Optical arithmetic using signed-digit symbolic substitution

A class of digital arithmetic algorithms for supporting massively parallel computing with state-of-the-art optical technology is presented. A two-dimensional symbolic substitution approach is used. Signed-digit (SD) representation is used to enable carry-free addition/subtraction. Based on SD addition, parallel algorithms for SD multiplication and division are developed. The potential advantages of performing digital arithmetic with optics include the significant increase in speed, full exploitation of massive parallelism, higher communication bandwidth, and higher system throughput, as compared with existing electronic arithmetic computers. Emphasis is placed on optical computing using the signed digit set {-1, 0, 1}. The parallel algorithms presented can be easily extended to perform optical arithmetic with higher radices.