对布尔代数中卡诺图的研究

Research on Karnaugh map in Boolean algebra

由于卡诺图具有几何相邻与逻辑相邻之间的良好对应关系 ,故在布尔代数中得到广泛应用 ,文章分析了传统卡诺图在简化多变量 ( n >5 )函数时 ,其对应关系所面临的困难 ,提出三维卡诺图及卡诺图阵列的概念。采用适当的排列方式可将图中几何相邻与逻辑相邻的对应项增加到 6个以上 ,为了使其具有实用性 ,又引入一定的画图规则 ,对三维卡诺图加以改进 ,并举例说明它们的使用方法。结果表明 ,采用该方法对六变量至八变量的逻辑函数进行综合化简时 ,仍具有简便直观、可靠性高及易操作等优点 ,且有较好的实用价值。

Karnaugh map can be used largely in Boolean algebra because it has fine correspondence between adjacency on geometry and adjacency on logic. In this paper,the difficulty of correspondence in simplifying the multiple-variable (n>5) function with the traditional Karnaugh map is analyzed, and the concepts of three-dimensional Karnaugh map and Karnaugh map array are proposed. By using proper range, the correspondence terms between adjacency on geometry and adjacency on logic can increase to six or more in the map. Some pictorial rules are adopted, and the three-dimensional Karnaugh map is improved for practicality of the map,and the usage of the improved map is illustrated with examples in the paper. The logic functions of six to eight variables are simplified and synthesized by using the improved map. The result shows that the presented method has the advantages of simplicity, intuition, good reliability and easy operation,so it is valuable in practical use.