The front-end system of the Silicon Drift Detectors (SDDs) of the ALICE experiment is made of two ASICs. The first chip performs the preamplification, temporary analogue storage and analogue-to-digital conversion of the detector signals. The second chip is a digital buffer that allows for a significant reduction of the connection from the front-end module to the outside world. In this paper, the results achieved on the first complete prototype of the front-end system for the SDDs of ALICE are presented