1.2 [15/10] <1.6> Assume—as in the Amdahl’s Law Example on page 41—that we make
ID: 3624120 • Letter: 1
Question
1.2 [15/10] <1.6> Assume—as in the Amdahl’s Law Example on page 41—that we make
an enhancement to a computer that improves some mode of execution by a factor of 10. Enhanced
mode is used 50% of the time, measured as a percentage of the execution time when
the enhanced mode is in use. Recall that Amdahl’s Law depends on the fraction of the original,
unenhanced execution time that could make use of enhanced mode. Thus, we cannot
directly use this 50% measurement to compute speedup with Amdahl’s Law.
a. [15] <1.6> What is the speedup we have obtained from fast mode?
b. [10] <1.6> What percentage of the original execution time has been converted to fast
mode?
this is the content of page 41 for Amdahl's Law
Explanation / Answer
This question explores the effects of Amdahl’s Law, but the data given in the question is in a form that cannot be directly applied to the general speedup formula.
Part A:
What is the speedup we have obtained from fast mode?
Because the information given does not allow direct application of Amdahl’s Law, we start from the definition of speedup:
Speedupoverall = Timeunenhanced/Timeenhanced
The unenhanced time is the sum of the time that does not benefit from the 10 times faster speedup, plus the time that does benefit, but before its reduction by the factor of 10. Thus,
Timeunenhanced = 50% Timeenhanced + 10 * 50% Timeenhanced = 5.5 Timeenhanced
Substituting into the equation for speedup gives us:
Speedupoverall = 5.5*Timeunenhanced/Timeenhanced = 5.5
Part B:
What percentage of the original execution time has been converted to fast mode?
Using Amdahl’s Law, the given value of 10 for the enhancement factor, and the value for Speedupoverall from Part(a), we have:
5.5 = Fractionenhanced / [(1- Fractionenhanced) + (Fractionenhanced /10)]
Solving shows that the enhancement can be applied 91% of the original time.
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