Consider a computer system with 57-bit virtual addressing using multi-level…
2023
Consider a computer system with 57-bit virtual addressing using multi-level tree-structured page tables with L levels for virtual to physical address translation. The page size is 4 KB (1 KB = 1024 B) and a page table entry at any of the levels occupies 8 bytes.
The value of L is _______ .
Attempted by 110 students.
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Correct answer: 5
Final answer: L = 5.
Page offset bits: 4 KB = 4096 bytes = 2^12, so offset = 12 bits.
Virtual page number (VPN) bits: 57 total bits − 12 offset bits = 45 bits.
Entries per page table page: 4096 bytes / 8 bytes per entry = 512 entries = 2^9, so each level uses 9 index bits.
Number of levels L = VPN bits / bits per level = 45 / 9 = 5.