Can someone please explain step by step how to break this down to get the answer

Question

Can someone please explain step by step how to break this down to get the answer.

This is from Computer Architecture book by Behrooz

Given a system with an L1 cache with a local hit rate of 95%. For the L2 cache a hit incurs a penalty of 10 clock cycles, while a miss has a 50-cycle penalty. a. Assuming the system has a CPI of 1.8 with no cache misses, calculate the effective CPI if L2's local miss rate is 20%. b. Changing the mapping scheme of L2 from set-associative to direct changes the local miss rate to 30%, but decreases the hit penalty to 8 clock cycles. Is the effective CPI an improvement?

Explanation / Answer

For no cache miss:
   L1 hit: 95/100 * x
   L1 miss and L2 hit: 5/100 * 100/100 * 10x
----------------------------------------------
              total: 0.95x + .5x = 1.45x

therefore x = 1.8/1.45 = 1.2414

For L2 miss rate 20%
   L1 hit: 95/100 * x
   L1 miss and L2 hit: 5/100 * 80/100 * 10x
   L1 miss and L2 miss: 5/100 * 20/100 * 50x
----------------------------------------------
              total: 0.95x + 0.4x + 0.5x= 1.85x

We know the value of x, therefore : total = 1.85 * 1.8 / 1.45 = 2.3 CPI

For L2 miss rate 30% and L1 miss penalty 8cycle
   L1 hit: 95/100 * x
   L1 miss and L2 hit: 5/100 * 70/100 * 8x
   L1 miss and L2 miss: 5/100 * 30/100 * 50x
----------------------------------------------
              total: 0.95x + 0.28x + 0.75x= 1.45x = 1.98x

So we can say that configuration with L2 miss rate 20% was better

I hope the answer is clear to you

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