Questions

To find the hit rate needed to reduce the mean overhead to 200 nsec or less, we can use the effective access time formula for a memory hierarchy with a TLB:

$\text{Effective Access Time (EAT)} = \text{TLB Hit Rate} \times (\text{TLB Access Time} + \text{Memory Access Time}) + \text{TLB Miss Rate} \times (\text{TLB Access Time} + \text{Page Table Access Time} + \text{Memory Access Time})$

Given information:

• TLB Access Time = 100 ns
• Memory Access Time = 600 ns
• Page Table Access Time = 600 ns
• TLB holds 64 page-frame pairs
• TLB lookup time = 100 ns
• Mean Overhead ($EAT - \text{Memory Access Time}$) = 200 ns

Now, let's calculate the hit rate needed:

$200 \, \text{ns} \leq \text{TLB Hit Rate} \times (100 \, \text{ns} + 600 \, \text{ns}) + (1 - \text{TLB Hit Rate}) \times (100 \, \text{ns} + 600 \, \text{ns} + 600 \, \text{ns} + 600 \, \text{ns})$

Simplify and solve for TLB Hit Rate:

$200 \, \text{ns} \leq 700 \, \text{ns} \times \text{TLB Hit Rate} + 1900 \, \text{ns} \times (1 - \text{TLB Hit Rate})$

$200 \, \text{ns} - 700 \, \text{ns} \times \text{TLB Hit Rate} \leq 1900 \, \text{ns} - 1900 \, \text{ns} \times \text{TLB Hit Rate}$

$500 \, \text{ns} \times \text{TLB Hit Rate} \leq 1700 \, \text{ns}$

$\text{TLB Hit Rate} \leq \frac{1700 \, \text{ns}}{500 \, \text{ns}}$

$\text{TLB Hit Rate} \leq 3.4$

Therefore, the TLB hit rate needs to be $\leq 3.4$ or 340%. However, hit rates are typically expressed as percentages, so it should be $\leq 340\%$. This is not practically possible, so it seems there might be an error in the given information or the calculation. Please double-check the values and the question.