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We experimentally demonstrate on-chip dual-channel all-optical AND logic operations based on four-wave mixing (FWM) for on-off keying (OOK) signals in a multimode silicon waveguide. A two-mode (de)multiplexing circuit consisting of tapered directional coupler-based (de)multiplexers and a multimode waveguide is designed and fabricated for this application. Experimental results show open eye-diagrams and confirm the logic operations with moderate power penalties for both modes.