A memory hierarchy is composed of an upper level and a lower level. Assume a CPU with 1ns clock cycle time. Data is requested by the processor. 8 out of 10 requests find the data in the upper level and return the data in 0.3ns. The remaining requests require 0.7 ns to return the data. Determine the corresponding values for the upper level memory. Hit rate =
Miss rate =
Hit time =
Miss penalty =
AMAT =

Hit rate = 80%

Miss rate = 20%

Hit time = 0.3 ns  

Miss penalty = 0.4 ns

AMAT ≈ 3.875 ns

Explanation:

8 out of 10 = 0.3ns. to return data  ( also finds data in the upper level )

2 out of 10 = 0.7 ns to return data

a) Hit rate in upper level memory

= 8/10 * 100 = 80%

b) Miss rate

= 2/ 10 * 100 = 20%

c) Hit time in the upper level memory

Hit time = 0.3 ns

d) Miss penalty

This is the time taken by the missed requests to return their own data

= 0.7 ns -  0.3 ns =  0.4 ns

e) AMAT ( average memory access time )

Hit rate = 80% , Hit time = 0.3ns

miss rate = 20%  Miss time = 0.7 ns

hence AMAT = (0.3 / 0.8 ) +  (0.7 / 0.2 )

                      ≈ 3.875 ns

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