The performance of multiplexer (MUX) and multiplexer (MUX) using GaAs–AlGaAs based optical microring resonator (OMRR) is presented. The MUX is designed with two OMRR and MUX is designed with three OMRR. The proposed structure of 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 MUX, 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 , full-width half maximum (FWHM), -factor, extinction ratio , contrast ratio amplitude modulation , are also analyzed.