Question

Explain using Amdahl's Law how we can possibly improve the overall per- formance of a computer cheaper by buying better memory than buying better processor.

Answer 1

Amdahl's Law looks at the potential speedup of a set of instructions to be executed when multiple processors are used as compared to a single processor.

Let us consider a program running on a single processor with (1-f) proportion being inherently serial and the remaining f proportion being parallelizable.

Let T be the total execution time using a single processor.

Then a speedup using N parallel processors is given as:

$\frac{T(1-f)+Nf}{T(1-f)+\frac{Tf}{N}}=\frac{1}{(1-f)+\frac{f}{N}}$

Thus we see that the more the value of f, higher is the speed up for a given value of N.

Hence if we increase the proportion of the parallelizable content of the program by buying better memory then it improves the performance of the computer for a given processor.