A computer uses 46-bit virtual address, 32-bit physical address, and a three-level paged page table organization. The page table base register stores the base address of the first-level table ( $T_1$ ), which occupies exactly one page. Each entry of $T_1$ stores the base address of a page of the second-level table ( $T_2$ ). Each entry of $T_2$ stores the base address of a page of the third-level table ( $T_3$ ). Each entry of $T_3$ stores a page table entry (PTE). The PTE is 32 bits in size. The processor used in the computer has a 1 MB 16-way set associative virtually indexed physically tagged cache. The cache block size is 64 bytes. What is the size of a page in KB in this computer?

Select one answerSingle correct

Pick an option to check

Solution

Step-by-step verified solution

Official answer: C) 8

Memory Management and Virtual Memory

Let the page size be $P = 2^p$ bytes. The page offset requires $p$ bits.

The size of a Page Table Entry (PTE) is given as 32 bits $= 4\text{ bytes} = 2^2\text{ bytes}$ .

The number of entries per page in each level of the page table is:

\text{Entries per page} = \frac{2^p}{2^2} = 2^{p-2}

Thus, each level of the page table requires $(p - 2)$ bits to index its entries.

In a 3-level page table scheme, the virtual address is divided into:

\text{Virtual Address} = \text{Index}(T_1) + \text{Index}(T_2) + \text{Index}(T_3) + \text{Page Offset}

Given that the total virtual address length is 46 bits:

(p - 2) + (p - 2) + (p - 2) + p = 46

4p - 6 = 46

4p = 52 \implies p = 13

Therefore, the page size is:

2^{13}\text{ bytes} = 8192\text{ bytes} = 8\text{ KB}

Hence, the correct option is (C).

Try the question first, then check your work.

Think the official key or this write-up is wrong?

Report error or challenge

Examiner trap

The misconception this question tests

This Memory Management and Virtual Memory previous year question is Q52 of the GATE CSE 2013 paper. Find more GATE CSE PYQs on Memory Management and Virtual Memory in Operating Systems, or browse all GATE CSE PYQs.

Free diagnostic

Where do you stand for GATE?

Take the 20-minute diagnostic: the 3 topics that cost you the most marks, and a rank range. Or sit 5 related Memory Management and Virtual Memory PYQs now with no account.

One GATE CSE PYQ every morning

An official question by email at 7 AM IST, with a link to its verified solution. Unsubscribe in one click.

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. 6 of them are 2-mark MCQs like this one, and it is the only one in GATE CSE 2013.

How GATE tests Memory Management and Virtual Memory

More from GATE CSE 2013

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