One of the longstanding challenges in synthetic biology is rational design of complex regulatory circuitry with multiple biological inputs, complex internal processing, and physiologically active outputs. We have previously proposed how to address this challenge in the case of transcription factor inputs. Here we describe the methods used to construct these synthetic circuits, capable of performing logic integration of transcription factor inputs using microRNA expression vectors and RNA interference (RNAi). The circuits operate in mammalian cells and they can serve as starting point for more complex synthetic information processing networks in these cells.