SUMMARY DISCUSSION ON PERFORMING BINARY MULTIPLICATION WITH THE FEWEST POSSIBLE ADDITONS

Abstract

Under conventional binary multiplication procedures an addition (or, equivalently, a subtraction) is performed for each non-zero digit of the multiplier or its absolute value, and the statistically expected number of additions per multiplication is one-half the number of these digits. This discussion develops Boolean functions for the recursive definition of substitute sets of multiplier digits for which the numbers of non-zeros are irreducible with statistically expected values very near one-third the number of digits which express the signed multiplier and applies these functions to the three known binary representations: 2's complement, 1's complement, and magnitude with appended sign.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1957
Accession Number
AD0645766

Entities

People

  • George W. Reitwiesner

Organizations

  • Ballistic Research Laboratory

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  • C4I

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Fields of Study

  • Mathematics

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  • Applied Combinatorial Optimization and Logic Circuit Design.
  • Linear Algebra
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