This work is concerned with the practical stabilization of discrete–time SISO linear systems under assigned quantization of the input and output spaces. A controller is designed which guarantees effective practical stability properties. Unlike most of the existing literature, quantization is supposed to be a problem datum rather than a degree of freedom in design. Moreover, in the framework of control under assigned quantization, results are concerned with state quantization only and do not include the quantized output feedback case considered here. While standard stability analysis techniques are based on Lyapunov theory and invariant ellipsoids, our study of the closed loop dynamics involves a particularly suitable family of sets, which are hypercubes in controller form coordinates.