# Page Size and Address Translations

• pages should be fairly large (KBs) because we pay the access time to get them from the disk
• virtual page number (VPN) to physical page frame number (PPFN) is done by memory management unit (MMU)
• instead of using tags to make them fully-associative (too many tags to compare) we use page tables
• page table is an in-memory data structure for hardware memory management unit to convert from virtual page number to physical page frame number
• like breaking 555-123-4567 to three levels of hash map [555] → [123] → [4567]
• using multi-level page table can save space.
• example: for 32-bit virtual address, 1 GB physical memory, and 4 kB pages how many bits do we need for the frame number? 1GB = 30 physical address bits. 4KB is 12 offset bits. Thus we need 30-12 = 18 bits for the frame number.
• but this multi-level can also be very expensive, because we need to lookup that many times
• potential solution: cache this! called translation look-aside buffers.