Optical EngineeringOptical scalable parallel modified signed-digit algorithms for large-scale array addition and multiplication using digit-decomposition-plane representation
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Optical scalable parallel and high-speed 2D-data array computing based on modified signed-digit arithmetic and digit- decomposition-plane representation is presented. The digit- decomposition-plane coding uses m binary planes or m blocks of a binary plane to code an m-digit data array. Therefore, we can easily access each digit individually and can implement array addition with only 13 combinatorial logic formulas. A duplication-shifting-superimposition algorithm for digital array multiplication is proposed. The algorithm generates and records all the bitwise products in mn binary planes simultaneously, and then processes them based on a modified signed-digit (MSD) adder tree. Only five basic operations of bitwise product, duplication, shifting, masking and magnification are required for digital computing. The features of the proposed algorithm are that it requires no bistable devices, no decimal point, no sign, and no carry. The algorithm and its implementing scheme are scalable because they are independent to the sizes of data arrays. Therefore it has great promise for large- scale array computing. Optical implementation with classical optical elements, such as beamsplitters, parallel plates, and mirrors, is discussed. A preliminary demonstration experiment with an optoelectronic scheme is described.