Answer with detailed steps?
In an enhancement of a design of a CPU, the speed of a floating point until has been increased by 20% and the speed of a fixed point unit has been increased by 10%. What is the overall speedup achieved if the ratio of the number of floating point operations to the number of fixed point operations is 2:3 and the floating point operation used to take twice the time taken by the fixed point operation in the original design?
(A) 1.155 (B) 1.185 (C) 1.255 (D) 1.285
(A) 1.155 (B) 1.185 (C) 1.255 (D) 1.285
Replies
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sookieLet say the total no. of instructions to be executed is 100
By the ratio of 2:3
Floating point instructions N(Ft): 40
Fixed point instruction N(Fd): 60
Before scenario
Time taken to process a floating point instruction T(Ft):2 units
Time taken to process a fixed point instruction T(Fd): 1 unit
Total time to execute T(B)=N(Ft) * T(Ft) + N(Fd) * T(Fd)=40*2+60*1=140 units
After scenario
When speed of floating point processing is increased by 20% means time to execute a floating instruction in reduced by 20%
Before T(Ft) was 2 units
Now time taken to process a floating point instruction T(Ft):2 - 20% of 2 =1.6 units (After)
Similarly speed of fixed point processing is increased by 10% hence
Before T(Fd) was 1 units
Now time taken to process a fixed point instruction T(Fd): 1 - 10% of 1=0.9 units (After)
Total time to execute T(A)= 40*1.6+60*0.9=118units
So Speed up gained is T(B)/T(A) =140/118=1.186 (approx)
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