Digital partitioning for optical negabinary modular multiplication

Instead of using the truth look-up table residue arithmetic, a technique for multiplying two N -bit negabinary numbers, modulo (−2) N −1 with digital partitioning, is introduced for optical computing. Both numbers are decomposed into k -bit bytes, and the product is obtained by the cyclic convolution of the sequences of the bytes. The operation with respect to other moduli can be performed similarly. The algorithm has such features as smaller computational complexity, ease of implementation, the ability to handle bipolar numbers without signs, and simple pre- and post-processing. As a proof-of-principle experiment, an optical correlator is used to perform the multiplication in parallel. The experimental results are given.