Question

1) Suppose that an application can take advantage of the parallelism provide by a dual core processor 33% of execution time. Use Amdahl's Law to determine the overall speedup of the application on a dual core processor versus a single core processor.

PLEASE EXPLAIN IN DETAIL

Answer 1

Amdahl's Law for maximum speedup:

• Let S be the serial component of the program
• Let n be the number of CPU cores

Then, according to Amdahl's Law,

$speedup \leq \frac{1}{S + \frac{1-S}{n}}$

In the above problem, it is given that 33% of the application works in parallel. Hence, the serial component(S) of this application is ( 100 - 33 ) 67%.

Therefore, S = 0.67

For two processing cores, (n = 2) speedup gain

$=\frac{1}{0.67 + \frac{1-0.67}{2}}$

$=1.1976$

For a single core processor, (n=1), the speedup gain

$=\frac{1}{0.67 + \frac{1-0.67}{1}}$

$=1$

Thus, for a dual core processor, the overall speedup is 1.1976 and for a single core processor the speedup is 1.