Building biological devices to perform computational and signal processing tasks is one of the main research issues in synthetic biology. Herein, two modular biological systems that could mimic multiplexing and demultiplexing logic functions are proposed and discussed. These devices, called multiplexer (mux) and demultiplexer (demux), respectively, have a remarkable importance in electronic, telecommunication, and signal processing systems and, similarly, they could play a crucial role if implemented in a living organism, such as Escherichia coli. BioBrick standard parts were used to design mux and demux and to construct two genetic circuits that could carry out the desired tasks. A modular approach, mimicking basic logic gates (AND, OR, and NOT) with protein/autoinducer or protein/DNA interactions and interconnecting them to create the final circuits, was adopted. A mathematical model of the designed gene networks was been defined and simulations performed to validate the expected behavior of the systems. In addition, circuit subparts were tested in vivo and the results used to determine some of the parameters of the mathematical model. According to both the experimental and simulated results, guidelines for future finalization of mux and demux are provided.