Q5,paper 3,j 12.Suppose that a given application is run on a 64-processor machine and that 70 percent of the application can be parallelized. Then the expected performance improvement using Amdahl’s law is

Options (A) 4.22 (B) 3.22 (C) 3.32 (D) 3.52
Answer(B) 3.22
Amdahl's Law is a law governing the speedup of using parallel processors on a problem, versus using only one serial processor. Before we examine Amdahl's Law, we should gain a better understanding of what is meant by speedup.
Speedup:
The speed of a program is the time it takes the program to excecute. This could be measured in any increment of time. Speedup is defined as the time it takes a program to execute in serial (with one processor) divided by the time it takes to execute in parallel (with many processors). The formula for speedup is:

S =t(i)/t(j)

Where T(j) is the time it takes to execute the program when using j processors. Efficiency is the speedup, divided by the number of processors used. This is an important factor to consider. Further it is solved as.S=
N
-----------------------
(B*N)+(1-B)
In our case N=64 processors. B= 30% of algorithm that is serial. S= 64/((64*.3)+(1-.3))=3.22.