Quantum-dot cellular automata is an ideal computational model that offers lowered size, reduced energy consumption, higher speed, and deliberate design at nanometer scale. It was created as a solution to the scalability issue inherent in conventional Complementary Metal Oxide Semiconductor technologies. Coulomb repulsion is the foundation upon which the revolutionary nanotechnology known as QCA is built. On the nanoscale, the field of quantum computing has surfaced as a powerful model for the development of technology that is very effective in terms of energy consumption. In this article an Energy Efficient QCA based BEC-1 code Converter is proposed. It is designed by employing Feynman Gate and implemented in QCA Designer Tool. By optimizing its layout, BEC-1 has reduced the number of parameters to achieve efficiency, such as the cell count, space occupied in μm2, 2.5 clock cycles latency, Average Energy dissipation in meV, Power dissipation in nano watt. According to the findings of the simulation, the proposed design functions without a single glitch and working as per its truth table and exhibits very little energy consumption.