Please design a computational system whose transfer function is defined as follows. A series of $8-$bit positive integer is generated as the input of the computational system by the test bench. The output value Y is a $10-$bit positive integer, which is calculated according to equations $(1),(2),(3)$ and $(4).$

Xavg$=(1)$

where Xi is the value of the ith input data and j$>=1.$

n$-9$ in this homework

XS XXXjXjen$-1\}(2)$

Xappr Xappr $=$ Xavg, if Xvg EXS $($X$)($X$,$ E XS$)$ and $($X$,$