Abstract: A lookahead (guessahead) prefetching technique is used to reduce the average access time, for accessing memory modules when program addresses are modified into effective addresses for addressing the modules. A first memory address register stores the column address and module designation portions of the current effective address, a second memory address register stores the row address portion of the current effective address, and a third memory address register stores the module designation portion of the prior effective address. Since the same module is frequently accessed many times in succession, the average access time is reduced by starting an access based upon the contents of the second and third memory address registers without waiting until the column address and module designation portions of the current effective address are available for storage in the first memory address register.