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. $($Hint: System A $-$ original system,$=$

System B $-$ Floating Point Enhanced System, System C $-$ Floating Point Enhanced & Cache Slowed$=$

Down System$)$

a$.$ If the new fast floating$-$point unit speeds up floating$-$point operations by$,1\mathrm{.}85x,$ and floating$-$

point operations take $38\mathrm{.}25\%$ of the original program's execution time, what is the overall

speedup $($ignoring the penalty to any other instructions$)?($speed up from A to B$)$

b$.$ Now assume that after speeding up the floating$-$point unit we also slow down data cache

accesses, resulting in a $1\mathrm{.}75x$ slowdown $($or $\frac{4}{7}$ speedup$).$ Cache accesses consume $27\mathrm{.}5\%$ of

the execution time. What is the overall speedup now? $($speed up from B to C$)$

c$.$ hat is the overall speedup? $($speed up from A to C$)$