Problem $2$: A binary adder Let $0\backslash$Sigma contains all size $3$ columns of $0$s and $1$s$.$ A string of symbols in $\backslash$Sigma gives three rows of Os and $1$s$.$ Consider each row to be a binary number and let B $=\{$w $\backslash$epsi $\backslash$Sigma $.[$the bottom row of w is the sum of the top two rows$)$ Show that B is regular. Hint: it is easier to work with B and construct a finite automaton that checks the sum from right to left. Assume the result obtained in Problem $1$