All-optical logic gates OR, XOR, AND, and NOT based on two-dimensional (2D) plasmonic metal-insulator-metal (MIM) coupled with an elliptical ring resonator (ERR) are presented, simulated, and investigated by using the numerical method of the FEM (finite elements method). The results are compared and validated with the finite difference time domain (FDTD) method. The proposed logic gates are achieved with the same structure using the constructive and destructive optical interferences between a control signal and input signal(s). Their characterization was mainly done for two spectral regions, visible and near-infrared. A high-intensity contrast ratio (CR) between the logic states (“1” and “0”) can be achieved (28 dB) at these spectral regions. We introduce a new parameter, “gap-threshold ratio (GTR),” to characterize the gap between the maximum and minimum of the transmitted signal intensity for all logic gates. The suggested value of transmission threshold between logic “0” and logic “1” states is \(T_{th}=0.2\). A comparison of the two parameters, CR and GTR, with previous works shows that the proposed structure gives very good results for all logic gates configurations. The proposed all-optical logic gates configuration can be a key component in optical processing and telecommunication devices.