$2\mathrm{.}7$ Consider the example in Section $2\mathrm{.}5$ for the calculation of average CPI and MIPS rate, which yielded the result of $\frac{C}{P}$I $=2\mathrm{.}24$ and MIPS rate $=178.$ Now assume that the program can be executed in eight parallel tasks or threads, with roughly equal number of instructions executed in each task. Execution is on an $8-$core system, with each core $($processor$)$ having the same performance as the single processor originally used. Coordination and synchronization between the parts adds an extra $25,000$ instruction executions to each task. Assume the same instruction mix as in the example for each task, but increase the $\frac{C}{P}$I for memory reference with cache miss to $12$ cycles due to contention for memory.

a$.$ Determine the average $\frac{C}{P}$I $.$

b$.$ Determine the corresponding MIPS rate.

c$.$ Calculate the speedup factor.

d$.$ Compare the actual speedup factor with the theoretical speedup factor determined by Amdhal's law.