Q$4.[20$ points$]$ 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,

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$.$ What is the speedup we have obtained from

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

enhanced mode?

Q$5.[20$ points$]$ When making changes to optimize part of a processor, it is often the

case that speeding up one type of instruction comes at the cost of slowing down

something else. For example, if we put in a complicated fast floating point unit, that takes

space, and something might have to be moved farther away from the middle to

accommodate it$,$ adding an extra cycle in delay to reach that unit. The basic Amdahl's law

equation does not take into account this trade$-$off.

a$.$ If the new fast floating$-$point unit speeds up floating$-$point operations by$,$ on average,

$2,$ and floating$-$point operations take $20\%$ of the original program's execution time,

what is the overall speedup $($ignoring the penalty to any other instructions$)?$

b$.$ Now assume that speeding up the floating$-$point unit slowed down data cache

accesses, resulting in a $1\mathrm{.}5$ slowdown $($or $\frac{2}{3}$ speedup$).$ Data cache accesses consume

$10\%$ of the execution time. What is the overall speedup now?

c$.$ After implementing the new floating$-$point operations, what percentage of

execution time is spent on floating$-$point operations? What percentage is spent on data

cache accesses.