A 2-bit booth encoder with Josephson Transmission Lines (JTLs) and Passive Transmission Lines (PTLs) is designed. The booth encoding method is one of the algorithms to obtain partial products. With this method, the number of partial products decreases down to the half compared to the AND array method. The circuit area of the multiplier designed with the Booth encoder method is compared to that designed with the AND array method. The proposed 4-bit modified booth encoders are designed using Quartus II.