$4\mathrm{.}37$ A combinational circuil has four inputs $(A,B,C,D),$ which represent a binarycoded$-$decimal digit. The circuit has two groups of four oulpuls$-S,T,U,V,$ and $W,x,Y,Z.$ Each group represents a $BCD$ digit. The oulpul digils represent a decimal number which is live limes the input number. For example, if ABCD$=0111,$ the outputs are $0011010)1.$ Assume that invalid $BCD$ digits do not occur as inputs.

$($a$)$ Construct the truth table.

$($b$)$ Write down the minimum expressions for the outpuls by inspection of the truth table. $($IIint: Try to match oulput columns in the table with input columns.$)$