Question

For the logic circuit shown in the figure, the simplified Boolean expression for the output Y is

• A. 0
• B. C
• C. A
• D. A+B+C

Answer 1

The correct option is A 0



$Y=\overline{X+D}$
$\overline{Y}=X+D$
$D=\overline{(Z+\overline{C})}=\overline{Z}.C$
$\overline{Y}=\overline{Z}+B+\overline{Z}.C$
$X=\overline{(Z.\overline{B})}=\overline{Z}+B$
$\overline{Y}=\overline{Z}+B$
$Z=\overline{P.\overline{B}}=\overline{P}+B$
$\overline{Y}=\left(\overline{\overline{P}+B}\right)+B$
$P=\overline{AB}$
$\overline{Y}=P.\overline{B}+B=B+P$
$=B+\overline{AB}=B+\overline{A}+\overline{B}=1$
$\therefore Y=0$