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

Abdallah K. Cherri, Mohammed S. Alam
1998 Applied Optics  
Highly-efficient two-step recoded and one-step nonrecoded trinary signed-digit ͑TSD͒ carry-free adderssubtracters are presented on the basis of redundant-bit representation for the operands' digits. It has been shown that only 24 ͑30͒ minterms are needed to implement the two-step recoded ͑the one-step nonrecoded͒ 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
more » ... s, 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.
doi:10.1364/ao.37.004405 pmid:18285891 fatcat:q2cgbkhfkvgdddztrwi3oxib3e