SYMBOLIC SUBSTITUTION BY MEANS OF ONE-OF-MANY CODING

Symbolic substitution (SS) for digital optical computing initially use d intensity coding with one pixel representing one bit. This required recognition of both the dark and the bright pixels in a pattern for co mplete recognition. To avoid this double recognition, dual-rail coding was introduced, where it is sufficient to recognize either the dark o r the bright pixels alone for complete recognition. Subsequently, the modified signed-digit number system was proposed to fully exploit the parallelism of SS for arithmetic operations. This introduces a third s ymbol -1, and with dual-rail coding, this again necessitates recogniti on of both dark and bright pixels. We argue the usefulness of triple-r ail coding to avoid this double recognition. We show that the nature o f this one-of-three coding enables simplified recognition of a set of patterns. We present a new implementation of SS based on this coding. We also show that this one-of-many coding can be extended to high-radi x arithmetic with equal efficiency. We present an evaluation scheme ba sed on the number of optical hardware elements required by each implem entation and use it to compare the different implementations of SS.