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By using two main e ects of cross-gain modulation and cross-phase modulation in semiconductor optical ampli er-based devices, many logic functions of logic AND, OR, XOR, NOR and XNOR are successfully demonstrated. Also, complex systems including all-optical half and full adders in a combination of multiple logic functions are successfully demonstrated. These functions will provide not only increased speed and capacity of telecommunication systems, but also various functionalities including optical packet switching, decision making, basic or complex optical computing, and many other optical signal-processing systems.