GATE CS 2025 Set 2 — Question 58
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Operating System → Memory Management → Multilevel & Inverted Page Tables
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Question
A computer system supports a logical address space of bytes. It uses two-level hierarchical paging with a page size of 4096 bytes. A logical address is divided into a -bit index to the outer page table, an offset within the page of the inner page table, and an offset within the desired page. Each entry of the inner page table uses eight bytes. All the pages in the system have the same size.The value of is ___________. (Answer in integer)
Correct answer
11 to 11
Solution
1.Logical Address Space: The logical address space is bytes, which means the logical address is 32 bits long.
2.Page Size: The page size is 4096 bytes, which is bytes. This implies that the page offset (offset within the desired page) is 12 bits.
3.Total bits for Page Table Indexing: The remaining bits for indexing the two levels of page tables are bits.
4.Inner Page Table Constraints: The problem states that all pages in the system have the same size (4096 bytes). In a standard hierarchical paging system, an inner page table is designed to fit exactly within one page.
- Size of one page = bytes.
- Size of each inner page table entry = 8 bytes = bytes.
- Number of entries in the inner page table = .
- Therefore, the number of bits required to index the inner page table (referred to in the question as the 'offset within the page of the inner page table') is bits.
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