ONLY SOLVE D$,$ THIS IS ALL ONE QUESTION!!!!

$($a$)$ A scalar pipeline has $4$ pipeline stages A$,$ B$,$ C$,$ D$.$ A data item entering this pipeline must be processed by the four units A$,$ B$,$ C$,$ and D in the order A $->$ B $->$ C $->$ D$.$ Suppose that units A$,$ B$,$ and D take $2$ clock cycles to process a data item, and unit C takes $3$ clock cycles to process a data item. How many clock cycles does it take for this scalar pipeline to process $1000$ independent operations? What is the speedup of this scalar pipeline?

$($b$)$ If the $3$rd stage $($C$)$ is increased to $2$ same$-$function units to make the scalar pipeline a superscalar pipeline, then how many clock cycles does it take for this superscalar pipeline to process $1000$ independent operations? How many cycles does it take to process $1$ operation in this superscalar pipeline?

$($c$)$ Instead of increasing the number of processing units at stage C to $2,$ we partition stage A into sub$-$stages A$1$ and A$2,$ partition stage B into B$1$ and B$2,$ partition stage C into C$1,$ C$2,$ and C$3,$ and partition stage D into D$1$ and D$2,$ with each sub$-$stage having a processing latency of $1$ cycle. Then we can view this new pipeline as a $9-$stage scalar pipeline. For this $9-$stage scalar pipeline, how many clock cycles does it take to process $1000$ independent operations?

$($d$)$ Suppose that there are $1000$ operations to be processed by the $9-$stage scalar pipeline in $($c$),$ and the $1000$ operations have data dependence only between the $8$th and the $10$th operations in the following way: the input to stage B$1$ of the $10$th operation is the output of stage C$3$ of the $8$th operation. How many cycles does it take this scalar pipeline to process these $1000$ operations?

$($e$)$ If the dependency in $($d$)$ is detectable during software development, can you think of a software solution to eliminate the stalling caused by the dependence described in $($d$)?$

$($f$)$ Instead of further partitioning each stage into sub$-$stages as in $($c$),$ we use two processing units for stages A$,$ B$,$ and D$,$ and three processing units for stage C$,$ obtaining a superscalar pipeline. How many clock cycles does it take this superscalar pipeline to process $1000$ independent operations?