Cherri A K, Alam M S
Appl Opt. 1998 Jul 10;37(20):4405-18. doi: 10.1364/ao.37.004405.
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.
基于操作数数字的冗余位表示，提出了高效的两步重编码和一步非重编码三进制符号位（TSD）无进位加减法器。研究表明，对于任何操作数长度，实现两步重编码（一步非重编码）TSD加法仅需24（30）个最小项。所提出算法的光学实现可通过使用基于相关或矩阵乘法的方案来进行，节省50%的系统内存。此外，我们基于所提出的重编码和非重编码TSD加法器提出了四种不同的乘法设计。我们的乘法设计需要少量简化的最小项来生成乘法部分积。最后，最近提出的流水线迭代树算法可用于TSD加法器 - 乘法器；因此，可以有效利用所有可用的加法器。
