Optical logical operations have sparked major interest in the past decade since they can enable many applications, particularly those involving high-throughput and on-the-fly data processing such as secured wireless communication and autonomous driving. However, the reported optical logic gates rely heavily on the precise control of input light/pump light, including the phase, polarization, and amplitude. Due to the complexity and difficulty in these precise controls, the two output states may suffer from an inherent instability and a low contrast ratio of intensity. Moreover, the miniaturization of optical logic gates becomes difficult if the extra bulky apparatus for these controls is considered. As such, it is desirable, albeit challenging, to get rid of these complicated controls and to achieve full logic functionality in a compact photonic system.