A standard membrane model, based on the continuous deterministic Hodgkin-Huxley equations, is compared to an alternative membrane model, based on discrete stochastic ion channel populations represented through Markov processes. Simulations explore the relationship between these two levels of description: the behavior predicted by the macroscopic membrane currents versus the behavior predicted by their microscopic ion channels. Discussion considers the extent to which these random events underlying neural signals mediate random events in neural computation.