Optical multiplication and division using modified-signed-digit symbolic substitution

The modified-signed-digit (MSD) number system offers parallel addition and subtraction of any two numbers, with carry propagation constrained only between two adjacent digits. Based on MSD addition, parallel algorithms for multiplication and division are developed. The optical implementations of these MSD arithmetic algorithms are developed on the basis of symbolic substitution (SS). The space-invariant nature of SS matches with the parallel nature of the MSD arithmetic algorithms presented. The potential advantages of using these algorithms for optical computing include the increase in speed, full exploitation of parallelism, and higher system throughput compared with existing electronic arithmetic processors. The performance of the proposed optical arithmetic system is analyzed and compared with that of state-of-the-act electronic counterparts.