In this paper, a novel ergodic cellular automaton neuron model and its network is presented. Additionally, a learning method of the presented network to mimic a network of biologically plausible neuron models is presented. It is shown that the learning method enables the presented network to reproduce input-output relations of the biologically plausible neuron network model. Furthermore, the presented network and the learning method are implemented in an FPGA and it is shown that the presented network is more hardware-efficient compared to the biologically plausible neuron network model.