逻辑函数在布尔减-除-非代数系统中的标准展开式及其化简

Standard expansions and its minimization of an logic function in Boolean SUBTRACTION-DIVISION-NOT algebraic system.

布尔减、布尔除与非运算构成完备集.从与-或-非代数系统中的最小项、最大项展开式出发,推导了任意逻辑函数在减-除-非代数系统中的标准DOS(减之除)和标准SOD(除之减)展开式.在此基础上给出了DOS和SOD逻辑函数的代数化简法和图形化简法,给出的化简实例验证了上述化简方法的有效性.

Boolean SUBTRACTION, DIVISION and NOT operations make up a complete set. According to the operation regulations of Boolean SUBTRACTION, DIVISION and NOT, the standard DOS and SOD expansions of an arbitrary logic function in these complete sets were deduced from the minterm expansion and maxterm expansion in AND-OR-NOT algebraic system, Based on the standard expansions and operation regulations, the methods of algebraic and graphic minimization about SUBTRACTION-DIVISION-NOT logic functions were given, and several simplification examples were presented. These practical examples proved the effectiveness of the above simplification methods.