Question

A certain processor has access to three levels of memory. The access time of Level 1 memory is 10 ns. The access time of Level 2 memory is 50 ns. The access time of Level 3 memory is 200 ns. Assume the hit ratio of Level 1 is 0.8. The hit ratio of Level 2 is 0.95. If a word to be accessed is in Level 1 memory, it can be accessed directly; if it is in Level 2, then it is first transferred to Level 1 memory and then accessed by the processer; if it is in Level 3, it is first transferred from Level 3 to Level, then from Level 2 to Level 1, and then accessed by the processer. What is the average memory access time?

Answer 1

Answer:

Average access time = 24.5 ns

Explanation:

Given data:

Level 1 access time = L1 = 10 ns

Level 2 access time = L2 = 50 ns

Level 3 access time = L3 = 200 ns

Hit ratio of level 1 = R1 = 0.8

Hit ratio of level 2 = R2 = 0.95

Step 1: Formula

Average access time = AAT

AAT = (R1*L1) + [(1-R1)(R2)(L1+L2+L1)] + [(1-R1)(1-R2)(L1+L2+L3+L2+L1)]

Step 2: Computation

AAT

= 0.8*10 + (1-0.8)(0.95)(10+50+10) + (1-0.8)(1-0.95)(10+50+200+50+10)

AAT = 8 ns + 13.3 ns + 3.2 ns

AAT = 24.5 ns

Hope this helps!