Abstract

The standard digital or binary number representation provides an exponential trade-off between the number of digits used (i.e., number of parallel optical channels required to represent one number) and the accuracy of computation achievable. For example, an 8-bit number uses eight binary optical channels but has a potential for resolving 256 (2⁸) distinct levels. Such a trade-off, however, comes at the expense of requiring nonmonotonically nonlinear operations for performing the linear arithmetic operations of multiplications and additions. Here we propose a simple redundant number representation that will provide only a trade-off between the number of channels and the achievable accuracy while keeping the operations of multiplications of addition and multiplication in a simple linear form. Such a representation can be described by the following equation: Where a is the analog number, a represents a digit that can take on a value less than or equal to m, giving the dynamic range of the representation to be (n × m). We outline several different schemes for optically implementing multiplication and analyze their performance via computer simulations.

© 1986 Optical Society of America