A pulse-mode digital multilayer neural network (DMNN) based on stochastic computing techniques is implemented with simple logic gates as basic computing elements. The pulse-mode signal representation and the use of simple logic gates for neural operations lead to a massively parallel yet compact and flexible network architecture, well suited for VLSI implementation. Algebraic neural operations are replaced by stochastic processes using pseudorandom pulse sequences. The distributions of the results from the stochastic processes are approximated using the hypergeometric distribution. Synaptic weights and neuron states are represented as probabilities and estimated as average pulse occurrence rates in corresponding pulse sequences. A statistical model of the noise (error) is developed to estimate the relative accuracy associated with stochastic computing in terms of mean and variance. Computational differences are then explained by comparison to deterministic neural computations. DMNN feedforward architectures are modeled in VHDL using character recognition problems as testbeds. Computational accuracy is analyzed, and the results of the statistical model are compared with the actual simulation results. Experiments show that the calculations performed in the DMNN are more accurate than those anticipated when Bernoulli sequences are assumed, as is common in the literature. Furthermore, the statistical model successfully predicts the accuracy of the operations performed in the DMNN.