A finite collection of finite subsets of the integers (the tiles) is said to tile if the integers can be written as a disjoint union of translates of tiles. The set of all tilings is a symbolic dynamical system known to be sofic. Here it is shown that any shift of finite type has some power realised as a tiling system. Using the known calculation of the topological entropy for shifts of finite type this gives a description of the set of possible entropies of tiling systems.