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This paper tries to explain the network structures and methods of single-layer perceptron and multi-layer perceptron. It also analyses the linear division and un-division problems in logical operation performed by single-layer perceptron. XOR is linear un-division operation, which cannot be treated by single-layer perceptron. With the analysis, several solutions are proposed in the paper to solve the problems of XOR. Single-layer perceptron can be improved by multi-layer perceptron, functional perceptron or quadratic function. These solutions are designed and analyzed.