A microprocessor chip has a floating-point unit and an integer unit. The instruc

Question

A microprocessor chip has a floating-point unit and an integer unit. The instruction mix in terms of time for a scitific computation is 60% floating point, and 50% integer and other instructions. The engineers say that they can increase the speed of the floating unit by a factor of 3, which would increase the cost of the chip by 25%. The sales people report that customers will accept the additional 25% cost if the over all performane (spped up) s doubled. Is is worh making this modification? Explain.

Explanation / Answer

In parallel computing, Amdahl's law is mainly used to predict the theoretical maximum speed up for program processing using multiple processors.Let T(N) be the time required to complete to complete the task on processors.The speed up S(N)=T(1)/T(N).

Formula for speed up using percentage of algorithm is

S=N/((B*N)+(1-B)).

Number of processors used in the problem were 2.one processor is for floating point unit and second processor is for integer unit.

Percentage of time for serial part for floating point instructions is

B=60% =0.6 and parallel part (1-B)=40%=0.4. and N=1 by taking individually

Speed up=S=1/((1*0.6)+0.4)=(1/(1))=1.

For integer unit,percentage of time for serial part=B=50%=0.5. and for parallel part (1-B)=50%=0.5.

Speed up=S=1/((1*0.5)+0.5)=1/(1)=1. for p=0.5

Now,if speed up is increasing by factor 3,then cost also increased by 25%.

In microprocessor chip,performance (speed up) is very important.

If speed is increased by factor 3 for floating point unit

3S=1/(T)-->T=1/3.

Over performance definitely =speedup=2/1=2

Cost is increased by 25%.

If x is cost for s,then cost for 3S is x.25

For getting performance of 2 ,the percentage of cost for floating point should decrease 10% to get 0.5.

Now Speed up=2/1=2.

So,Finally for increasing speedup time should decrease and cost also increased.

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