1. A decoder for decoding a video encoded in a data stream, wherein the video is predictively decoded by motion compensated prediction using motion vectors and motion vector differences, the decoder comprising: an entropy decoder configured to, for horizontal and vertical components of each of the motion vector differences, obtain, from the data stream, two fixed-length binary codes and an Exp-Golomb code, wherein a first of the two fixed-length binary codes indicates whether an absolute value of a motion vector difference is greater than zero and a second of the two fixed-length binary codes indicates whether the absolute value of the motion vector difference is greater than one, and the Exp-Golomb code represents a difference between the absolute value of the motion vector difference and a fixed value, decode each of the two fixed-length binary codes using context-adaptive binary entropy decoding with exactly one context associated with the respective fixed-length binary code, wherein the context is shared by the horizontal and vertical components of the motion vector difference, and decode the Exp-Golomb code using a constant equi-probability bypass mode, to obtain the horizontal and vertical components of the motion vector difference; and a reconstructor configured to reconstruct the video based on the horizontal and vertical components of the motion vector differences.