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Nonvolatile stateful logic computing in memristors is a promising paradigm with which to realize the unity of information storage and processing in the same physical location that has shown great feasibility for breaking the von Neumann bottleneck in traditional computing architecture. How to reduce the computational complexity of memristor-based logic functions is a matter of concern. Here, based on a general logic expression, we proposed a method to implement the arbitrary logic of complete 16 Boolean logic in two steps with one memristor in the crossbar architecture. A representative functional complete NAND logic is successfully experimentally demonstrated in the filamentary Ag–AgGeTe–Ta memristors to prove the validity of our method. We believe our work may promote the development of the revolutionary logic in memory architectures.