Let [Formula: see text], where [Formula: see text] are integers and [Formula: see text] be a digit set. Then the pair [Formula: see text] generates a fractal set [Formula: see text] satisfying [Formula: see text] which is a unit square. However, if we remove one digit from [Formula: see text], then the structure of [Formula: see text] will become very interesting. A well-known example is the Sierpinski carpet. In this paper, we study the resulting self-affine sets of moving a digit in [Formula: see text] to a different place. That is, we consider a digit set [Formula: see text], where [Formula: see text]. We give a complete characterization for the connectedness of self-affine carpet [Formula: see text] in terms of the domains of [Formula: see text] and [Formula: see text].