GATE CSE 2023 Q58: Levels of page table for 57-bit virtual addresses

Operating System
2 marks
NAT
No negative marking

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 _______.

Try it: numerical answer: type the value

Your answer

Numerical answer. No negative marking.

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Answer: 5 (official GATE 2023 final answer key)

Concept used: Each level of a page table fits in one page and resolves $\log_2(\text{entries per page})$ bits.

First step: Subtract the 12 offset bits, and note that one 4 KB page holds $2^{12}/8 = 2^9$ entries.

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Source: official GATE 2023 CS question paper and final answer key, organised by IIT Kanpur. Question paper · Answer key

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GATE CSE 2023 Q58: Levels of page table for 57-bit virtual addresses

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