Microfluidic technology plays an essential role in various lab on a chip devices due to its desired advantages. An automated microfluidic system integrated with actuators and sensors can further achieve better controllability. A number of microfluidic actuation schemes have been well developed. In contrast, most of the existing sensing methods still heavily rely on optical observations and external transducers, which have drawbacks including: costly instrumentation, professional operation, tedious interfacing, and difficulties of scaling up and further signal processing. This paper reports the concept of electrofluidic circuits - electrical circuits which are constructed using ionic liquid (IL)-filled fluidic channels. The developed electrofluidic circuits can be fabricated using a well-developed multi-layer soft lithography (MSL) process with polydimethylsiloxane (PDMS) microfluidic channels. Electrofluidic circuits allow seamless integration of pressure sensors with analog and digital operation functions into microfluidic systems and provide electrical readouts for further signal processing. In the experiments, the analog operation device is constructed based on electrofluidic Wheatstone bridge circuits with electrical outputs of the addition and subtraction results of the applied pressures. The digital operation (AND, OR, and XOR) devices are constructed using the electrofluidic pressure controlled switches, and output electrical signals of digital operations of the applied pressures. The experimental results demonstrate the designed functions for analog and digital operations of applied pressures are successfully achieved using the developed electrofluidic circuits, making them promising to develop integrated microfluidic systems with capabilities of precise pressure monitoring and further feedback control for advanced lab on a chip applications.