The use of networks in control systems to connect controllers and sensors/actuators has become common practice in many applications. This new technology has also posed a theoretical control problem of how to use the limited data rate of the network effectively. In this paper, we consider a system where its sensor and actuator are connected by a finite data rate channel. A design method to stabilize a continuous-time, linear plant using a switching controller is proposed. In particular, to prevent the actuator from fast switching, or chattering, which can not only increase the necessary data rate but also damage the system, we employ a dwell-time switching scheme. It is shown that a systematic partition of the state-space enables us to reduce the complexity of the design problem.