This paper pertains to the design of a dynamic output-feedback controller for linear systems subject to both actuator and sensor quantization. The quantization errors affecting the measured output and the control input are embedded into compact sector through appropriate sector conditions. Then, the global asymptotic stabilization problem of an ellipsoidal set containing the origin is tackled. To deal with the discontinuity induced by quantization, the notion of Krasovskii solution is adopted to tackle the considered problem. The controller is designed via a convex optimization setup, providing a constructive method that can be efficiently implemented. Finally, the effectiveness of the proposed methodology is shown in a numerical example.