A combinational circuit has four inputs $(A,B,C,D),$ which represent a binary$-$coded$-$decimal digit. The circuit has two groups of four outputs $-S,T,U,V,$ and $W,x,Y,Z.$ Each group represents a $BCD$ digit. The output digits represent a decimal number which is five times the input number. For example, if ABCD$=0111,$ the outputs are STUV $=0011$ and $WxYZ=0101.$ Assume that invalid $BCD$ digits do not occur as inputs.

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

$\backslash$table$[[ABCD,$sTUV,$WxYZ$