We study partitions of the space F2n of all the binary-n-tuples-into disjoint sets, such that each set is an additive coset of a given set V. Such a partition is called a perfect tiling of F2n and denoted (V,A), where A is the set of coset representatives. A sufficient condition for a set V to be a tile is given in terms of the cardinality of V + V. A perfect tiling (V,A) is said to be proper if V generates F2n. We show that the classification of perfect tilings can be reduced to the study of proper perfect tilings. We then prove that each proper perfect tiling is uniquely associated with a perfect binary code. A construction of proper perfect tilings from perfect binary codes is presented. Furthermore, we introduce a class of perfect tilings obtained by iterating a simple recursive construction. Finally, we generalize the well-known Lloyd theorem, originally stated for tilings by spheres, for the case of arbitrary perfect tilings.