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Digital Arithmetic

  1. Florent de Dinechin1,2,
  2. Miloš D. Ercegovac3,
  3. Jean-Michel Muller2,4,
  4. Nathalie Revol2,5

Published Online: 16 MAR 2009

DOI: 10.1002/9780470050118.ecse578

Wiley Encyclopedia of Computer Science and Engineering

Wiley Encyclopedia of Computer Science and Engineering

How to Cite

de Dinechin, F., Ercegovac, M. D., Muller, J.-M. and Revol, N. 2009. Digital Arithmetic. Wiley Encyclopedia of Computer Science and Engineering. 935–948.

Author Information

  1. 1

    École Normale Supérieuse de Lyon

  2. 2

    Université de Lyon LIP (UMR 5688 CNRS-ENS Lyon-INRIA-UCBL), France

  3. 3

    University of California at Los Angeles, Computer Science Department

  4. 4

    CNRS

  5. 5

    INRIA

Publication History

  1. Published Online: 16 MAR 2009

Abstract

Digital arithmetic includes all aspects of the specification, analysis, and implementation of arithmetic operations (±, ×, ÷, inline image, etc.) in digital systems such as general-purpose processors, digital signal processors, graphics, and various embedded systems. These aspects include number systems, arithmetic algorithms, hardware implementation of arithmetic operators (adders, multipliers, dividers), elementary function implementation, and floating-point arithmetic. The implementors of arithmetic units and systems must compromise between various objectives: speed, area (cost), power consumption, accuracy, reusability… hence, no “best solutions” exist in general, but solutions that can be significantly different depending on whether you are designing a circuit for a cellular phone or for a supercomputer.

Keywords:

  • number systems;
  • arithmetic operators;
  • addition;
  • multiplication;
  • division;
  • floating-point arithmetic;
  • elementary functions;
  • multiple-precision;
  • interval arithmetic