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A demand paging system provides a TLB (15 ns access time), cache memory (25 ns access time), main memory (75 ns access time, NOT including the cache “miss”) and 5 ms to service a page fault.  The page table is found in the TLB 70% of the time, not in the TLB but in the cache 10% of the time, and in main memory 10% of the time. A process memory location is found in the cache 70% of the time and in main memory 20% of the time. Calculate the effective access time.

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$EMAT = Hit_{Tlb}(Tlb_{access} + Hit_{Cache}(Cache_{access}) + Miss_{cache}((1-PF)*Mem_{access} + PF*PFST))      + Miss_{Tlb}(Tlb_{access} + Pagetable_{access} + Hit_{Cache}(Cache_{access}+Miss_{cache}((1-PF)*Mem_{access} + PF*PFST))$

$EMAT$ = $0.7(15 + 0.1(25) + 0.9(0.1*75 + 0.9*(5))) + 0.3( 15 +75 +0.1(25) + 0.9(0.1*75 + 0.9*(5)))$

$EMAT$ = $50.8$ $ns$

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