This article is concerned with the input-to-state stability (ISS) of linear systems with quantized state measurements under both external disturbances and denial-of-service attacks. Piecewise constant state quantizers taking a set of finite values are considered in this article. Depending on whether the bound of disturbances is known or not, two impulsive controllers that ensure ISS are designed. Leveraging the disturbance bound, the first controller can counteract the disturbances and guarantee that the quantizer never saturates at successful transmission instants. The second controller, which though cannot prevent the quantizer from saturation, is able to stabilize the system under disturbances whose bound is unknown, if the quantizer’s saturation duration is small enough. Moreover, analysis shows that with appropriate control parameter design, the resultant saturation duration always remains small. Finally, a numerical example is given to corroborate the practical merits of the proposed controllers and theory.