Method and optical apparatus for converting residue numbers into positionally notated numbers

An optical device for processing residue numbers comprising one unit including an encoder means for converting differently encoded input numbers in parallel into residue numbers by selectively interrupting a plurality of light paths respectively allocated to each possible numeral in said residue number, an arithmetic means for airthmetically operating on said residue numbers, and a decoder means for converting a result of said residue numbers, and a decoder means for converting a result of said arithmetic operation into a positionally notated number, said decoder means comprising a light source and a plurality of linear periodic structures irradiated by said light source having respectively different constant periods for differently modulating light incident thereon and being disposed such that light modulated by each linear period structure is superimposed with light modulated by all of the other linear periodic structures, said linear periodic structures being respectively allocated to each module utilized for said residue numbers, a scale of equidistantly spaced positionally notated numbers on which said modulated light is superimposed, and a means for individually shifting said linear periodic structures with respect to said scale until an end of a period in each linear periodic structure is aligned with an end of a period in each of the other linear periodic structures, the period for each linear periodic structure being the product of the spacing between adjacent positionally notated numbers on said scale and the module allocated to the linear periodic structure and a reading on said scale when said ends of periods are aligned indicating a positionally notated number for said residue number.