Optical design of programmable logic arrays

Abstract

Regular free-space interconnects such as the perfect shuffle and banyan provided by beam splitters, lenses, and mirrors connect optical logic gates arranged in 2-D arrays. An algorithmic design technique transforms arbitrary logic equations into a near-optimal depth circuit. Analysis shows that an arbitrary interconnect makes little or no improvement in circuit depth and can even reduce throughput. Gate count is normally higher with a regular interconnect, and we show cost bounds. We conclude that regularly interconnected circuits will have a higher gate count compared with arbitrarily interconnected circuits using the design techniques presented here and that regular free-space interconnects are comparable with arbitrary interconnects in terms of circuit depth and are preferred to arbitrary interconnects for maximizing throughput.

Organization of the Topical Meeting on Optical Computing Held in Toulon, France on 29 August-2 September 1988

“…(2) is not needed (e.g. the four rules of binary subtraction in simple intensity coding of arithmetic data can be reduced to only two rules (21); and 3) if Q) = Q for all I < i < p (this happens in those cases that a class of search-patterns is defined by a set of reference image pairs RA 0 , i = 1, 2,...,p), we should combine the results of the hit or miss transforms first and then replace them bv the same replacement-pattern Q instead of implementing p substitution units for realizing the same substitution step, i.e. P (U X (R' ) ) 0 Q.…”

Redundant interconnections for fault-tolerant digital optical computing

“…Optical logic devices act as threshold logic gates and achieve the best noise margins and error rates when operated as NOR gates that detect the absence of any light, 24 so we use the quadded NOR-NOR architecture. An example of a layered double banyan regularly interconnected NOR gate circuit for generating four logical combination of two variables is shown 25 in Fig. 2͑a͒ along with a quadded version in Fig.…”

“…2. A simple twoinput minterms-generating unit implemented using dual-rail double-banyan NOR gate topology appropriate for optical realization with the help of programmable regular interconnections is shown 25 in Fig. 2͑a͒.…”

Optically interconnected switching networks

“…As was mentioned in the introduction, very many of the MIN's, which have been proposed, are mutually isomorphic, but when free-space optical interconnects are used there are definite advantages in using one pattern over another. Because of the magnification step the perfect shuffle inherently involves a 3-dB loss in space-bandwidth product; it has been noted that the butterfly [24] and the crossover [39] interconnections are better choices for optical interconnects in MIN's. In this section we will develop mapping rules to generate a number of different 2-D interconnect patterns.…”