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

Cherri, AK, Alam, MS. (1998). Recoded and nonrecoded trinary signed-digit adders and multipliers with redundant-bit representations . APPLIED OPTICS, 37(20), 4405-4418. 10.1364/AO.37.004405

cited authors

  • Cherri, AK; Alam, MS

authors

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.

publication date

  • June 10, 1998

published in

Digital Object Identifier (DOI)

start page

  • 4405

end page

  • 4418

volume

  • 37

issue

  • 20