In this paper, our main concern is the problem of stabilization of discrete-time linear systems with both quantization and noise input. Stabilizability by means of quantizers that perform adaptations called “zooming” is analyzed. The noise input can be separated into an additive white noise part and a deterministic constant input disturbance. The analysis of mean-square stability of the system with noise input is essentially the asymptotic stability of the system disturbed by a constant input. It is shown that the system with the constant input disturbance is asymptotically stabilized by the quantized feedback control policy if the system without noise input can be stabilized by a linear state feedback law. Both the state quantization and the input quantization are studied.