Plasmonic metal-insulator-metal (MIM) waveguides sustain excellent property of confining the surface plasmons up to a deep subwavelength scale. In this paper, linear and S-shaped MIM waveguides are cascaded together to design the model of Mach-Zehnder interferometer (MZI). Nonlinear material has been used for switching of light across its output ports. The structures of even and odd parity generators are projected by cascading the MZIs. Parity generator and checker circuit are used for error correction and detection in an optical communication system. Study and analysis of proposed designs are carried out by using the MATLAB simulation and finite-differencetime- domain (FDTD) method.