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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 37, Iss. 20 — Jul. 10, 1998
  • pp: 4405–4418

Recoded and nonrecoded trinary signed-digit adders and multipliers with redundant-bit representations

Abdallah K. Cherri and Mohammed S. Alam  »View Author Affiliations


Applied Optics, Vol. 37, Issue 20, pp. 4405-4418 (1998)
http://dx.doi.org/10.1364/AO.37.004405


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Abstract

Highly-efficient two-step recoded and one-step nonrecoded trinary signed-digit (TSD) carry-free adders–subtracters are presented on the basis of redundant-bit representation for the operands’ digits. It has been shown that only 24 (30) minterms are needed to implement the two-step recoded (the one-step nonrecoded) TSD addition for any operand length. Optical implementation of the proposed arithmetic can be carried out by use of correlation- or matrix-multiplication-based schemes, saving 50% of the system memory. Furthermore, we present four different multiplication designs based on our proposed recoded and nonrecoded TSD adders. Our multiplication designs require a small number of reduced minterms to generate the multiplication partial products. Finally, a recently proposed pipelined iterative-tree algorithm can be used in the TSD adders–multipliers; consequently, efficient use of all available adders can be made.

© 1998 Optical Society of America

OCIS Codes
(200.0200) Optics in computing : Optics in computing
(200.4540) Optics in computing : Optical content addressable memory processors
(200.4560) Optics in computing : Optical data processing
(200.4860) Optics in computing : Optical vector-matrix systems

History
Original Manuscript: August 18, 1997
Revised Manuscript: January 22, 1998
Published: July 10, 1998

Citation
Abdallah K. Cherri and Mohammed S. Alam, "Recoded and nonrecoded trinary signed-digit adders and multipliers with redundant-bit representations," Appl. Opt. 37, 4405-4418 (1998)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-37-20-4405


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