Efficient designs of one-step trinary signed-digit optical adders and multipliers based on new spatial encodings

An efficient one-step trinary signed-digit symbolic substitution based opti cal adder-instead of a two-step one that has been described recently-is pro posed. The adder is used as the basic module for designing optical multipli cation using cascaded correlators. Two different multiplication designs wil l be presented and we introduce new spatial encodings for the trinary signe d-digit numbers. The proposed encodings allow the reduction of the number o f symbolic substitution computation rules involved in the optical multiplic ation. Furthermore, the proposed spatial encodings scheme effectively incre ases the space bandwidth product of the spatial light modulators of the opt ical system.