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parallelfifths

In the hierarchical cache architecture like this, what happens if L1 is a write through cache? L2 must immediately request from data from L1. Does L2 then immediately write this data back to memory and neither L1 or L2 stores the data?

In other words, is there any point of having both an L1 and an L2 cache if L1 is write through? (I think no.)