CRM型对称函数及其逻辑综合

Symmetric function based on OR-coincidence algebraic system and its logic synthesis.

逻辑函数的CRM展开式是逻辑函数在或-符合代数系统中的一种基本表示形式,而对称函数又有许多独特的优点.在讨论了与-或-非代数系统中和最大项对应的对称函数定义、性质基础上,研究了CRM型基本对称函数的定义及其性质.进而提出了基于全加器以及CRM型PLA网络的逻辑综合,还举例说明了逻辑综合过程.该综合的PLA网络是以或、符合二种运算作为基本运算的,类似于与、异或的电路实现,CRM型对称函数常常可以导致使用较少的门及较少的连线,更重要的是它具有易于测试等特点.本文的讨论揭示了CRM型基本对称函数的内在规律,有助于开拓或-符合代数系统的应用.

CRM expansion is one of the basic expansions under OR-Coincidence algebraic system.Symmetry is a significant property of a logic function.Based on analysing symmetric function in the AND～OR-NOT algebraic system,symmetric functions were investigated based on OR-Coincidence algebraic system.The definition and properties of CRM type fundamental symmetric functions were also discussed.Based upon it,one kind of syntheses of an arbitrary symmetric function based on CRM type fundamental symmetric function was proposed： the logic synthesis using full-adder and CRM type PLA.The corresponding synthesis procedure was shown by analysing an example.The method has several advantages that the logic synthesis based on the symmetry of logic function is simpler and more effective as compared with conventional design.