Quantum Dot Cellular Automata (QCA) is a prominent technology in Quantum Electronics. This is implemented with the help of quantum cells which are also known as basic building blocks of Quantum Electronics. In QCA technology there are four different clock pulses, clock delay for each clock cycle is 0.25 ns. Using this technology now we are implementing the Binary to Gray code converter. In this paper, we are proposing a design to reduce the number of cells when compared to the previous designs and we are also extending the implementation of the converter up to 5-bits. The number of cells in the proposed design is improved by 2.5%, 36.44%, and 50.66% for 2-bit, 3-bit, and 4-bit respectively. Also, for 3-bit and 4-bit, the total occupied area is improved by 55.56% and 74.680% respectively. In our proposed design it helps us to decrease the area from the previous circuit, which may also lead to the decrease in the power consumption.