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We present a novel design method and potential application for optical XOR, XNOR, NAND, and OR logic gates for binary-phase-shift-keyed signal processing devices. The devices are composed of multi-mode interference waveguides and convert the phase information of the input signal to amplitude at the output. We apply the finite element method for numerical simulations, and the evaluated least ON to OFF logic-level contrast ratios for the XOR, XNOR, NAND, and OR logic gates are 21.5 dB, 21.5 dB, 22.3 dB, and 22.3 dB, respectively. The proposed logic gates are extremely promising signal processing devices for binary-phase-shift-keyed signals in packet switching systems.