Symbolic substitution is a spatial logic which is adapted well to optical processing. Unlike Boolean logic it also includes spatial information in the coding. It requires only regular interconnections and nonlinear devices with limited fan-out. Nevertheless the potential of this kind of logic ranges from parallel binary arithmetic to a programmable MIMD processor. Fundamentals of symbolic substitution and its applications are presented.

Digital Optical Computing With Symbolic Substitution

The authors discuss digital optics, a technology for processing, transport, and storage of optical digital information. Digital optics offers both the high temporal bandwidth of fiber communications and the high connectivity and information density of optical imaging. The energy dissipation per bit of communicated information, as well as the chip area dedicated to interconnections, can be significantly lower in optics than in high-speed electronics. This motivates the introduction of parallel optical interconnections through free space in communication-intensive areas of digital information processing such as switching in telecommunications and within multiprocessors. Digital optical circuits can be constructed by cascading two-dimensional planar arrays of optical logic gates interconnected in free space. The state of the art and the trends in digital optical information processing systems for optical logic, optoelectronic interfaces, and optical free-space interconnection systems are reviewed. >

Digital optics

This paper introduces programmable arrays of optically inter-connected electronic processors and compares them with conventional symbolic substitution (SS) systems. The comparison is made on the basis of computational efficiency, speed, size, energy utilization, programmability, and fault tolerance. The small grain size and space-invariant connections of SS lead to poor computational efficiency, difficult programming, and difficult incorporation of fault tolerance. Reliance on optical gates as its fundamental building elements is shown to give poor energy utilization. Programmable optoelectronic multiprocessor (POEM) systems, on the other hand, provide the architectural flexibility for good computational efficiency, use an energy-efficient combination of technologies, and support traditional programming methodologies and fault tolerance. Although the inherent clock speed of POEM systems is slower than that of SS systems, for most problems they will provide greater computational throughput. This comparison does not take into account the recent addition of crossover interconnect and space-variant masks to the SS architecture.

Programmable Optoelectronic Multiprocessors And Their Comparison With Symbolic Substitution For Digital Optical Computing

A binary image algebra (BIA) that gives a mathematical description of parallel processing operations is described. Rigorous and concise BIA representations of parallel arithmetic and symbolic substitution operations are given. A sequence of programming steps for implementation of these operations on a parallel architecture is specified by the BIA representation. Examples of arithmetic operations implemented on a digital optical cellular image processor architecture are given.

Image algebra representation of parallel optical binary arithmetic.

Position-coded modulo m lookup tables (LUTs) with gate complexities equal to m(2), 2m, and 4 radicalm are discussed. The design of practical miniaturized LUTs is described along with results obtained from a prototype 7 x 7 laser diode LUT. A factored m(2) LUT technique that achieves large dynamic range is presented. Several LUT performance issues are also discussed.

Optical processing with residue LED/LD lookup tables

There has been difficulty in achieving a fully parallel, digital optical adder or multiplier. The primary obstacle is the carry operation inherent in any fixed-radix number system. The concepts of residue number representation and symbolic substitution can be combined to produce a parallel optical arithmetic/logic unit.

Optical arithmetic/logic unit based on residue arithmetic and symbolic substitution.

Cet article decrit le concept d'une unite arithmetique logique d'un calculateur numerique optique base sur une architecture «crossbar»

Arithmetic/logic unit based on optical crossbar architecture.

Recent work on optical table look-up devices has been generalized to include control functions. These functions introduce programmability to this approach to optical digital computing. A general formalism for performing logic functions using positionally encoded look-up tables is developed and applied to a programmable Boolean gate and a residue arithmetic module. Hardware implementations of the tables are described.

T. L. Houk

Papers

Optical arithmetic/logic unit based on residue arithmetic and symbolic substitution.

Arithmetic/logic unit based on optical crossbar architecture.

Optical Table Look-Up Approach To General Purpose Digital Computing