A mechanism implemented by a controller enables efficient access to an interleaved memory system that includes M modules, M being (2n+1) or (2n−1), n being a positive integer number. Upon receiving an address N, the controller performs shift and add/subtract operations to obtain a quotient of N divided by M based on a binomial series expansion of N over M. The controller computes a remainder of N divided by M based on the quotient. The controller then accesses one of the modules in the memory based on the remainder.