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The purpose of this research paper is to present a new all-optical scheme to implement the logical behavior of generalized $n$th-order (2${}^n$:1) multiplexer logic. The proposed all-optical design is based on micro-ring resonator (MRR)-based all-optical switches and constructed by using “2${}^{n+1}$-2” MRR structures, arranged in a series “$n$” stage architecture. The presented configuration enjoys advantageous features like compact-sized systematic structure and ultra-fast speed. To validate the logical behavior of the proposed $n$th-order multiplexer, a second-order (2²:1) multiplexer is derived (from the proposed scheme) and discussed. Further, the usability of the presented all-optical multiplexer is demonstrated by developing an all-optical reconfigurable logic gate that can be reconfigured to perform various logic operations. To verify the logical behavior of MRR-based all-optical switch and presented all-optical multiplexer logic, numerical simulations through MATLAB software have been performed. The reported reconfigurable logic structure is also simulated in the MATLAB environment to validate the desired behavior.