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Assume that for a given system, virtual addresses are $40$ bits long and physical addresses are $30$ bits long. The page size is $8$ KB. The Translation Look-aside Buffer (TLB) in the address translation path has $128$ entries. At most how many distinct virtual addresses can be translated without any TLB miss?

  1. $2^7$
  2. $2^{20}$
  3. $2^{13}$
  4. $2^8$
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This question has been taken from page $7-$ https://www3.nd.edu/~mniemier/teaching/2011_B_Fall/lectures/2009_Final_Exam_Solutions.pdf

Coincidently GATE has also copied the same question from this university in year $2019$. Check -

https://gateoverflow.in/302815/gate-cse-2019-question-33

There are $128\left(2^7\right)$ entries in the TLB and there are $8192\left(2^{13}\right)$ entries per page. Therefore $2^7 \times 2^{13}$ implies $2^{20}$ (or $1 \mathrm{MB}$ ) addressable entries are covered by the TLB.

The answer would get better $b / c \;2^{13}$ would be larger.

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