SUMMARY DISCUSSION ON PERFORMING BINARY MULTIPLICATION WITH THE FEWEST POSSIBLE ADDITONS
ARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND MD
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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.
- Theoretical Mathematics