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Detailed investigations have been carried out on a Josephson parallel full adder as an example of a functional circuit using Josephson junctions. This circuit can be constructed with fewer devices as compared with conventional Josephson adders. Two-junction interferometers (d.c.-SQUIDs) are utilized as switching elements of the circuit. Only (2N+1) d.c.-SQUIDs are required for construction of an N bit circuit. Discussions focus on design theory of the full adder circuit. An experimental 4 bit circuit operation is also demonstrated.