Microfluidic technology has developed greatly in recent years, enabling multiple analysis systems to be placed on a microfluidic chip. However, microfluidic large-scale integration of control elements analogous to those achieved in the microelectronics industry is still a challenge. We present an integrated microfluidic valve, compatible with standard soft-lithography processes, which has a pressure gain much greater than unity. We show that this enables integration of fully static digital control logic and state storage directly on-chip, ultimately enabling microfluidic-state machines to be designed. Outputs from this digital control logic can then be used to control traditional analyte flow valves. This strategy enables much of the bulky external hardware at present used to control pneumatically driven microfluidic chips in the laboratory to be transferred onto the microfluidic chip, which drastically reduces the required number of external chip connections.