Quantum dot-cellular automata (QCA) is an emerging nanotechnological archetype and has widespread applications in designing nanoscale reversible circuit for nanocomputing. The low power consumption, faster operating speed, and low circuit area of QCA pledge the energy efficient design of logic circuit having high device complexity. This paper demonstrates the design of reversible binary to grey and grey to binary code converter based on Feynman gate using QCA for the first time. Both the proposed reversible code converter circuits have quantum cost as 2. The conversion of binary to grey code is achieved with only one garbage value and the grey to binary code conversion is achieved without any garbage value. The proposed Feynman gate circuit required only 38,880 nm 2 areas and three clocking zones. The reversible binary to grey circuit required only 92,664 nm 2 areas and three clocking zones whereas the reversible grey to binary circuit required only 139,968 nm 2 areas and four clocking zones. The proposed design can be used to realise the nanoarchitecture in computer communication having low power consumption. The evaluation of simulation outcomes of proposed circuit with theoretical knowledge established the functional efficiency of the circuits. The circuits are designed and simulated by QCA Designer-2.0.3.