A computer system contains a processor that includes a software programmable memory mapper. The memory mapper maps an address generated by the processor into a device address for accessing physical main memory. The processor also includes a cache controller that maps the processor address into a cache address. The cache address places a block of data from main memory into a memory cache using an index subfield. The physical main memory contains RDRAM devices, each of the RDRAM devices containing a number of memory banks that store rows and columns of data. The memory mapper maps processor addresses to device addresses to increases memory system performance. The mapping minimizes memory access conflicts between the memory banks. Conflicts between memory banks are reduced by placing a number of bits corresponding to the bank subfield above the most significant boundary bit of the index subfield. This diminishes page misses caused by replacement of data blocks from the cache memory because the read of the new data block and write of the victim data block are not to the same memory bank. Adjacent memory bank conflicts are reduced for sequential accesses to memory banks by reversing the bit order of a bank number subfield within the bank subfield of the device address.