FULLY PARALLEL ARITHMETIC ALGORITHM FOR AN N-BIT PARALLEL ADDER AND ITS OPTICAL IMPLEMENTATIONS

A fully parallel arithmetic algorithm is proposed for adding multiple numbers of any radix, in which Linear operations and nonlinear operations are completely separated. The algorithm can be implemented using an optical one-stage system with shifting, weighting, summing, and thresholding functions, in favor of fully utilizing the parallelism of optics. A carry ripple propagating method and a carry look-ahead method are suggested for adding longer numbers. Three kinds of optical systems, which use respectively a cylindrical lens, a lens-array, and pairs of parallel partial reflectors, are designed for optical implementation. In particular, the system based on parallel partial reflectors can be packaged into a planar optical device. Furthermore, in this system neither the encoding nor the decoding of data is necessary and the results can be directly used for following processing.