The dc-to-dc boost converter is a single-switch, single-inductor, switching circuit used to efficiently transform energy from one dc voltage level to a greater voltage level of the same relative polarity. For a specific resistive load range, as the duty cycle decreases, the boost converter inductor enters a discontinuous current mode of operation - the output load current having decreased to a definable level. This paper analyses the fact that a further reduction of load current, as the duty cycle decreases towards zero, will always result in the re-emergence of a continuous inductor current condition. Further, at the other load extreme, high-current, progressively for increasing load current, starting at low duty cycle conditions, the minimum inductor current always increases from a fixed normalised current level, for a specific load range. These and other hitherto unexplored boost converter properties are analysed and verified mathematically and with PSpice simulations.