The Internet of Bio-Nano Things (IoBNT) is an envisioned extension of the Internet of Things (IoT), which aims to connect natural and synthetic biological systems and networks to the Internet. Due to the access to new domains (e.g., human body) this concept may help to enable transformative applications in healthcare and nanomedicine. However, it also faces several challenges, such as suitable interfaces and appropriate communication methods. Synthetic Molecular Communications (MC), a molecule-based bio-compatible communication concept, is among the most promising solution, which also defines the requirements for the respective interfaces. Typically, MC systems require a digital representation of the information to be transmitted and, thus, the development of devices for the conversion of analog biological signals to digital signals is crucial, but not well investigated. Thus, in this paper we propose a novel Molecular Analog-to-Digital converter (MADC). The MADC is based on a new neural network representation of the electronic flash ADC concept. This representation enables the implementation of the MADC using the recently proposed Molecular Nano Neural Networks (M3N). In particular, the proposed MADC consists of two matrix multiplication layers that are connected via a ReLU and threshold layer. We derive general design guidelines for the MADC and successfully validate it through computer simulations.