If the floating$-$point $($FP$)$ instructions of an application on a specific processor C$1$ consumes $60\%$ of the total execution time. Moreover, in the same application, $20\%$ of the floating$-$point time is taken to do square root calculations.

$4\mathrm{.}1$ A new processor C$2$ is developed. This new processor could either enhance the performance of FP instructions by a factor of $1\mathrm{.}3$ or alternatively increase the performance of the square root operation by a factor of $8.$ Which is the better design for the aforementioned application? $(5$ pts$)$

$4\mathrm{.}2$ If we decide to parallelize the code within the application. What speedup can be reached if we can perfectly parallelize $90\%$ of the code and run the applications on a system with $16$ cores? What fraction of the code has to be parallelized if we want to get a speedup of $10$ on the same system? $(10$ pts$)$