We report the design and implementation of an Analog-to-Information Converter (AIC) based on Compressed Sensing (CS). The system is realized in a CMOS 180 nm technology and targets the acquisition of bio-signals with Nyquist frequency up to 100 kHz. To maximize performance and reduce hardware complexity, we co-design hardware together with acquisition and reconstruction algorithms. The resulting AIC outperforms previously proposed solutions mainly thanks to two key features. First, we adopt a novel method to deal with saturations in the computation of CS measurements. This allows no loss in performance even when 60% of measurements saturate. Second, the system is able to adapt itself to the energy distribution of the input by exploiting the so-called rakeness to maximize the amount of information contained in the measurements. With this approach, the 16 measurement channels integrated into a single device are expected to allow the acquisition and the correct reconstruction of most biomedical signals. As a case study, measurements on real electrocardiograms (ECGs) and electromyograms (EMGs) show signals that these can be reconstructed without any noticeable degradation with a compression rate, respectively, of 8 and 10.