A processor provides a register for storing an address space number (ASN). Operating system software may assign different ASNs to different processes. The processor may include a TLB to cache translations, and the TLB may record the ASN from the ASN register in a TLB entry being loaded. Thus, translations may be associated with processes through the ASNs. Generally, a TLB hit will be detected in an entry if the virtual address to be translated matches the virtual address tag and the ASN matches the ASN stored in the register. Additionally, the processor may use an indication from the translation table entries to indicate whether or not a translation is global. If a translation is global, then the ASN comparison is not included in detecting a hit in the TLB. Thus, translations which are used by more than one process may not occupy multiple TLB entries. Instead, a hit may be detected on the TLB entry storing the global translation even though the recorded ASN may not match the current ASN. In one embodiment, if ASNs are disabled, the TLB may be flushed on context switches. However, the indication from the translation table entries used to indicate that the translation is global may be used (when ASNs are disabled) by the TLB to selectively invalidate non-global translations on a context switch while not invalidating global translations.