One-step optical negabinary and modified signed-digit adder

A one-step algorithm for parallel negabinary addition of two negabinary numbers is achieved by minimizing the truth-table for the two-step algorithm. Without increasing the encoding cell size or adding complexity of the corresponding optical system, the proposed one-step scheme doubles the computation speed. The optical system can also be used to realize a one-step modified signed digit adder. Additionally, optical implementation of negabinary multiplication using this proposed one-step optical adder is discussed.