CS 540 Operating Systems Test 2 - Name: Date: Thursday, April 25 ...

6. The time required to read an entry in memory (including the time to access associative memory) is130 nanoseconds when the page number is not in the associative memory. The associative memory canbe accessed in 10 nanoseconds. (10 points)(a) Find a formula that expresses the effective access time as a function of the hit ratio.(b) What hit ratio is needed to reduce the effective access time to 100 nanoseconds?Ans:a) Let E = associative memory lookup timeT = memory cycle timep = hit ratio.Effective Access Time (EAT)= p * (E + T) + (1 - p) * (E + 2 * T)= p * E + p * T + E + 2 * T - p * E - 2 * p * T= (2 - p) * T + EIn this case, E + 2 * T = 130. E = 10. T = 60.EAT = (2 - p) * 60 + 10 = 130 - 60 * pb) 130 - 60 * p = 10060 * p = 30p = 50%