A processor supports a processing mode in which the address size is greater than 32 bits and the operand size may be 32 or 64 bits. The address size may be nominally indicated as 64 bits, although various embodiments of the processor may implement any address size which exceeds 32 bits, up to and including 64 bits, in the processing mode. The processing mode may be established by placing an enable indication in a control register into an enabled state and by setting a first operating mode indication and a second operating mode indication in a segment descriptor to predefined states. Other combinations of the first operating mode indication and the second operating mode indication may be used to provide compatibility modes for 32 bit and 16 bit processing compatible with the x86 processor architecture (with the enable indication remaining in the enabled state).