Abstract. Quantum-dot cellular automata(QCA) is an emerging promising technology that implement digital circuits. It has advantage of nanoscale and low power consumption. Digital computers deal with binary numbers but other code must be used to process the numbers. One of important codes, a Gray code is important in digital communications. Variable gray code converters based on QCA have proposed but the circuits are not considered the scalability and complexity. In this paper, we propose low complexity design of binary to gray code converter. In the circuit, an exclusive-OR(XOR) gate is important so we uses small XOR gate using Nand-Nor-Inverter(NNI) gate. An NNI gate is universal gate that can be used to construct all other logic gates. By using the NNI gate, we propose two-bit binary to gray code converter. The proposed circuit is simulated and compared to other circuit so that verify its performance.