A Binary$-$Coded Decimal $($BCD$)$ to $7-$segment display decoder is a special decoder

which can convert binary coded decimals into another form which can be easily

displayed through a $7-$segment display.

Consider the BCD input is WXYZ to the decoder and the outputs are the segments a$,$

b$,$ c$,$ d$,$ e$,$ f$,$ & g for the display $($shown below$).$

Which of the following is the logical expression for output segment a$?$

Hint: ABCD input of $1($i$.$e $W=0,x=0,Y=0,Z=1)$ will result in segments $b$ and $c$ to

light up$.$

$a=W^{\text{'}}+Y^{\text{'}}+(x^{\text{'}}Z+x{Z}^{\text{'}})$

$a=W+Y+(x^{\text{'}}Z+x{Z}^{\text{'}})$

$a=W^{\text{'}}+Y^{\text{'}}+(xZ+x^{\text{'}}{Z}^{\text{'}})$

$a=W+Y+(xZ+x^{\text{'}}{Z}^{\text{'}})$

None of the others