please do the steps out step by step:$($a$)$ Given a program, its total running time is t using a single processor $($i$.$e$.,$ running

the program serially$).$ If $90\%$ of the program $($i$.$e$.,90\%$ of t$)$ can be executed parallelly,

according to Amdahl$$s law, what will be the speedup if running the program parallelly

on a computer with $8$ processors $($or CPU cores$)?$ If unlimited processors are available

in the computer, what is the maximum speedup?

$($b$)$ What is superlinear speedup? Under what conditions will it happen?

$($c$)$ Given a program which searches the target data in a sequence of $12$ data, assume

$($i$)$ without knowing the location of the target data, the CPU will examine the data one

by one; $($ii$)$ the whole program can be executed parallelly and the program will stop

immediately once the target data is found; and $($iii$)$ the program$$s running time except

data searching can be ignored, please calculate:

$(1)$ If the target data is the $3$rd in the sequence, what is the speedup gained by

running the program using $4$ CPUs over running the program using $1$ CPU.

Note: by default, the data will be equally dispatched to the CPUs $($i$.$e$.,$ CPU $1$

processes data $1,2,3$; CPU $2$ processes data $4,5,6,$ etc.$)$

$(2)$ If the target data is the $7$th in the sequence, what is the speedup by running the

programing using $4$ CPUs?

$(3)$ If the target data is the $7$th in the sequence, what is the speedup by running the

programing using $3$ CPUs?