Computer Multiplication and Division Using Binary Logarithms

TLDR

Approximate binary logarithms can introduce errors in multiplication and division results. The paper proposes a computer multiplication and division method that employs binary logarithms. The method obtains binary logarithms by shifting and counting, then performs multiplication or division using only simple add/subtract and shift operations. An error analysis is provided, and a technique to reduce multiplication error is demonstrated.

Abstract

A method of computer multiplication and division is proposed which uses binary logarithms. The logarithm of a binary number may be determined approximately from the number itself by simple shifting and counting. A simple add or subtract and shift operation is all that is required to multiply or divide. Since the logarithms used are approximate there can be errors in the result. An error analysis is given and a means of reducing the error for the multiply operation is shown.