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Applying the parallelism of optical computing, we present a novel method of vector-matrix multiplication (VMM) based on a new optical computing platform, the ternary optical computer, which can reconfigure any two-input trivalued logic optical processor at runtime, according to the decrease-radix design principle. In this work, we investigate a novel optical VMM (OVMM) using five logic operations with the modified signed-digit (MSD) number system. To simplify the computation process, we realize a carry-free optical addition in three steps, which is independent of the length of the operands. And a new implementation method is proposed that can be used to realize the MSD multiplication in parallel. Based on the generation of partial products in parallel and the binary-addition-tree algorithm, the multiplication can be implemented with the MSD addition. Our initial experiments have been performed to verify the proposed OVMM method. The results show that the proposed method of OVMM is feasible and correct.

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