We propose an all-optical design of NOT, AND, OR, one-bit half adder, and subtractor using a microring resonator-based 2:1 multiplexer. As a substitute for traditional CMOS technology, the sector is moving toward large-scale optical integrated circuits due to growing needs for ultraspeed terahertz data transport and processing. Furthermore, energy-efficient connections are becoming more and more crucial. Using MATLAB, the complete design is thoroughly simulated and verified at an operational speed of nearly 260 Gbps. The faster response times of the suggested multiplexer-based circuits make them especially useful for digital signal processing and communication systems. Also performance parameters, such as the “extinction ratio,” “contrast ratio,” “amplitude modulation,” “on–off ratio,” “quality factor,” “photon cavity lifetime,” and “relative eye opening,” are estimated. Circuit parameters that are optimized are chosen to construct the circuit practically.