The performance of 4 x 1 multiplexer (MUX) and 8 x 1 multiplexer (MUX) using GaAs-AlGaAs based optical microring resonator (OMRR) is presented. The 4 x 1 MUX is designed with two OMRR and 8 x 1 MUX is designed with three OMRR. The proposed structure of 8 x 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 x 1 MUX, 8 x 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 [tau(on-off(dB))], full-width half maximum (FWHM), Q-factor, extinction ratio [xi(ER(dB))], contrast ratio [chi(CR(dB))] amplitude modulation [eta(AM(dB))], are also analyzed. (C) 2016 Society of Photo-Optical Instrumentation Engineers (SPIE)