Canonical quaternary signed-digit arithmetic using optoelectronics symbolic substitution |
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Authors: | AK Cherri NI Khachab |
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Institution: | The authors are at Kuwait University, College of Engineering and Petroleum, Department of Electrical and Computer Engineering, PO Box 5969 Safat 13060, Kuwait |
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Abstract: | A higher radix based signed-digit number system, such as the quaternary signed-digit (QSD) number system, allows higher information storage density, less complexity, fewer system components, and fewer cascaded gates and operations. An optoelectronics symbolic substitution scheme to handle the parallel quaternary signed-digit (QSD) arithmetic operations is proposed. A conversion algorithm is employed on the QSD numbers to simplify the addition process and reduce the number of the optical symbolic substitution rules. The optical addition operation of two QSD numbers is performed in one-step. An efficient shared content-addressable memory (SCAM)-based optical implementation of the QSD addition/subtraction operations employs a fixed number of minterms for any operand length. The canonical QSD number addition/subtraction scheme requires a significantly reduced number of minterms when compared with a similar previously reported technique. |
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Keywords: | optical computing canonical quaternary signed-digit numbers symbolic substitution truth tables spatial light modulators shared content-addressable memory |
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