High-accuracy pipelined iterative-tree optical multiplication

A high-accuracy optical multiplier that uses an optical correlator is described. A symbolic substitution adder that uses the modified signed-digit number representation is used as the basic module. Emphasis is placed on the multiplication of many long words in parallel with minimum latency. The encoding method we employ in the adders permits the use of a new optical algorithm and architecture to generate partial products in symbolic form in parallel. Our multiplication algorithm and architecture are shown to be preferable to other optical techniques and to be competitive with digital technology; they are also shown to be particularly attractive for matrix-vector multiplication applications.