The Area-Time Complexity of Binary Multiplication,

Abstract

We consider the problem of performing multiplication of n-bit binary numbers on a chip. Let A denote the chip area, and T the time required to perform multiplication. Using a model of computation which is a realistic approximation to current and anticipated VLSI technology, we show that (A/A sub 0) (T/T sub 0) to the 2 alpha power > or = n to the (1 + alpha) power for all alpha is an element (0, 1), where A sub 0 and T sub 0 are positive constants which depend on the technology but are independent of n. The exponent 1 + alpha is the best possible. A consequence is that binary multiplication is 'harder' than binary addition if AT to the 2 alpha power is used as a complexity measure for any alpha > or = 0. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1979
Accession Number
ADA082388

Entities

People

  • H. T. Kung
  • R. P. Brent

Organizations

  • Carnegie Mellon University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Arithmetic
  • Binary Notation
  • Computational Complexity
  • Computations
  • Computer Science
  • Computers
  • Diameters
  • Discrete Fourier Transforms
  • Equations
  • Military Research
  • New York
  • Notation
  • Numbers
  • Prime Numbers
  • Sparse Matrix
  • Two Dimensional

Readers

  • Analytical Mechanics
  • Integrated Circuit Design and Technology.
  • Operations Research