A custom HW design of a Fully Convolutional Neural Network (FCN) is presented in this paper to implement an embeddable Human Posture Recognition (HPR) system capable of very high accuracy both for laying and sitting posture recognition. The FCN exploits a new base-2 quantization scheme for weight and binarized activations to meet the optimal trade-off between low power dissipation, a very reduced set of instantiated physical resources and state-of-the-art accuracy to classify human postures. By using a limited number of pressure sensors only, the optimized HW implementation allows keeping the computation close to the data sources according to the edge computing paradigm and enables the design of embedded HP systems. The FCN can be simply reconfigured to be used for laying and sitting posture recognition. Tested on a public dataset for in-bed posture classification, the proposed FCN obtains a mean accuracy value of 96.77% to recognize 17 different postures, while a small custom dataset has been used for training and testing for sitting posture recognition, where the FCN achieves 98.88% accuracy to recognize eight positions. The FCN has been prototyped on a Xilinx Artix 7 FPGA where it exhibits a dynamic power dissipation lower than 11 mW and 7 mW for laying and sitting posture recognition, respectively, and a maximum operation frequency of 47.64 MHz and 26.6 MHz, corresponding to an Output Data Rate (ODR) of the sensors of 16.50 kHz and 9.13 kHz, respectively. Furthermore, synthesis results with a CMOS 130 nm technology have been reported, to give an estimation about the possibility of an in-sensor circuital implementation.