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We present Virtual High-resolution Time (VHT), a power-proportional time-keeping service that offers a baseline power draw of a low-speed clock (e.g. 32 kHz crystal), but provides the time resolution that only a higher frequency clock could offer (e.g. 8 MHz crystal), and scales essentially linearly with access (i.e. the "reading" and "writing" of the clock). We achieve this performance by revisiting a basic assumption in the design of time-keeping systems -- that to achieve a given time-stamping resolution, a free-running timebase of equivalent frequency is needed. We show that this assumption is false and argue that the dependence is not on usage (i.e. whether on or off) but rather on access (i.e. reading and writing). Therefore, it is possible to duty cycle the free-running timebase itself, and augment it with a lower-frequency, temperature-compensated one, which achieves comparable resolution, at a fraction of the power, for typical workloads. The key technical challenge lies in duty cycling the fast clock and synchronizing the fast and slow clocks. To assess the viability of the approach, we explore how VHT could be implemented on several different platform architectures, and to study the power/performance tradeoff, we characterize VHT on one particular architecture in detail. Our results show power-proportional operation with a 10x improvement in average power and a synchronization accuracy exceeding 1 μs at duty cycles below 0.1%.