A combinational drouit has four inputs $),$ which represent a binary$-$coded$-$decimal digit. The circur has two graups of four outputs$-$S$,T,U,V,$ and $W,x,Y,Z.$ Esch

group represents a $BCD$ digit. The output digits represent a decimal number which is $1$ more than four times the input number. For example, if ABCD $-$ DO$11,$ the outputs are

STUV $=$ DOO$1$ and WXYZ $-$ DO$11.$ Acsume that irvalid BCD digits do not occur a inputs.

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

$($b$)$ Write down the minimum expressians far the outputs by inspectian of the truth table. $($Hint: Try to match autput columns in the table with input columns. Use the

following as nocresary: $A,B,C,$ and $D.$ Simplify your anawer completely.$)$

$5-$

$T=$

$u=$

$V=$

$W=1$

$x=$

$=$

$z=$