The main purpose of this study is to design combinational logic gates based on a novel configuration of insulator–metal–insulator (IMI) nanoring plasmonic waveguides. Plasmonic logic gates are half adder, full adder, half subtractor, full subtractor, and one-bit comparator and are realized in one structure. The performance of the logic circuits is based on constructive and destructive interferences between the input and control signals. The transmission threshold value is assumed to be 0.35 at the resonance wavelength of 1.310 μm. The transmission spectrum, contrast loss (CL), insertion loss (IL), modulation depth (MD), and contrast ratio (CR) are calculated in order to evaluate the structure’s performance. The maximum transmission of the proposed structure is 232% for full a adder logic gate, and MD exceeds 90% in all plasmonic combinational logic circuits. The suggested design plays a key role in the photonic circuits and nanocircuits for all-optical systems and optical communication systems. The combinational logic gates are analyzed and simulated using the finite element method (FEM).