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A generalized rotate-and-fire digital spiking neuron model that can be implemented by a simple asynchronous sequential logic circuit is proposed. The model can exhibit various nonlinear phenomena and responses to stimulation inputs. It is shown that the model can reproduce five types of inhibitory responses of Izhikevich's simplified ordinary differential equation neuron model. In addition, field programmable gate array experiments show that a learning algorithm enables the model to automatically reproduce nonlinear responses of a biological neuron and neuron models in the neuron simulator.