This paper presents a design of digitally controlled positional systems with Euler velocity estimation within the framework of the discrete-time sliding mode (DSM). The effects of quantization and simple velocity estimation on DSM quality are analyzed. It is shown that the introduced and amplified quantization noise degrades sliding motion into the quasi-sliding mode and threatens to provoke chattering. Furthermore, a new DSM control algorithm is proposed, featuring a two-scale reaching law and a supplemental integral action. This algorithm avoids chattering and provides excellent performance. The developed DSM controller has been experimentally tested in an induction motor position control.