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We have experimentally demonstrated 16-ary all-optical logic minterms for four-line inputs at 40 Gb/s utilizing delay interferometers (DIs) and cascading semiconductor optical amplifiers (SOAs) without any assisting light. Extinction ratios (ERs) of the intermediate results after the first SOA are all over 11 dB which ensures the capability to cascade to the second one. The final results are in the form of return-to-zero (RZ) format with correct and clear temporal waveforms. The proposed scheme should be a promising candidate for constructing arbitrary more complex logic functions.