This paper is devoted to the analysis of resonant MEMS sensors based on discrete relay feedback techniques. One drawback of such techniques is that some synchronization usually occurs between the discrete part and the continuous part of the system: this results in sensor responses that are very similar to the curves known as devil's staircases, i.e. the frequency does not vary smoothly with the sensor's input. The main contribution of this paper is a theoretical calculation of the resolution of such systems. The resolutions of two existing resonant MEMS architectures are then calculated and these results are discussed.