$2$ Straightforward $[70]$ Let x$=\{$a:$0\mathrm{.}80,$b:$0\mathrm{.}10,$c:$0\mathrm{.}05,$d:$0\mathrm{.}03,$e:$0\mathrm{.}017,$f:$0\mathrm{.}003\}$ be an alphabet of $6$ symbols. $2+3+(1+1)+(2+3)+8=20($a$)$ Compute the entropy H$($x$).($b$)$ Design a Huffman Code C:x$->\{0,1\}^(+)$ for x $.($c$)$ Compute the average code length L$($C$)$ and the efficiency $\backslash$eta $=($H$($x$))/($L$($C$))$ of your coding. $($d$)$ Encode the string x$=$ baaaacbadaafaaae over x by your C $.$ Show that your C$($x$)$ can be uniquely decoded to x $.($e$)$ Design an FSM to decode C $.$