Guest Editorial: Special Section on Computer Arithmetic for Optical Computing

Around the same time, non-binary systemssuch as multiple valued logic ~MVL!~Ref. 3! alsoachieved prominence both in optics and digital comput-ing. Since then a large number of papers have been pub-lished in optical computer arithmetic. This special sectionis an attempt to capture current research in computerarithmetic for optical computing. The ﬁve major areasthat are presented in this section are MSD-based algo-rithm and systems, optimization of MVL, novel architec-tures for binary optical computing, high accuracy analogoptical system implementations, and system studies forfault-tolerance and accuracy. Some of the papers mayhave overlap of two or more areas with one primary fo-cus; they are pointed out in the following discussion.The largest cluster of papers appears in the area ofsigned-digit arithmetic and its implementation. A numberof different techniques for addition, multiplication and di-vision are proposed by several authors. The number sys-tems addressed include redundant binary, MSD binary,negabinary, MSD trinary, recoded trinary and MSD qua-ternary. In terms of number of steps, addition/subtractionin single, dual and triple step has been proposed. Whilethe MSD number system leads to higher information den-sity, if the number of steps is reduced, the truth tablesmay become humongous, which may impose challengingrequirements on the actual implementation. Techniquesfor reducing the cost of such implementations have beenaddressed by some authors. Proposed implementations in-clude space-variant logic array, correlator~composite andpseudo-inverse ﬁlter! and non-holographic content ad-dressable memory ~CAM! using electron-trapping mate-rial. Several authors have proposed novel algorithms andtheir possible optical implementations while others havesuggested implementations and/or optimization on knownalgorithms.The ﬁrst paper in the area of signed-digit arithmetic byLi et al. presents negabinary arithmetic operations for ad-dition, subtraction and multiplication and implementsthem using electron trapping material. A carry free addi-tion technique in signed-digit negabinary ~SDN! is pre-sented with a conversion technique from SDN to normalnegabinary. Zhang and Karim propose modiﬁed two-step,one-step, canonical and three-input algorithms for addi-tion of redundant binary numbers and provide architectureand encoding for corresponding optical space-variantimplementation. Cherri demonstrates single step trinaryand quaternary signed-digit circuits. In general, the reduc-tion in step increases the complexity of the truth table.However, Cherri overcomes the problem by smart digitgrouping to reduce the number of rules and an intelligentpixel encoding to implement the system within a certainspace-bandwidth product. Huang, Itoh and Yatagai pro-pose a new technique for high-speed 2-D data array addi-tion and multiplication based on binary MSD addition anddigit-decomposition-plane representation. Huang, Itohand Yatagai generate all the partial products in paralleland propose to add them using an MSD adder tree. It isinteresting to note that they perform multiplication opera-tion using ﬁve elementary operations such as bitwiseproduct, duplication, shifting, masking and magniﬁcation.In the next paper, Alam introduces trinary division tech-nique based on recoded trinary addition and multiplica-tion. The proposed implementation uses a pseudo-inverseﬁlter correlator. The last two papers in this group byAhmed, Awwal and Power and by Zhang and Karim pro-pose novel implementations of trinary and binary MSDalgorithm. Ahmed, Awwal and Power implement an MSDtrinary adder using composite phase-only-ﬁlter correlatorarchitecture. In this framework, the truth table rules are