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Official PYQ · 2026Set 2 · Q44Memory Management and Virtual MemoryNAT2 marks

GATE CS 2026 Set 2 Q44 — Memory Management and Virtual Memory

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A system has a Translation Lookaside Buffer (TLB) that has a reach of 11 MB. TLB reach is defined as the total amount of physical memory that can be accessed through the TLB entries. The paging system uses pages of size 44 KB. The virtual address space is 6464 GB and physical address space is 11 GB. If each TLB entry stores a 44-bit process id, page number, frame number, and a 22-bit control field, then the size of the TLB (in bytes) is ______\_\_\_\_\_\_. (answer in integer)

Note: 1K=210,1M=220,1G=2301 \mathrm{K}=2^{10}, 1 \mathrm{M}=2^{20}, 1 \mathrm{G}=2^{30}
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Answer: 1536

To find the total size of the Translation Lookaside Buffer (TLB) in bytes, we can break down the calculation into three steps:

Step 1: Calculate the number of TLB entries

The TLB reach is the total amount of physical memory that can be mapped by the TLB at any given time. It is defined as:

TLB Reach=Number of TLB entries×Page Size\text{TLB Reach} = \text{Number of TLB entries} \times \text{Page Size}

Given:

  • TLB Reach=1 MB=220 bytes\text{TLB Reach} = 1 \text{ MB} = 2^{20} \text{ bytes}
  • Page Size=4 KB=212 bytes\text{Page Size} = 4 \text{ KB} = 2^{12} \text{ bytes}
Number of TLB entries=220 bytes212 bytes=28=256 entries\text{Number of TLB entries} = \frac{2^{20} \text{ bytes}}{2^{12} \text{ bytes}} = 2^8 = 256 \text{ entries}

Step 2: Calculate the size of a single TLB entry

Each TLB entry stores the following components:

  1. Process ID (PID): Given as 44 bits.
  2. Page Number (Virtual Page Number - VPN): Virtual Address Space=64 GB=236 bytes\text{Virtual Address Space} = 64 \text{ GB} = 2^{36} \text{ bytes} Page Offset=log⁡2(4 KB)=12 bits\text{Page Offset} = \log_2(4 \text{ KB}) = 12 \text{ bits} Page Number bits=36−12=24 bits\text{Page Number bits} = 36 - 12 = 24 \text{ bits}
  3. Frame Number (Physical Frame Number - PFN): Physical Address Space=1 GB=230 bytes\text{Physical Address Space} = 1 \text{ GB} = 2^{30} \text{ bytes} Frame Number bits=30−12=18 bits\text{Frame Number bits} = 30 - 12 = 18 \text{ bits}
  4. Control Field: Given as 22 bits.

Summing these up to find the total bits per TLB entry:

Size of one TLB entry=4 (PID)+24 (Page Number)+18 (Frame Number)+2 (Control Field)=48 bits\text{Size of one TLB entry} = 4 \text{ (PID)} + 24 \text{ (Page Number)} + 18 \text{ (Frame Number)} + 2 \text{ (Control Field)} = 48 \text{ bits}

Converting this to bytes:

Size of one TLB entry=48 bits8=6 bytes\text{Size of one TLB entry} = \frac{48 \text{ bits}}{8} = 6 \text{ bytes}

Step 3: Calculate the total size of the TLB

Total TLB Size=Number of TLB entries×Size of one TLB entry\text{Total TLB Size} = \text{Number of TLB entries} \times \text{Size of one TLB entry} Total TLB Size=256×6 bytes=1536 bytes\text{Total TLB Size} = 256 \times 6 \text{ bytes} = 1536 \text{ bytes}

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