Existing works on Binary Neural Network (BNN) mainly focus on model's weights and activations while discarding considerations on the input raw data. This article introduces Generic Learned Thermometer (GLT), an encoding technique to improve input data representation for BNN, relying on learning non linear quantization thresholds. This technique consists in multiple data binarizations which can advantageously replace a conventional Analog to Digital Conversion (ADC) that uses natural binary coding. Additionally, we jointly propose a compact topology with light-weight grouped convolutions being trained thanks to block pruning and Knowledge Distillation (KD), aiming at reducing furthermore the model size so as its computational complexity. We show that GLT brings versatility to the BNN by intrinsically performing global tone mapping, enabling significant accuracy gains in practice (demonstrated by simulations on the STL-10 and VWW datasets). Moreover, when combining GLT with our proposed block-pruning technique, we successfully achieve lightweight (under 1Mb), fully-binarized models with limited accuracy degradation while being suitable for in-sensor always-on inference use cases.