Assume to include in a processor a new fast floating$-$point unit that speeds up floating$-$point operations by

an average factor $2\backslash$times $.$ In addition, assume that floating$-$point operations take $40\%$ of the original program

execution. What is the overall speedup? $[3$ points$]$

$2.$ Assume that speeding up the floating$-$point operations causes a slowdown in the data cache accesses. For

example, given the additional space taken by the more sophisticated floating$-$point unit, memory operations

take some extra cycles to get to the cache. Specifically, assume that data cache accesses, which consume

$20\%$ of the original program execution time, are now slowed down by a factor $1\mathrm{.}5\backslash$times $.$ What is the overall

speedup? $[3$ points$]$

$3.$ After implementing the new floating$-$point unit, what percentage of the execution time is spent on floatingpoint operations and what percentage is spent on data cache accesses?