An all-optical half adder (AOHA) on a square lattice photonic crystal structure with silicon rods in air is proposed. The AOHA design consisted of constructive and destructive interference-based XOR gate and AND gate, which were respectively devised by Y- and T-shaped waveguides to produce Sum and Carry logical outputs. The band structure of the proposed device was assessed by the plane wave expansion (PWE) method, and the electric field distributions and functional parameters were estimated by the finite difference time domain (FDTD) method. The functional parameters obtained for the AOHA include a contrast ratio of 9.42 dB for the Sum and 12.87 dB for the Carry, response time of 0.888 ps, operating bit rate of 1.126 Tb/s, and footprint of 290  μm². The normalized intensity of the AOHA was >86  %   and <12  %   for logic “1” and logic “0,” respectively. Hence, the proposed AOHA design is highly suitable for photonic networks and photonic integrated circuits.