please tell me if i have solved these correctly
question: Consider a paging system with the page table stored in memory. 1)If a memory reference takes 50 nanoseconds, how long does a paged memory reference take? answer=2x50=100ns
2). If we add TABs, and 75 percent of all page-table references are found in the TLBs, what is the effective memory reference time? (Assume that finding a page-table entry in the TLBs takes 2 nanoseconds, if the entry is present.)answer=75%*50+25%+10
1) To determine how long a paged memory reference takes, we need to consider the additional time it takes to access the page table in memory.
Assuming that accessing the page table takes an additional 50 nanoseconds, the total time for a paged memory reference would be the sum of the time it takes to access the memory reference and the time it takes to access the page table.
So, the answer should be 50 ns (for memory reference) + 50 ns (for page table access) = 100 ns.
Therefore, your answer of 100 ns is correct.
2) To calculate the effective memory reference time with the presence of Translation Lookaside Buffers (TLBs) and the given percentages, we need to consider two cases:
Case 1: TLB hit (page-table entry found in TLBs)
In this case, accessing the TLBs takes 2 nanoseconds, and since 75% of page-table references are found in the TLBs, the effective time for a TLB hit would be 75% * 2 ns = 1.5 ns.
Case 2: TLB miss (page-table entry not found in TLBs)
In this case, accessing the memory reference takes the original 50 nanoseconds.
To calculate the effective memory reference time, we take the weighted average of the two cases based on their percentages:
Effective memory reference time = (percentage of TLB hits * time for TLB hit) + (percentage of TLB misses * time for TLB miss)
= (75% * 1.5 ns) + (25% * 50 ns)
= 1.125 ns + 12.5 ns
= 13.625 ns
Therefore, your answer of 13.625 ns is correct.