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Official PYQ · 2000Q2.22Memory Management and Virtual MemoryMCQ1 mark

GATE CS 2000 Q2.22 — Memory Management and Virtual Memory

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Suppose the time to service a page fault is on the average 1010 milliseconds, while a memory access takes 11 microsecond. Then a 99.99%99.99\% hit ratio results in average memory access time of

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Answer: D

To find the effective memory access time (EMATEMAT), we first convert all time measurements to the same unit (microseconds):

  • Memory access time (TmT_m) = 1 μs1\ \mu\text{s}
  • Page fault service time (TpfT_{pf}) = 10 ms=10,000 μs10\ \text{ms} = 10,000\ \mu\text{s}

We are given the hit ratio (hh):

  • Hit ratio (hh) = 99.99%=0.999999.99\% = 0.9999
  • Page fault rate / Miss ratio (pp) = 1−0.9999=0.00011 - 0.9999 = 0.0001

The standard formula for Effective Memory Access Time (EMATEMAT) is:

EMAT=(1−p)×Tm+p×TpfEMAT = (1 - p) \times T_m + p \times T_{pf}

Substituting the given values into the formula:

EMAT=0.9999×1 μs+0.0001×10,000 μsEMAT = 0.9999 \times 1\ \mu\text{s} + 0.0001 \times 10,000\ \mu\text{s}EMAT=0.9999 μs+1 μs=1.9999 μsEMAT = 0.9999\ \mu\text{s} + 1\ \mu\text{s} = 1.9999\ \mu\text{s}

Therefore, the average memory access time is 1.9999 μs1.9999\ \mu\text{s}, which corresponds to option D.

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