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If the average time to handle a page fault is 10 milliseconds, and a memory access requires 1 microsecond, then achieving a 99.99% hit ratio would lead to an average memory access time ofa.1 millisecondb.1.9999 millisecondsc.1.9999 microsecondsd.9.999 microseconds

Question

If the average time to handle a page fault is 10 milliseconds, and a memory access requires 1 microsecond, then achieving a 99.99% hit ratio would lead to an average memory access time ofa.1 millisecondb.1.9999 millisecondsc.1.9999 microsecondsd.9.999 microseconds

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Solution

To determine the average memory access time given the hit ratio, we need to use the following formula:

Average Memory Access Time=(Hit Ratio×Memory Access Time)+(Miss Ratio×Page Fault Time) \text{Average Memory Access Time} = (\text{Hit Ratio} \times \text{Memory Access Time}) + (\text{Miss Ratio} \times \text{Page Fault Time})

Given:

  • Hit Ratio = 99.99% = 0.9999
  • Miss Ratio = 1 - Hit Ratio = 1 - 0.9999 = 0.0001
  • Memory Access Time = 1 microsecond = 1 μ\mus
  • Page Fault Time = 10 milliseconds = 10,000 microseconds = 10,000 μ\mus

Now, plug these values into the formula:

Average Memory Access Time=(0.9999×1μs)+(0.0001×10,000μs) \text{Average Memory Access Time} = (0.9999 \times 1 \mu\text{s}) + (0.0001 \times 10,000 \mu\text{s})

Calculate each part:

  1. 0.9999×1μs=0.9999μs 0.9999 \times 1 \mu\text{s} = 0.9999 \mu\text{s}
  2. 0.0001×10,000μs=1μs 0.0001 \times 10,000 \mu\text{s} = 1 \mu\text{s}

Add these two results together:

Average Memory Access Time=0.9999μs+1μs=1.9999μs \text{Average Memory Access Time} = 0.9999 \mu\text{s} + 1 \mu\text{s} = 1.9999 \mu\text{s}

Therefore, the average memory access time is:

1.9999 microseconds \boxed{1.9999 \text{ microseconds}}

So, the correct answer is:

c. 1.9999 microseconds

This problem has been solved

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