Digital Arithmetic

1st Edition

Authors: Miloš D. Ercegovac Tomás Lang
Print ISBN: 9781493303670
eBook ISBN: 9780080530406
Imprint: Morgan Kaufmann
Published Date: 10th June 2003
Page Count: 709
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Digital arithmetic plays an important role in the design of general-purpose digital processors and of embedded systems for signal processing, graphics, and communications. In spite of a mature body of knowledge in digital arithmetic, each new generation of processors or digital systems creates new arithmetic design problems. Designers, researchers, and graduate students will find solid solutions to these problems in this comprehensive, state-of-the-art exposition of digital arithmetic.

Ercegovac and Lang, two of the field's leading experts, deliver a unified treatment of digital arithmetic, tying underlying theory to design practice in a technology-independent manner. They consistently use an algorithmic approach in defining arithmetic operations, illustrate concepts with examples of designs at the logic level, and discuss cost/performance characteristics throughout. Students and practicing designers alike will find Digital Arithmetic a definitive reference and a consistent teaching tool for developing a deep understanding of the "arithmetic style" of algorithms and designs.

Key Features

·Guides readers to develop sound solutions, avoid known mistakes, and repeat successful design decisions. ·Presents comprehensive coverage¾from fundamental theories to current research trends. ·Written in a clear and engaging style by two masters of the field. ·Concludes each chapter with in-depth discussions of the key literature. ·Includes a full set of over 250 exercises, an on-line appendix with solutions to one-third of the exercises and 600 lecture slides


Graduate students in Computer Engineering, Electrical Engineering, and Computer Science; Practicing digital design engineers and researchers

Table of Contents


  1. Review of Basic Number Representations and Arithmetic Algorithms
  2. Two-Operand Addition
  3. Multi-Operand Addition
  4. Multiplication
  5. Division by Digit Recurrence
  6. Square Root by Digit Recurrence
  7. Reciprocal, Division, Reciprocal Square Root and Square Root by Iterative Approximation
  8. Floating-Point Representation, Algorithms, and Implementations
  9. Digit-Serial Arithmetic
  10. Function Evaluation
  11. CORDIC Algorithm and Implementations


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Morgan Kaufmann
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About the Author

Miloš D. Ercegovac

Miloš D. Ercegovac is a professor and chair of the UCLA Computer Science Department. He earned his MS ('72) and PhD ('75) in computer science from the University of Illinois, Urbana-Champaign, and BS in electrical engineering ('65) from the University of Belgrade, Yugoslavia. Dr. Ercegovac specializes in research and teaching in digital arithmetic, digital design, and computer system architecture. His research contributions have been extensively published in journals and conference proceedings. He is a coauthor of two textbooks on digital design and of a monograph in the area of digital arithmetic. Dr. Ercegovac has been involved in organizing the IEEE Symposia on Computer Arithmetic since 1978. He served as an editor of the IEEE Transactions on Computers and as a subject area editor for the Journal of Parallel and Distributed Computing. Dr. Ercegovac is a senior member of the IEEE Computer Society and a member of the ACM.

Affiliations and Expertise

University of California, Los Angeles

Tomás Lang

Tomás Lang is a professor in the Department of Electrical and Computer Engineering at the University of California, Irvine. Previously he was a professor in the computer architecture department of the Polytechnic University of Catalonia, Spain, and a faculty member of the computer science department at the University of California, Los Angeles. He received a degree in electrical engineering from the Universidade de Chile in 1965, an MS from the University of California, Berkeley in 1966 and a Ph.D. from Stanford University in 1974. Dr. Lang's primary research and teaching interests are in digital design and computer architecture with current emphasis on high-speed and low-power numerical processors and multiprocessors. He is coauthor of two textbooks on digital systems, two research monographs, one IEEE Tutorial, and author or coauthor of research contributions to scholarly publications and technical conferences.

Affiliations and Expertise

University of California, Irvine


Ercegovac and Lang present a comprehensive yet easily readable treatment of computer arithmetic that spans from theory to current practice. This book should be on every digital designer's shelf. —William J. Dally, Stanford University Digital Arithmetic provides comprehensive coverage of the most important and useful concepts used in computer arithmetic. The scientific and academic community will benefit greatly from this book. —Alexandre F. Tenca, Oregon State University The extensive mathematical proofs and the discussions of their implementations make this book a significant scientific and technical contribution. —Paolo Montuschi, Politecnico di Torino, Italy