A programmable address translation system for a modular main memory is provided. The system is implemented using one or more General Register Arrays (GRAs), wherein each GRA performs logical-to-physical address translation for a predetermined address range within the system. Predetermined bits of a logical address are used to address a GRA associated with the logical address range. Data bits read from the GRA are then substituted for the predetermined bits of the logical address to form the physical address. In this manner, non-contiguous addressable banks of physical memory may be mapped to a selectable contiguous address range. By including within the GRA Address a number N of logical address bits used to address contiguous logical addresses, an address translation mechanism is provided which may be programmed to perform between 2-way and 2N-way address interleaving. Each GRA may be re-programmed dynamically to accommodate changing memory conditions as may occur, for example, when a range of memory is logically removed from a system because of errors. Furthermore, GRA reprogramming may occur while memory operations continue within other non-associated address ranges. Additionally, address interleaving may be selected for certain ones of the address ranges, whereas a non-interleaving scheme may be selected for other address ranges.