A Möbius number system represents real numbers by elements of a one-sided subshift over an alphabet \(A\) whose letters represent Möbius transformations. Concatenation of letters corresponds to composition of transformations. Given a collection \({\mathcal W}\) of open subsets of the one-point compactification of the real line whose closures cover, there is an associated expansion subshift consisting of those elements of the Möbius number system whose iterated intersections of inverse images of elements of the cover are nonempty. The paper studies expansion subshifts that are sofic or of finite type. Any sofic expansion subshift is a factor of one of finite type. This is of interest because there are effective methods of computing with those of finite type, although the systems of interest are often sofic but not of finite type. A detailed description of such a system, a bimodular system generated by eight transformations, is presented.