As exascale systems come online, more ways are needed to keep them within reasonable power budgets. This study aims to help uncover power advantages in algorithms likely ubiquitous in high-performance workloads such as searching. This study explored the power efficiency of binary search and its ternary variant, comparing consumption under different scenarios and workloads. Accurate modern on-chip integrated voltage regulators were used to get reliable power measurements. Results showed the binary version of the algorithm, which runs slower but relies on a barrel-shifter circuit, to be more power efficient in all studied scenarios offering an attractive time-power tradeoff. The cumulative savings were significant and will likely be valuable where the search may be a substantial fraction of workloads, especially massive ones.