic book on computer arithmetic. It is consistent with the newest recent standard developments in the field. The book shows how the arithmetic and mathematical capability of the digital computer can be enhanced in a quite natural way. The work is motivated by the desire and the need to improve the accuracy of numerical computing and to control the quality of the computed results (validity). The accuracy requirements for the elementary floating-point operations are extended to the customary product spaces of computations including interval spaces. The mathematical properties of these models are extracted into an axiomatic approach which leads to a general theory of computer arithmetic. Detailed methods and circuits for the implementation of this advanced computer arithmetic on digital computers are developed in part two of the book. Part three then illustrates by a number of sample applications how this extended computer arithmetic can be used to compute highly accurate and mathematically verified results. The book can be used as a high-level undergraduate textbook but also as reference work for research in computer arithmetic and applied mathematics.
Author : Peter Kornerup,David W. Matula
Publisher : Cambridge University Press
Page : 717 pages
File Size : 55,6 Mb
Release : 2010-09-30
Category : Mathematics
ISBN : 9781139643559
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.
Author : Mi Lu
Publisher : John Wiley & Sons
Page : 270 pages
File Size : 52,7 Mb
Release : 2005-03-04
Category : Computers
ISBN : 9780471726210
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.
Author : Earl E. Swartzlander
Publisher : Los Alamitos, CA : IEEE Computer Society Press
Page : 424 pages
File Size : 50,6 Mb
Release : 1990
Category : Computer arithmetic
ISBN : 0818689455
Mathematics of Computing -- Numerical Analysis.
Author : Vassil Dimitrov,Graham Jullien,Roberto Muscedere
Publisher : CRC Press
Page : 294 pages
File Size : 46,9 Mb
Release : 2017-12-19
Category : Computers
ISBN : 9781439830475
Computer arithmetic has become so fundamentally embedded into digital design that many engineers are unaware of the many research advances in the area. As a result, they are losing out on emerging opportunities to optimize its use in targeted applications and technologies. In many cases, easily available standard arithmetic hardware might not necessarily be the most efficient implementation strategy. Multiple-Base Number System: Theory and Applications stands apart from the usual books on computer arithmetic with its concentration on the uses and the mathematical operations associated with the recently introduced multiple-base number system (MBNS). The book identifies and explores several diverse and never-before-considered MBNS applications (and their implementation issues) to enhance computation efficiency, specifically in digital signal processing (DSP) and public key cryptography. Despite the recent development and increasing popularity of MBNS as a specialized tool for high-performance calculations in electronic hardware and other fields, no single text has compiled all the crucial, cutting-edge information engineers need to optimize its use. The authors’ main goal was to disseminate the results of extensive design research—including much of their own—to help the widest possible audience of engineers, computer scientists, and mathematicians. Dedicated to helping readers apply discoveries in advanced integrated circuit technologies, this single reference is packed with a wealth of vital content previously scattered throughout limited-circulation technical and mathematical journals and papers—resources generally accessible only to researchers and designers working in highly specialized fields. Leveling the informational playing field, this resource guides readers through an in-depth analysis of theory, architectural techniques, and the latest research on the subject, subsequently laying the groundwork users require to begin applying MBNS.
Author : F. H. George
Publisher : Elsevier
Page : 224 pages
File Size : 53,6 Mb
Release : 2014-05-09
Category : Mathematics
ISBN : 9781483180915
Computer Arithmetic provides information pertinent to the fundamental aspects of a digital computer. This book discusses how the control unit uses the arithmetic unit to produce, under commands, the answers asked by the user. Organized into four chapters, this book begins with an overview of the binary code and provides a preview of the use of other arithmetic codes outside the computer. This text then explains in detail the codes employed in the representation of numbers inside the computer. Other chapters consider the number systems as well as other related matters to be able to understand computer arithmetic. This book discusses as well the signed numbers and their conversations, as well as the problems of scaling. The final chapter deals with the methods of fixed- and floating-point arithmetic, rounding off, and overflow. This book is a valuable resource for sixth form as well as university students who are interested in arithmetic codes.
Author : C H C Little,K L Teo,B van Brunt
Publisher : World Scientific Publishing Company
Page : 240 pages
File Size : 49,9 Mb
Release : 2003-09-05
Category : Mathematics
ISBN : 9789813106185
Although students of analysis are familiar with real and complex numbers, few treatments of analysis deal with the development of such numbers in any depth. An understanding of number systems at a fundamental level is necessary for a deeper grasp of analysis. Beginning with elementary concepts from logic and set theory, this book develops in turn the natural numbers, the integers and the rational, real and complex numbers. The development is motivated by the need to solve polynomial equations, and the book concludes by proving that such equations have solutions in the complex number system.
Author : William Parks
Publisher : Unknown
Page : 34 pages
File Size : 40,5 Mb
Release : 2018-12-03
Category : Electronic
ISBN : 179067252X
"Computer Number Bases" was originally published by Williamsville Publishing Company as part of their popular computer math Tape'nText series. It has been adapted and republished by Hershey Books. Material in "Computer Number Bases" was submitted for review in "The Mathematics Teacher" and received praise - "The development is well done." ABOUT THE BOOK: "Computer Number Bases" covers Base Ten (Decimal), Base Two (Binary), Base Eight (Octal) and Base 16 (Hexadecimal). These four number systems are important to gain insight into how computer systems operate internally. Binary Arithmetic is introduced after a thorough study of the underlying structure of each of the four computer number bases. Questions are listed in exercises at the end of each section and the answer key is conveniently located after each exercise. This book is part of the "Computer Mathematics Series" that also includes: "Sets and Flowcharts," "Introduction to Logic," and "Boolean Algebra and Switching Circuits." The four titles in the series give an excellent introduction to these topics and provide a firm foundation for beginners to study more advanced topics in computer mathematics. This text contributes to STEM-based instruction. STEM is an acronym that includes education in the fields of science, technology, engineering, mathematics and computer science. These areas of knowledge help students learn to communicate better in mathematics and computer science using sets, numbers, logic and flowcharts and displaying information in various ways.ABOUT THE AUTHOR: William Parks, B.S., M.S., Ed.M., taught secondary level mathematics in private and public high schools in New York for five years. He taught community college mathematics and computer science for 25 years in New York, Tennessee, Maryland and Arizona. He was a computer science degree program developer at four colleges: SUNY Colleges at Buffalo and Fredonia, Elon University and D'Youville College. He was the technical editor for "Personal Computing" and "PC AI" magazines.
Author : Norman Ross Scott
Publisher : Prentice Hall
Page : 282 pages
File Size : 50,5 Mb
Release : 1985
Category : Mathematics
ISBN : UOM:39015010640558
Author : Amos R. Omondi,Benjamin Premkumar
Publisher : World Scientific
Page : 311 pages
File Size : 41,7 Mb
Release : 2007
Category : Technology & Engineering
ISBN : 9781860948664
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.
Author : Earl E Swartzlander
Publisher : World Scientific
Page : 398 pages
File Size : 45,8 Mb
Release : 2015-03-17
Category : Mathematics
ISBN : 9789814651585
The book provides many of the basic papers in computer arithmetic. These papers describe the concepts and basic operations (in the words of the original developers) that would be useful to the designers of computers and embedded systems. Although the main focus is on the basic operations of addition, multiplication and division, advanced concepts such as logarithmic arithmetic and the calculations of elementary functions are also covered. This volume is part of a 3 volume set: Computer Arithmetic Volume I Computer Arithmetic Volume II Computer Arithmetic Volume III The full set is available for sale in a print-only version. Contents:OverviewAdditionParallel Prefix AdditionMulti-Operand AdditionMultiplicationDivisionLogarithmsElementary FunctionsFloating-Point Arithmetic Readership: Graduate students and research professionals interested in computer arithmetic. Key Features:It reprints the classic papersIt covers the basic arithmetic operationsIt does this in the words of the creatorsKeywords:Computer Arithmetic;Adders;Parallel Prefix Adders;Multi-operand Adders;Multipliers;Dividers;Logarithmic Arithmetic;Elementary Function Evaluation
Author : Ulrich W. Kulisch
Publisher : Springer Science & Business Media
Page : 151 pages
File Size : 50,5 Mb
Release : 2012-09-07
Category : Computers
ISBN : 9783709105252
The number one requirement for computer arithmetic has always been speed. It is the main force that drives the technology. With increased speed larger problems can be attempted. To gain speed, advanced processors and pro gramming languages offer, for instance, compound arithmetic operations like matmul and dotproduct. But there is another side to the computational coin - the accuracy and reliability of the computed result. Progress on this side is very important, if not essential. Compound arithmetic operations, for instance, should always deliver a correct result. The user should not be obliged to perform an error analysis every time a compound arithmetic operation, implemented by the hardware manufacturer or in the programming language, is employed. This treatise deals with computer arithmetic in a more general sense than usual. Advanced computer arithmetic extends the accuracy of the elementary floating-point operations, for instance, as defined by the IEEE arithmetic standard, to all operations in the usual product spaces of computation: the complex numbers, the real and complex intervals, and the real and complex vectors and matrices and their interval counterparts. The implementation of advanced computer arithmetic by fast hardware is examined in this book. Arithmetic units for its elementary components are described. It is shown that the requirements for speed and for reliability do not conflict with each other. Advanced computer arithmetic is superior to other arithmetic with respect to accuracy, costs, and speed.
Author : Earl E Swartzlander
Publisher : World Scientific
Page : 486 pages
File Size : 45,7 Mb
Release : 2015-03-17
Category : Mathematics
ISBN : 9789814641487
This is the new edition of the classic book Computer Arithmetic in three volumes published originally in 1990 by IEEE Computer Society Press. As in the original, the book contains many classic papers treating advanced concepts in computer arithmetic, which is very suitable as stand-alone textbooks or complementary materials to textbooks on computer arithmetic for graduate students and research professionals interested in the field. Told in the words of the initial developers, this book conveys the excitement of the creators, and the implementations provide insight into the details necessary to realize real chips. This second volume presents topics on error tolerant arithmetic, digit on-line arithmetic, number systems, and now in this new edition, a topic on implementations of arithmetic operations, all wrapped with an updated overview and a new introduction for each chapter. This volume is part of a 3 volume set: Computer Arithmetic Volume I Computer Arithmetic Volume II Computer Arithmetic Volume III The full set is available for sale in a print-only version. Contents:Error Tolerant ArithmeticOn-Line ArithmeticVLSI Adder ImplementationsVLSI Multiplier ImplementationsFloating-Point VLSI ChipsNumber RepresentationImplementations Readership: Graduate students and research professionals interested in computer arithmetic. Key Features:It reprints the classic papersIt covers advanced arithmetic operationsIt does this in the words of the original creatorsKeywords:Computer Arithmetic;Fault Tolerant;Arithmetic;On-Line Arithmetic;Adder Implementations;Multiplier Implementations;Floating Point Chips;Number Representation;Implementations