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Memory Management and Virtual Memory

GATE CSE 2016 Set 1 · Q47

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Consider a computer system with 40-bit virtual addressing and page size of sixteen kilobytes. If the computer system has a one-level page table per process and each page table entry requires 48 bits, then the size of the per-process page table is ________ megabytes.

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Official answer: 384

Memory Management and Virtual Memory
  1. Virtual Address Space: The virtual address is 4040 bits, so the virtual address space is 240 bytes2^{40}\text{ bytes}.

  2. Page Size:

    Page Size=16 KB=16×210 bytes=214 bytes\text{Page Size} = 16\text{ KB} = 16 \times 2^{10}\text{ bytes} = 2^{14}\text{ bytes}

    Therefore, the page offset requires 1414 bits.

  3. Number of Pages (Entries in Page Table):

    Number of Pages=240214=226\text{Number of Pages} = \frac{2^{40}}{2^{14}} = 2^{26}
  4. Size of Page Table Entry (PTE):

    PTE Size=48 bits=6 bytes\text{PTE Size} = 48\text{ bits} = 6\text{ bytes}
  5. Total Page Table Size:

    Page Table Size=226×6 bytes=6×26×220 bytes=6×64 MB=384 MB\text{Page Table Size} = 2^{26} \times 6\text{ bytes} = 6 \times 2^6 \times 2^{20}\text{ bytes} = 6 \times 64\text{ MB} = 384\text{ MB}

Thus, the size of the per-process page table is 384 megabytes.

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This Memory Management and Virtual Memory previous year question is Q47 of the GATE CSE 2016 Set 1 paper. Find more GATE CSE PYQs on Memory Management and Virtual Memory in Operating Systems, or browse all GATE CSE PYQs.

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Memory Management and Virtual Memory in GATE CSE

Memory Management and Virtual Memory has 32 GATE CSE PYQs across 22 papers from 2011 to 2026. 15 of them are 2-mark NAT questions like this one, and GATE CSE 2016 Set 1 has 2.

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GateAI solution cardGATE CSE 2016 Set 1 · Q47 · NAT

Consider a computer system with 40-bit virtual addressing and page size of sixteen kilobytes. If the computer system has a one-level page table per process and each page table entry requires 48 bits, then the size of the per-process page table is … megabytes.

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.