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Optoelectronic symbolic substitution based canonical modified signed-digit arithmetic |
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| Authors: | A.K. Cherri M.S. Alam A.A.S. Awwal |
| Affiliation: | aAKC is at Kuwait University, Department of Electrical and Computer Engineering, P.O. Box 5969, Safat 13060, Kuwait;bMSA is at Purdue University, Department of Engineering, Fort Wayne, IN 46805-1499, USA;cAASA is at Wright State University, Department of Computer Sciences and Engineering, Dayton, Ohio 45435, USA |
| Abstract: | A single-step optoelectronics symbolic substitution scheme to handle parallel modified signed-digit (MSD) arithmetic operations is proposed. Conversion algorithms from MSD numbers into a canonical MSD representation are provided. The canonical MSD numbers have the property that no two consecutive digits are non-zero. The addition operation of two CMSD numbers is performed in one step. It will be shown that through the use of CMSD representation, the number of symbolic substitution rules in an optical content-addressable memory (CAM) based system is significantly reduced. The number of symbolic substitution rules can be further reduced to an optimum value through a proposed shared content-addressable memory optical set-up. Further, the proposed optical scheme doubles the storage efficiency of the shared content-addressable memory. |
| Keywords: | optical computing canonical binary representation signed-digit numbers symbolic substitution truth tables spatial light modulators shared content-addressable memory |
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