The convergence analysis of an online system identification method based on binary-quantized observations is presented in this paper. This recursive algorithm can be applied in the case of finite impulse response (FIR) systems and exhibits low computational complexity as well as low storage requirement. This method, whose practical requirement is a simple 1-bit quantizer, implies low power consumption and minimal silicon area, and is consequently well-adapted to the test of microfabricated devices. The convergence in the mean of the method is studied in the presence of measurement noise at the input of the quantizer. In particular, a lower bound of the correlation coefficient between the nominal and the estimated system parameters is found. Some simulation results are then given in order to illustrate this result and the assumptions necessary for its derivation are discussed.