Final answer:
The correct answer is option 3, with a potential maximum speedup of 1.18. This is calculated using Amdahl's Law, which takes into account the percentage of execution time affected by the improvement and the speedup of the improved component.
Step-by-step explanation:
The correct answer is option 3, which calculates to a 1.18 factor of potential speed increase. To determine the maximum possible speedup due to making the floating point adder twice as fast, we use Amdahl's Law, which is a formula used to find the limit of how much a system can be sped up by improving a particular part of it. Given that 30% of execution time is spent on floating point addition, the speedup for that portion is now doubled. However, the rest of the execution time (the remaining 70%) is unaffected by this change. The formula for Amdahl's Law is:
S = 1 / ((1 - P) + (P/Snew))
Where S is the overall speedup, P is the proportion of execution time that the improvement is applicable to (in this case, 30% or 0.3), and Snew is the speedup of the improved part (here, it's 2 since the floating point addition is twice as fast).
Therefore, the maximum possible speedup (S) can be calculated as:
S = 1 / ((1 - 0.3) + (0.3/2)) = 1 / (0.7 + 0.15) = 1 / 0.85 ≈ 1.18
This maximum potential speedup means that the entire processor can execute tasks approximately 1.18 times faster than before, on tasks that are limited by the speed of floating point addition.