Question

Truth table for system of four NAND gates as shown in figure is

• A.
• B.
• C.
• D.

Answer 1

The correct option is D


As shown in logic diagram,
$P=\overline{AB}$
$Q=\overline{A.\overline{AB}}$
$=\overline{A}+AB$
$R=\overline{B.\overline{AB}}$
$R=\overline{B}+AB$
$\Rightarrow y=\overline{(\overline{A}+AB).(\overline{B}+AB)}$
$y=(\stackrel{=}{A}.\overline{AB})+\left(\stackrel{B}{.}\overline{AB}\right)y=(A.\overline{AB})+(B.\overline{AB})$
$y=\left[A\right(\overline{A}+\overline{B}\left)\right]+\left[B\right(\overline{A}+\overline{B}\left)\right]$
But $A.\overline{A}=0\&+B.\overline{B}=0$
$y=A\overline{B}+B\overline{A}$
$\therefore \text{XOR gate}$
And the truth table for XOR is