We propose a concise hardware architecture supporting efficient exclusive OR (XOR) and exclusive NOR (XNOR) operations, by employing a single photonic spiking neuron based on a passive add-drop microring resonator (ADMRR). The threshold mechanism and inhibitory dynamics of the ADMRR-based spiking neuron are numerically discussed on the basis of the coupled mode theory. It is shown that a precise XOR operation in the ADMRR-based spiking neuron can be implemented by adjusting temporal differences within the inhibitory window. Additionally, within the same framework, the XNOR function can also be carried out by accumulating the input power over time to trigger an excitatory behavior. This work presents a novel, to the best of our knowledge, and pragmatic technique for optical neuromorphic computing and information processing utilizing passive devices.