If there are multiple layers in the cache (more than just L1 and L2), then it seems like they all need the bits that the L2 Cache currently have. Is this correct?
ykt
Yes, seems so.
Also, now when L1 cache just wants to remove a line even if it is in the shared state, it would need to tell L2 cache about it. And, L2 cache can not remove a line from its cache as long as L1 cache still has it.
If there are multiple layers in the cache (more than just L1 and L2), then it seems like they all need the bits that the L2 Cache currently have. Is this correct?
Yes, seems so.
Also, now when L1 cache just wants to remove a line even if it is in the shared state, it would need to tell L2 cache about it. And, L2 cache can not remove a line from its cache as long as L1 cache still has it.