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In this paper, a twin-structured photonic crystal by means of the alternative square and the circular ring is constructed to design the optical AND gate and XOR gates. Devising these gates, the half-adder is derived from the cohesive twin-structured photonic crystal ring resonator. The designed structure for the proposed gates and half-adder exhibits the desired functionality through the nonlinear Kerr effect, which controls the optical behavior of the resonator. The phase excitation is controlled by an appropriate alteration in the locus of the scatter rods. The transmission of wave and photonic band gap in the proposed structures is obtained by the finite-difference time-domain method. The resonant wavelength for the designed structure is 1550 nm, and the contrast ratio for AND gate, XOR gate and half-adder is 8.6, 7.6, and 15.7 dB, respectively.