Abstract

Optical crossbar arithmetic/logic units (OALUs) described by Falk et al.¹ perform residue arithmetic addition and multiplication without internal carry operations. This makes residue arithmetic algorithms practical in high-speed devices. Two tasks in connecting customary weighted number arithmetic processors to residue number processors are to convert binary or decimal numbers to residue numbers and vice versa. The latter task may advantageously convert residue representation to mixed radix digits, a special form of weighted number, as an intermediate representation through an algorithm which uses residue arithmetic. The mixed radix digits themselves may be used to find sign, magnitude, and overflow conditions without further conversion to binary or decimal digits. Methods for connecting OALUs to binary, decimal, and binary-coded decimal digit signals for conversion to residue numbers and to residue number signals for conversion mixed radix digits are derived from standard algorithms. Where these algorithms involve multiplying by a constant, a simplified faster OALU based on fixed mapping may be inserted.

© 1987 Optical Society of America