Suppose that we can improve the floating-point instruction performance of a machine by a factor of 10 (i. e. , the same floating-point instructions run 10 times faster on this new machine). What percentage of the instructions must be floating point to achieve an overall speedup of at least 4 (or 4X)?

83.33 percent

Explanation:

In order to solve this problem, we have to use the Amhadl's law.

We define x as the percentage of floating point instruction.

The speedup is 4, therefore we will have 100/4 cycles if the original program is executed in 100 cycles.

100/4 = 25 cycles

So we continue solving this problem as

100/4 = x/10 + 100-x

25 = x/10+100-x

When we solve this out

x = 83.33 percent

Check attachment for the full calculation

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