A computer with cache access time of 100 ns and hit ratio of 0·9 produces an average access time ofans.c)190nsb)200nsa)250nsd)none of these.This Question Is Marked For Review Previous Remove From Review Next

The average access time of a computer system can be calculated using the formula:

Average Access Time = Hit Time + Miss Rate * Miss Penalty

Given in the question:

• Cache access time (Hit Time) = 100 ns
• Hit ratio = 0.9, therefore, Miss ratio (Miss Rate) = 1 - Hit ratio = 1 - 0.9 = 0.1

We need to find the Miss Penalty (the time it takes to access the main memory when a cache miss occurs) using the given average access time.

Let's denote the Average Access Time as 'A', Hit Time as 'H', Miss Rate as 'M', and Miss Penalty as 'P'. The formula becomes:

A = H + M * P

We can rearrange the formula to solve for P:

P = (A - H) / M

Substituting the given values:

P = (A - 100 ns) / 0.1

We know that the Average Access Time 'A' is one of the following: 190 ns, 200 ns, or 250 ns. We can substitute each of these values into the equation to see which one gives a reasonable value for 'P'.

If A = 190 ns, then P = (190 ns - 100 ns) / 0.1 = 900 ns If A = 200 ns, then P = (200 ns - 100 ns) / 0.1 = 1000 ns If A = 250 ns, then P = (250 ns - 100 ns) / 0.1 = 1500 ns

The Miss Penalty 'P' should be greater than the Hit Time 'H' (100 ns) because it takes longer to access the main memory than the cache. Therefore, the only reasonable value for the Average Access Time 'A' is 190 ns.

So, the answer is c) 190 ns.