Our purpose is to realize discrete neural networks (NNs), whose some parameters are discretized, as a low-resource and fast NNs for acoustic models. Two essential problems should be tackled for its realization; 1) the reduction of discretization errors and 2) the implementation method for fast processing. We propose a new parameter training algorithm for 1) and an implementation using look-up table (LUT) on general-purpose CPUs for 2), respectively. The former can set proper boundaries of discretization at each node of NNs, resulting in the reduction of discretization error. The latter can reduce the memory usage of NNs within the cache size of CPU by encoding parameters of NNs. Experiments with 2-bit discrete NNs showed that our algorithm maintained almost the same word accuracy as 8-bit discrete NNs and achieved a 40% increase in speed of the NN's forward calculation.