Please answer both:

$1.$ Consider a computer running a program that takes $250$ s$.$

$(80$ s spent on floating$-$point, $100$ s on load$/$store$,40$ s on branch$/$jump$,$ and the rest on other operations$).$

a$)$ What would the overall speedup be$,$ if we can cut the execution time of ONLY floating point ops by $50\%?$

b$)$ Could you possibly reduce the total time by $20\%,$ just by speeding up branch$/$jump$?$ c$)$ We can afford to buy better tech and improve performance of any one type $$ floating point, memory, or branch$/$jump $$ by a factor of $2.$ Which one would you choose, and why? And after optimization, suppose I am so impressed I give you funds to make one MORE such improvement; which one would you choose now?

$($Hint: Amdahl$$s Law. Show how much speedup each choice gives.$)$

$2.$ Consider a program that can execute with CPI $=1$ if we could magically service every load instruction within $1-$cycle $($L$1$ cache hit$).$

Now in practice, $9\%$ of all load instructions suffer from an L$1$ cache miss, $6\%$ of all load instructions suffer from an L$2$ cache miss, and $3\%$ of all load instructions suffer from an L$3$ cache miss $($and are serviced by the memory system$).$

An L$1$ cache miss stalls the processor for $8$ cycles while the L$2$ is looked up$.$ An L$2$ cache miss stalls the processor for $25$ cycles while the L$3$ is looked up$.$ An L$3$ cache miss stalls the processor for $200$ cycles while data is fetched from memory. What is the CPI for this program if $35\%$ of the program's instructions are load instructions? $($Assume these delays add, i$.$e$.$ the worst case stalls for $8+25+200$ cycles.$)$