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
(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
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)