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A custom Human Activity Recognition system is presented based on the resource-constrained Hardware (HW) implementation of a new partially binarized Hybrid Neural Network. The system processes data in real-time from a single tri-axial accelerometer, and is able to classify between 5 different human activities with an accuracy of 97.5% when the Output Data Rate of the sensor is set to 25 Hz. The new Hybrid Neural Network (HNN) has binary weights (i.e. constrained to +1 or −1) but uses non-binarized activations for some layers. This, in conjunction with a custom pre-processing module, achieves much higher accuracy than Binarized Neural Network. During pre-processing, the measurements are made independent from the spatial orientation of the sensor by exploiting a reference frame transformation. A prototype has been realized in a Xilinx Artix 7 FPGA, and synthesis results have been obtained with TSMC CMOS 65 nm LP HVT and 90 nm standard cells. Best result shows a power consumption of $6.3~\mu \text{W}$ and an area occupation of 0.2 mm $^{\mathbf {2}}$ when real-time operations are set, enabling in this way, the possibility to integrate the entire HW accelerator in the auxiliary circuitry that normally equips inertial Micro Electro-Mechanical Systems (MEMS). [ABSTRACT FROM AUTHOR]