Assume 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, measure 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$.$ What is the speed up we have obtained from fast mode?

b$.$ What percentage of the original execution time has been converted to fast mode?