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目的:为基于RTD器件的任意n变量函数实现提供一个简单有效的三变量通用逻辑门,简化基于RTD器件的集成电路设计。创新点:使用谱技术和Reed-Muller展开提出一种新的算法。此算法可将三变量非阈值函数转化成三变量阈值函数,并利用此算法设计一种新的基于RTD的三变量通用逻辑门ULG3。方法:首先,介绍阈值逻辑、谱技术和Reed-Muller展开的基本概念。然后,提出一种新的算法。此算法可将三变量非阈值函数转化成三变量阈值函数,并发现除两个特殊的三变量非阈值函数以外,其他所有的三变量非阈值函数都可以分解成两个三变量阈值函数异或的形式。最后,利用此算法并基于UTLG(图1)设计一个新的三变量通用逻辑门ULG3(图4)。结论:新的三变量通用逻辑门ULG3由两个UTLG和一个XOR3组成,对任意的三变量函数都可由一个ULG3门来实现。
OBJECTIVE: To provide a simple and effective three-variable general-purpose logic gate for any n-variable function implementation based on RTD devices and to simplify the design of integrated circuits based on RTD devices. Innovations: Using spectral techniques and Reed-Muller expansion to propose a new algorithm. This algorithm can transform the three-variable non-threshold function into a three-variable threshold function and use this algorithm to design a new RTG-based three-variable universal logic gate ULG3. Methods: First, we introduce the basic concepts of threshold logic, spectral techniques and Reed-Muller expansion. Then, a new algorithm is proposed. This algorithm transforms the three-variable non-threshold function into a three-variable threshold function and finds that all three-variable non-threshold functions except for two special three-variable non-threshold functions can be decomposed into two three-variable threshold functions XOR form. Finally, we use this algorithm to design a new three-variable general purpose logic gate ULG3 based on UTLG (Figure 1) (Figure 4). Conclusion: The new three-variable general purpose logic gate ULG3 consists of two UTLGs and one XOR3, which can be implemented by a ULG3 gate for any three-variable function.