Abstract

Optical systems and algorithms are presented for implementing digit-serial (or on-line) computations. These systems achieve high accuracy without the need for A–Ds and incorporate parallelism and carry-free addition to achieve high processing speed. On-line arithmetic allows parallel calculations to be performed by concurrent execution of operations. (Consecutive operations can start before all digits of the previous operations are available.) The algorithms are problem- and step-invariant and inherently allow variable precision as we show. To achieve parallelism, we introduce the modified signed-digit number representation into these algorithms and architectures. This results in new arithmetic rules (new addition rules, a different number of bits needed, a different number of cycles required) from those in conventional digital digit-serial systems. We include sufficient detail (not readily available elsewhere) needed for the design of the units we include. New architectures using optical bistable devices and optical interconnects are described that can implement digit-serial addition, subtraction, multiplication, and division algorithms in this new approach.

© 1989 Optical Society of America

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