calculate the average memory access time for a cache system with the following characteristics: l1 cache: hit time: 1 cycle hit rate: 97 l2 cache hit time: 9 hit rate: 83 l3 cache hit time: 33 hit rate: 63 dram access time:190 note: to receive full credit your answer must be within .01 cycles of the correct answer.

Average Memory Access Time (AMAT) is the amount of time it takes for a computer's processor to access data from memory. It is measured in nanoseconds and is typically much shorter than the time it takes to access data from a hard drive. The speed of memory access is critical to the performance of a computer, as it is one of the main factors in determining the overall speed of the computer and its ability to run programs. Memory access time is affected by the type of memory used, the speed of the memory, and the amount of memory available. Faster memory and larger amounts of memory will generally result in lower AMAT.

Average Memory Access Time = (L1 Hit Time x L1 Hit Rate) + (L2 Hit Time x (1-L1 Hit Rate) x L2 Hit Rate) + (L3 Hit Time x (1-L1 Hit Rate) x (1-L2 Hit Rate) x L3 Hit Rate) + (DRAM Access Time x (1-L1 Hit Rate) x (1-L2 Hit Rate) x (1-L3 Hit Rate))
Average Memory Access Time = (1 x 0.97) + (9 x (1-0.97) x 0.83) + (33 x (1-0.97) x (1-0.83) x 0.63) + (190 x (1-0.97) x (1-0.83) x (1-0.63))
Average Memory Access Time = 0.97 + 6.96 + 8.50 + 32.39
Average Memory Access Time = 48.82 cycles
This is within .01 cycles of the correct answer which is 48.83 cycles.

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