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Binary Neural Networks (BNNs) have been shown to be robust to random bit-level noise, making aggressive voltage scaling attractive as a power-saving technique for both logic and SRAMs. In this work, we introduce the first fully programmable IoT end-node system-on-chip (SoC) capable of executing software-defined, hardware-accelerated BNNs at ultra-low voltage. Our SoC exploits a hybrid memory scheme where error-vulnerable SRAMs are complemented by reliable standard-cell memories to safely store critical data under aggressive voltage scaling. On a prototype in 22nm FDX technology, we demonstrate that both the logic and SRAM voltage can be dropped to 0.5Vwithout any accuracy penalty on a BNN trained for the CIFAR-10 dataset, improving energy efficiency by 2.2X w.r.t. nominal conditions. Furthermore, we show that the supply voltage can be dropped to 0.42V (50% of nominal) while keeping more than99% of the nominal accuracy (with a bit error rate ~1/1000). In this operating point, our prototype performs 4Gop/s (15.4Inference/s on the CIFAR-10 dataset) by computing up to 13binary ops per pJ, achieving 22.8 Inference/s/mW while keeping within a peak power envelope of 674uW - low enough to enable always-on operation in ultra-low power smart cameras, long-lifetime environmental sensors, and insect-sized pico-drones.