The performance of 4×1 multiplexer (MUX) and 8×1 multiplexer (MUX) using GaAs–AlGaAs based optical microring resonator (OMRR) is presented. The 4×1 MUX is designed with two OMRR and 8×1 MUX is designed with three OMRR. The proposed structure of 8×1 MUX is further used to design 8-bit logic shifter circuit. The nonlinear property of OMRR is used as an optical switch in all the optical logic circuits. The performance of 4×1 MUX, 8×1 MUX, and 8-bit logic shifter circuit is analyzed using Z-domain model. The various important parameters of the proposed model, such as on–off ratio [τon-off(dB)], full-width half maximum (FWHM), Q-factor, extinction ratio [ξER(dB)], contrast ratio [χCR(dB)] amplitude modulation [ηAM(dB)], are also analyzed.