Computer experiments have become increasingly popular in both scientific research and industrial applications. Recently, there are emerging interests in the analysis of computer experiments with binary outputs. Statistical modeling for such deterministic black-box systems can be challenging, since they require model interpolation and appropriate uncertainty quantification. The commonly used Gaussian process-based methods consider a latent-space approach to model the binary output, but cannot directly interpolate the output in the observational space. In this work, we propose a novel probabilistic predictive model based on the Hopfield process, which focuses on enabling model interpolation on binary outputs and desirable uncertainty quantification. An efficient model estimation is developed. We also enhance uncertainty quantification and model inference via an empirical Bayesian approach. Moreover, we propose a new active learning procedure to efficiently identify the decision boundary. Both theoretical investigations and numerical studies are conducted to elaborate on the merits of the proposed methods.