In this paper, two Feynman logic gates based on insulator-metal-insulator (IMI) and metal-insulator-metal (MIM) waveguides are proposed. The gates are modeled using the finite-difference time-domain method. The IMI-based Feynman gate shows high extinction ratio (ER) values of 11.06 dB and 7.61 dB for the output bits P and Q, respectively. The ER values of the MIM-based Feynman gate are also 12.83 dB and 7.29 dB for the output bits P and Q, respectively. The footprint of the gates is less than 2µm2. The proposed gates benefit from high ERs in the wavelength range of 1.5-1.6 µm (band C), ultra-compact footprints, and CMOS-compatible structures, which make them potential candidates for use in integrated photonic circuits.