Numerical simulations of optimized MSD multiplication on ternary optical computer

Abstract

Multiplication is a fundamental operation in computer systems but is often constrained by the carry-delay inherent to conventional addition methods. Ternary optical computing offers an efficient solution, leveraging its advantages such as large data capacity, reconfigurable processing, and MSD adder without carry-delay. This study introduces and develops a modified signed digit (MSD) multiplication routine. The proposed MSD multiplication algorithm is thoroughly analyzed, employing M-transformations to generate partial products and an optimization method designed to minimize processing time. The final product is computed using an MSD adder with four transformations: T, T', W, and W', to aggregate all partial products. Additionally, a pipelining strategy is introduced to further enhance performance. The routine’s construction steps are outlined, followed by extensive simulation experiments to validate its accuracy. The results demonstrate strong consistency and alignment with theoretical predictions. Finally, a comparative analysis with traditional electronic computers indicates superior performance of the proposed MSD multiplication routine.