$($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 Amdahls 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 programs 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?