逻辑函数FGOC展开的最小化技术  

Technique simplifying OR-coincidence expansion of logic functions under fixed polarities

作　　者：应时彦[1] 肖林荣[2] 杭国强[2] 

机构地区：[1]浙江工业大学信息工程学院,浙江杭州310014 [2]浙江大学信息与电子工程学系

出　　处：《浙江大学学报（工学版）》2007年第3期423-426,455,共5页Journal of Zhejiang University：Engineering Science

基　　金：浙江省自然科学基金资助项目(Y105124)

摘　　要：为了减少已有图形法的最小化算法的计算量,提出了新的逻辑函数在固定极性下的或-符合(FGOC)展开最小化算法.引入了逻辑函数FGOC展开的矩阵,分析了单变量与二变量逻辑函数的FGOC展开及其矩阵.基于符合运算的性质,推导出此矩阵的递推律.推广至任意多变量逻辑函数,可以得到全部FGOC的展开矩阵.并提出了FGOC展开最小化方法.通过分析逻辑函数的FGOC展开过程,研究了变量数与符合算法的运算次数的规律.结果表明,与图形法的FGOC展开最小化方法相比较,随着变量数的增加,符合运算次数大幅度减少.该方法适合于计算机编程实现,并能快速获得计算结果.In order to reduce the amount of computation based on original graphic simplifying method, a new simplifying algorithm for the fixed-polarity generalized OR-coincidence （FGOC） expansion of logic functions was proposed. The matrix for FGOC expansion of logic functions was introduced. The FGOC expansion of logic functions with single and 2 variables and their matrixes were analyzed. Recursive relationship of the matrix was deduced based on the properties of coincidence operation. After the recursive re- lationship of the matrix was expanded to the arbitrary multi-variable logic functions, all the FGOC expansion of matrix was expressed, and the method for simplifying FGOC expansions was proposed. Process of the FGOC expansion in logic functions was investigated, and the rule of calculation number and variable number was studied. Results show that compared with the graphic simplifying method, the calculation number is dramatically reduced with the increasing variable number. The algorithm is suitable for programming on computers and can rapidly achieve outcome.

关 键 词：或-符合展开 固定极性 逻辑函数化简 逻辑设计 

分 类 号：TP331[自动化与计算机技术—计算机系统结构]