Abstract
A high-speed optical system capable of performing <i>n</i>-bit multiplication in a time proportional to log<sub>2</sub><i>n</i> is presented. The simultaneous generation and the optical regrouping of all the partial products and the pairwise addition of the partial products by means of a binary tree of adders capable of adding any two numbers in a single stage (by completely eliminating the carry propagation chain) are unique features of this multiplier. The input data to the multiplier can be in either a binary or a modified signed digit number system. The simultaneous generation and the pairwise addition of the partial products are accomplished by means of the principle of symbolic substitution logic that was originally proposed by Brenner.
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