Question

A new smartphone just out on the market has a L1 cache with an access time of 1 cycle, an L2 cache with an access time of 5 cycles and DRAM with access time of 30 cycles. The latest benchmarks indicate that for most applications the L1 hit rate is 80% and L2 hit rate is 95%. Compute the Average Memory Access Time for the memory hierarchy in this device.

(More interested in the explanation of how to get the answer, than the answer itself. Thanks in advance!)

Answer 1

Well, the formula for average access time is given as below:

Average Memory Access Time (AMAT)

  = Hit Time + Miss Rate * Miss Penalty

Now, there are two levels of cache in this problem, L1 and L2. If we get a miss in L1, we check for the same in L2. And still if there is a miss in L2, we check in the main memory, i.e the DRAM.

So, average access time = Hit_Time_L1 + Miss_Rate_L1 * Miss_Penalty_L1

where Miss_Penalty_L1 = Hit_Time_L2 + Miss_Rate_L2 * Miss_Penalty_L2

Here, Hit_Time_L1 = 1 cycle

Miss_Rate_L1 = 1 - 0.80 = 0.2

Hit_Time_L2 = 5 cycles

Miss_Rate_L2 = 0.05

Miss_Penalty_L2 = 30 cycles

Now, AMAT = 1 + 0.2 * ( 5 + 0.05 * 30) = 1 + 0.2 * 6.5 = 1 + 1.3 = 2.3 cycles

Let me know if you have any doubts in the comments. Please upvote if the answer helped you.