In this paper we consider state estimation problems with Boolean measurements for a genetic network governed by a piecewise affine (PWA) model. In the first part, an observer is proposed for the case where full state Boolean measurements are available. In particular sliding modes may occur and this leads to finite time convergence for the observer. In the second part we discuss on state estimation with partial state Boolean measurements. A naive approach based on algebraic computation is proposed to solve the initial condition inverse problem. In the third part the observer is used to identify some unknown but fixed parameter of the model. We also undertake an investigation of the robustness of the observer for a parametric uncertain model.