Optical arithmetic using high-radix symbolic substitution rules

New optical representations and symbolic substitution (SS) rules are presented for performing high-radix arithmetic in optics. A set of SS rules is proposed for high-radix optical arithmetic, which satisfies the arithmetic completeness property. Tradeoff parameters like representational efficiency, projected speedup, and estimated implementation cost are analyzed. The SS mechanism together with the signed-digit (SD) representation reinforces massive parallelism in optics. A digit-plane architecture, blending very well with the SS technique and SD representation, is considered for implementing high-radix arithmetic. An optical adder, exploiting massive parallelism, is proposed. The set of SS rules and their implementations on a digit-plane architecture provide the basis for achieving pipelining, systolization, and online arithmetic in future optical computers