GATE CS 2021 Set 2 — Question 58
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Operating System → Memory Management → Multilevel & Inverted Page Tables
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Question
Consider a three-level page table to translate a 39-bit virtual address to a physical address as shown below.
The page size is 4KB ( bytes) and page table entry size at every level is 8 bytes. A process is currently using 2GB ( bytes) virtual memory which is mapped to 2GB of physical memory. The minimum amount of memory required for the page table of across all levels is ________ KB.
Correct answer
4108 to 4108
Solution
Given:
Total memory required = KB.
- Virtual Address = 39 bits
- Page size = 4 KB = bytes Page offset = 12 bits
- Level 1, 2, and 3 offsets are each 9 bits each table has entries.
- PTE size = 8 bytes.
- Size of one page table at any level = bytes = 4096 bytes = 4 KB.
- Number of pages = pages.
1.Level 3: Each L3 table covers 512 pages. Number of L3 tables = tables.
2.Level 2: Each L2 table covers 512 L3 tables. Number of L2 tables = tables.
3.Level 1: One L1 table is always required to start the translation. It points to the 2 L2 tables.
Total number of page tables = tables.Total memory required = KB.
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