Question

To get output $‘1’$ at $R$, for the given logic gate circuit the input values must be :

• A. $X=0,Y=0$
• B. $X=0,Y=1$
• C. $X=1,Y=0$
• D. $X=1,Y=1$

Answer 1

The correct option is C

$X=1,Y=0$

Step 1: Given Data

Output at $R=1$

Step 2: Diagram

Step 3: Truth Table

$X$	$Y$	$\overline{X}$	$\overline{Y}$	$\overline{X}+Y$	$X.\overline{Y}$	$\overline{X.\overline{Y}}$	$\left(\overline{X}+Y\right)+\overline{X.\overline{Y}}$	$R=\overline{\left(\overline{X}+Y\right)+\overline{X.\overline{Y}}}$
$0$	$0$	$1$	$1$	$1$	$0$	$1$	$1$	$0$
$0$	$1$	$1$	$0$	$1$	$0$	$1$	$1$	$0$
$1$	$0$	$0$	$1$	$0$	$1$	$0$	$0$	$1$
$1$	$1$	$0$	$0$	$1$	$0$	$1$	$1$	$0$

Therefore, from the above truth table, we can see that for $R$ to be $1$, $X=1,Y=0$.

Hence, the correct answer is option (C).