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A Memristor is a nonlinear resistor with memory, and is considered as the fourth type of basic circuit element except resistor, capacitor and inductor. With special circuitry characteristics, memristor can be used for both information storage and logic operations. In traditional Von Neumann computer architecture, address decoder is an important component connecting processor and memory. This paper aims at designing a decoder based on memristors. We first analyze and model the characteristics of memristor with HSPICE, and then design decoders based on NOR operation with memristors and compare their performance. The experimental results and analysis show that our design is right in function and has good scalability.