Signed-digit arithmetic for optical computing: digit grouping and pixel assignment for spatial encoding

Novel fully parallel one-step adders that use the redundant signed-digit nu mber representation are proposed for optical computing. A new method for sp atially encoding the signed-digit is proposed based on digit grouping and p ixel assignment. The scheme of digital grouping of the signed-digit numbers enables a huge reduction of the number of symbolic substitution computatio n rules involved in the arithmetic computations and consequently increases the speed of arithmetic operations. Furthermore, the proposed spatial encod ing scheme effectively increases the space bandwidth product of the spatial light modulators and decreases the size of the matched spatial filters of the optical system. (C) 1999 Socioty of Photo-Optical Instrumentation Engin eers. [S0091-3286(99)00403-1].