Accession Number:

AD0645766

Title:

SUMMARY DISCUSSION ON PERFORMING BINARY MULTIPLICATION WITH THE FEWEST POSSIBLE ADDITONS

Descriptive Note:

Technical note

Corporate Author:

ARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND MD

Personal Author(s):

Report Date:

1957-02-01

Pagination or Media Count:

16.0

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 2s complement, 1s complement, and magnitude with appended sign.

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE