A programmable optical arithmetic/logic device employs a first and second plurality of positionally encoded optical light paths. For arithmetic operations, these light paths represent residue numbers. The arithmetic/logic device includes first and second reordering units which are responsive to a third and fourth plurality of light sources serving to select one of a plurality of arithmetic or logic operations to be performed by the arithmetic/logic device. The arithmetic/logic device further employs an optical arithmetic/logic unit which is identically constructed for all of the selectable arithmetic/logic operations and which implements an optical table look-up function to obtain the desired output. Finally, the arithmetic/logic device used an output reordering device to reorder the output of the arithmetic/logic unit depending upon the originally selected arithmetic/logic operation. For arithmetic operations, the final output is provided as an output residue number representation.