An optical parallel quaternary signed digit (QSD) two-dimensional array multiplier based on digit-decomposition (DDP) representation and duplication-shifting-superimposing algorithm is proposed in this paper. The multiplication operation is done in three steps; one for partial products generation and the other two steps perform accumulation to find the DDP planes of the final result array. QSD multiplication and addition rules are used to obtain a newly derived equations which are suitable for easy optical implementation using basic optical tools. Finally, simulation results are presented to validate the successful of the multiplication operation.
In this paper, optical scalable parallel and high-speed 2D data array adder for trinary signed-digit (TSD) number is proposed. The digit-decomposition-plane (DDP) coding method is used to represent the 2D TSD data arrays. The algorithm performs parallel TSD addition in constant time independent of the size of the TSD data arrays. The design describes methodology to involve two-step TSD adder. The TSD addition is expressed with several combination logic formulas that are newly derived. Optical implementation with classical optical elements is suggested for proposed TSD adder. Preliminary demonstration example is also described.