speed up gain

Question

Consider the cache memory which is 30 times fasterthan main memory and it uses 90% of the total time. The speed up gain of cache memory ( in 2 decimal places)

Answer 1

This is a question based on Amdahl's law..Amdahl's law can be used wherever a section of a program uses some form of enhancement and other part remains unenhanced..

Speedup according to Amdahl's law is found as :

Speedup   =    1 / [ 1 - f1 - f2  + ..  +( f1 / S1) + ( f2/S2)  + ( f3/S3) .. ]

where f1 , f2 etc.  : fraction of enhancements

          S1 , S2 etc : Speedup corresponding to each fraction of enhancement

So here  f1   =  90%   =   0.9

            S1   =  30

Hence

Speedup      =   1 / [ 1 - 0.9  + 0.9 / 30 ]

                   =   1 / [ 0.1 + 0.03 ]

                   =   7.69         [ Correct to 2 decimal places ] 

Comments

Habibkhan what is the problem in my solution;

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Here they are treating both memory as independent memory.

Here they have given that 90% of time we use cache so 10% time we use only memory. We will not use heirarchial access formula here.

if we will use mem+cahe in 10% case also then that statement will become wrong.