A cache memory that has a hit rate of 0.8 has an access latency 10 ns and miss penalty 100 ns. An optimization is done on the cache to reduce the miss rate. However, the optimization results in an increase of cache access latency to 15 ns, whereas the miss penalty is not affected. The minimum hit rate (rounded off to two decimal places) needed after the optimization such that it should not increase the average memory access time is _____________.
Correct Answer:
0.85
Solution:
The average memory access time (AMAT) can be calculated using the formula:
AMAT Before = 0.8(10) + 0.2(100) = 8+20 = 28.
Let x be the cache hit rate after optimization.
AMAT After = x(15) + (1-x)100
= 15x + 100 -100x
= 100 - 85x
AMAT Before >= AMAT After
= 28 >= 100 - 85x
= 72 = 85x
= x = 72/85
x = 0.85
