基于冗余位表示的修正符号数算术运算。

Modified signed-digit arithmetic based on redundant bit representation.

作者信息

Huang H, Itoh M, Yatagai T

出版信息

Appl Opt. 1994 Sep 10;33(26):6146-56. doi: 10.1364/AO.33.006146.

DOI:10.1364/AO.33.006146

PMID:20936032

Abstract

Fully parallel modified signed-digit arithmetic operations are realized based on redundant bit representation of the digits proposed. A new truth-table minimizing technique is presented based on redundant-bitrepresentation coding. It is shown that only 34 minterms are enough for implementing one-step modified signed-digit addition and subtraction with this new representation. Two optical implementation schemes, correlation and matrix multiplication, are described. Experimental demonstrations of the correlation architecture are presented. Both architectures use fixed minterm masks for arbitrary-length operands, taking full advantage of the parallelism of the modified signed-digit number system and optics.

摘要

基于所提出的数字冗余位表示实现了完全并行的修正符号数算术运算。基于冗余位表示编码提出了一种新的真值表最小化技术。结果表明，使用这种新表示法，仅34个最小项就足以实现一步修正符号数加法和减法。描述了两种光学实现方案，即相关和矩阵乘法。给出了相关架构的实验演示。两种架构都使用固定的最小项掩码来处理任意长度的操作数，充分利用了修正符号数系统和光学的并行性。