A three-layer back-propagation artificial neural network (BPANN) with four input nodes, two in middle layer nodes, and one output node is constructed for simulating the learning process of performing a four-input logical exclusive-or function. After the training, it is observed that one of the node in the middle layer, say X, calculates any combination of the two inputs are set at the same time. The other node in the middle layer, say Y, calculates any of the input is set. The node in output layer calculates and sets if X is not true and Y is true. The logical exclusive-or of four inputs in the BPANN is reformulated as "if none of any combination of two inputs are set at the same time and at least one of the input is set, then the output is set".
