Given the ordered alphabet $\{$A$,$ B$,$ C$,$ D$\}=\backslash$Sigma

with probabilities P$($A$)=0\mathrm{.}1,$ P$($B$)=0\mathrm{.}3,$ P$($C$)=0\mathrm{.}2,$ P$($D$)=0\mathrm{.}4.$

The interval is divided according to the lexicographic order $\{$A$,$ B$,$ C$,$ D$\}=\backslash$Sigma $,$ where A covers the half$-$open interval $[0,0\mathrm{.}1),$ and so on$...$

a$.$ Given that the message T consists of $5$ characters, it was encoded using static arithmetic compression to $0\mathrm{.}644.$ We saw two ways to decode the static arithmetic code. Decode the message using Table Based Decoding and show all the steps and calculations.