Given below are four different codes used to code the alphabet $A$ of an information source where $A=\{\begin{array}{c}{a}_1\\ a_2\\ a_3\end{array},\{$:$a_4,a_5\}.$ Identify which of the codes are $($i$)$ uniquely decodable, $($ii$)$ instantaneous & $($iii$)$ prefix codes. Give reasons for your answers. Also, determine the average code$-$word length of all the uniquely decodable codes and identify the code having the least length.

$\backslash$table$[[$Letter$,$Probability,Code $1,$Code $2,$Code $3,$Code $4],[a_1,p_1=0\mathrm{.}5,1,1,0,00],[a_2,p_2=0\mathrm{.}25,01,10,10,01],[a_3,p_3=0\mathrm{.}125,001,100,110,10],[a_4,p_4=0\mathrm{.}0625,0001,1000,1110,11],[a_5,p_5=0\mathrm{.}0625,00001,10000,1111,110]]$