Derive the formula for calculating the average access time for a word in a system with three levels of cache. Assume the following values for a theoretical system containing an L1, L2, and L3 cache. Location Latency L1 L2 L3 Main Memory 2 ns 5 ns 20 ns 100 ns If an application has following hit rates, what is the average memory access time for a memory word? Location Hit rate L1 L2 L3 Main Memory 50% 70% 90% 100%