Empirical evidence demonstrates that every region of the neocortex represents information using sparse activity patterns. This paper examines Sparse Distributed Representations (SDRs), the primary information representation strategy in Hierarchical Temporal Memory (HTM) systems and the neocortex. We derive a number of properties that are core to scaling, robustness, and generalization. We use the theory to provide practical guidelines and illustrate the power of SDRs as the basis of HTM. Our goal is to help create a unified mathematical and practical framework for SDRs as it relates to cortical function.