$1.$ Design a one$-$bit full subtractor using two $8-$to$-1$ MUXes. $($Lecture Unit $9$ slide $4$ to $15)$

a$)$ Complete the truth table. Consider d to be the result of the subtraction $\backslash (\backslash$mathrm$\{$X$\}-\backslash$mathrm$\{$Y$\},$ b$\_\{$i n$\}\backslash )$ to be the borrow input, and $\backslash ($ b$\_\{\backslash$text $\{$out $\}\}\backslash )$ to be the output borrow $(20$ marks$)($Lecture Unit $1$ slide $54$ to $65)$

b$)$ Let the control signals to your MUXes be $\backslash (\backslash$mathrm$\{$X$\},\backslash$mathrm$\{$Y$\}\backslash )$ and bin $($borrow in$).$ Connecting the MUX inputs to only $"0"$ or $"1,"$ implement the subtractor. Label each output. Explain your reasoning $(20$ marks$)($Lecture Unit $9$ slide $4$ to $15)$