A method and apparatus for translating a large logical address as a large virtual address (LVA) when a dynamic address translation (DAT) mode is on. Each LVA is separated into three concatenated parts: 1. a highest-order part (ADEN) for indexing into an access directory (AD) to locate an entry (ADE) for locating one access list (AL); 2. an intermediate part (ALEN) for indexing into a selected AL to access an entry (ALE) that enables location of an associated conventional address translation table which represents a conventional size virtual address space; and 3. a low-order DAT virtual address (VA) part having the same size as a conventional type of virtual address. The low-order DAT VA part is translated by the associated conventional address translation table. If a carry signal is generated during the creation of the low-order DAT VA part, then a change in the selection of an ALE results. An offset value of ALEs can be utilized to generate an effective ADEN and ALEN, which are utilized for the address translation of the LVA.