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GATE CSE 2025 Session 2 Q58: Outer page table index bits in two-level paging

Question

A computer system supports a logical address space of 2322^{32} bytes. It uses two-level hierarchical paging with a page size of 4096 bytes. A logical address is divided into a bb-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 bb is ___________. (Answer in integer)

Try it: numerical answer: type the value

Numerical answer. No negative marking.
Show answer and explanation

Answer: 11 (official GATE 2025 final answer key)

Concept used: Each inner page table fits in one page, so its index width is log⁡2(page size/entry size)\log_2(\text{page size} / \text{entry size}).

First step: Page offset is 12 bits and an inner page holds 4096/8=294096 / 8 = 2^9 entries; the rest of the 32 bits index the outer table.

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Source: official GATE 2025 Session 2 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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