At some time in the future, while working at ZikZak corporation, you are asked t

Question

At some time in the future, while working at ZikZak corporation, you are asked to choose a memory architecture for a new entertainment product. Future DRAM (F-DRAM) used by ZikZak has 10 ns access times which makes it too slow for this application. Option A is to use a fast new DRAM (FN-DRAM) with 5 nsec access times (just fast enough) which is twice as expensive as F-DRAM . Option B is to use F-DRAM with a cache memory. The cache memory would have a 1 ns access time, but is 10 times as expensive as the F-DRAM.

a) What hit rate is needed for option B to have an average access time equal to option A?

b) An experiment determines that for your application the relationship between the hit ratio (H) and the ratio of cache size to main memory size (R = Size of cache/size of main memory) can be well approximated by the equation H = (sin(pi * R/2))1/2 (where the argument of the sine function is in radians). Which option is preferred and why?

c) If instead, the experiment determines that for your application the best approximation is H = (sin(pi * R/2))1/4, which option is preferred and why?

Explanation / Answer

a)

let us take a small example of 10 instructions.

for oprion a time taken will be 50ns

now for option B time should be less than or equal to 50.

If we consider 50% hit rate then time will be 1*10(cache will always happen if it is a miss or hit) +5*10 (in case of misses we need to go to main memory)= 55ns which is more

if we consider 60% hit rate then time will be 1*10+4*10 = 50 which is what we want.

So basically with cache we should have a 60% hit rate in order to make the access time equal in both the cases.

b)

Now here ratio H = (sin(pi * R/2))1/2 . Now cache memory is very expensive and we need to get a hit rate of 60% as dicussed in order to meet the requirement. If we do that then size of cache memory should almost be half of main memory in which case. let us assume that we want 10 units. so 6 units will be main memory and 4 units will be cache. now here the cost will be more in this case.

Hence option A is better here.

c)

Now here if we notice that hit rate is more in this case as it is twice the value. we can achieve the same hit rate with less cache size and hence here Option B is better.

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