The question of continuous-versus-discrete information representation in the brain is a fundamental yet unresolved question. Historically, most analyses assume a continuous representation without considering the discrete alternative. Our work explores the plausibility of both, answering the question from a communications systems engineering perspective. Using Shannon's communications theory, we posit that information in the brain is represented in discrete form. We address this hypothesis using 2 approaches. First, we identify the fundamental communication requirements of the brain. Second, we estimate the symbol error probability and channel capacity for a continuous information representation. Our work concludes that information cannot be communicated and represented reliably in the brain using a continuous representation - it has to be in a discrete form. This is a major demarcation from conventional and current wisdom. We apply this discrete result to the 4 major neural coding hypotheses, and illustrate the use of discrete ISI neural coding in analyzing electrophysiology experimental data. We further posit and illustrate a plausible direct link between Weber's Law and discrete neural coding. We end by outlining a number of key research questions on discrete neural coding.