基于择多门的QCA自动逻辑综合

QCA automatic logic synthesis based on majority gate

为了实现三输入布尔函数的自动综合,文章提出了卡诺图八位二进制表达式的概念。对于任意3-feasible布尔函数,它的卡诺图八位二进制表达式范围为00000000-11111111(0～255),以量子元胞自动机(quantum cellular automata,QCA)中的择多门为基础,将40个基本函数按照M(M1,M2,M3)的规则充分搭配,得到的结果范围为0～255,即实现了任意3-feasible布尔函数逻辑功能。输入目标函数F,按照择多门最少、反相器最少、门输入最少的原则编程筛选出能实现F逻辑功能的最优M (M1,M2,M3)组合。仿真结果表明,对于任意的3-feasible函数,最后都可以用不超过4个择多门、2级逻辑层的择多逻辑表达式表示,从而实现了三输入的自动逻辑综合,方便QCA电路的搭建。

The concept of the eight-bit K-maps binary expression is presented in order to realize the automatic synthesis of three-input Boolean functions.For any 3-feasible Boolean function,its eight-bit K-maps binary expression has a range of 00000000-11111111(0-255).Based on the majority gate in quantum cellular automata(QCA),forty primitive functions are fully matched according to the rules of M(M 1,M 2,M 3),and the results are in the range of 0-255.This means that logic function of any 3-feasible Boolean function can be implemented.The optimal combination of M(M 1,M 2,M 3)that can achieve logic function of the objective function F is selected according to the principle of least number of majority gates,least number of inverters and minimum gate input.The simulation results show that for any 3-feasible function,it can be represented by no more than four majority gates and two logic levels.So the three-input automatic logic synthesis could be achieved to facilitate the QCA circuit design.