The Galileo National Telescope (TNG) is a 3.6 meter Alt-Az telescope installed at the Astronomical Observatory of the Roque de Los Muchachos in La Palma, Canary Islands (Spain). The TNG motion control system, designed and realized by the Technology Working Group (TWG), is completely digital because of the versatility of this system topology. In a digital control system using an encoder as transducer means to have a digital feedback signal, therefore directly comparable with the reference without any conversion that is essential with other kinds of transducers. In the following the Galileo telescope (TNG) encoder system with its control electronics and the management software are described. It has been realized by a collaboration between the Heidenhain Company and the TWG. The TNG encoder system, at the state of the art, has one of the highest performances in the telescopes field, in terms of resolution, accuracy, readout time, reliability.