Thus, binary to quaternary and quaternary to binary converters are designed using down literal circuits. Circuits for modulo-4 addition and multiplication require only 4 gates. With the help of quaternary logic levels, the authors have reduced the interconnections. They have also used less number of gates and hence less area for modulo-4 arithmetic operations. The proposed circuit is Galois addition and multiplication which requires fewer gates, so that the complexity of the circuit will get reduce. Proposed circuits are suitable for implementing in VLSI with less number of inter-connections and less area.