Problem $4.$ Amdahl$$s Law $(20$ points$)$

Please show all work and calculations in your answers.

Assume a program requires the execution of $50$e$6$ FP instructions, $110$e$6$ INT instructions, $80$e$6$ L$/$S instructions, and $16$e$6$ branch instructions. The CPI for each type of instruction is $1,1,4,$ and $2,$ respectively. Assume that the processor has a $2$ GHz clock rate.

Execution Time $=($Number of Instructions $*$ CPI$)/$ Clock Rate

FP: $(50$e$6*1)/2=25$e$-6$ Seconds

INT: $(110$e$6*1)/2=55$e$-6$ seconds

L$/$S: $(80$e$6*4)/2=160$e$-6$ seconds

Branch: $(16$e$6*2)/2=16$e$-6$ seconds

Total Execution time $=$

By how much must we improve the CPI of FP instructions if we want the program to run two times faster?

By how much must we improve the CPI of L$/$S instructions if we want the program to run two times faster?

By how much is the execution time of the program improved if the CPI of INT and FP instructions is reduced by $40\%$ and the CPI of L$/$S and Branch is reduced by $30\%?$

Suppose we can improve the floating$-$point instruction performance of a CPU by a factor of $15($The floating$-$point instructions are accomplished $15$ times faster.$)$ If floating point instructions account for $75\%$ of the total time executing a program, how much speed$-$up can be achieved with this improvement?