Question

The following logic gate is equivalent to:

• A. NOR Gate
• B. AND Gate
• C. OR Gate
• D. NAND Gate

Answer 1

The correct option is A

NOR Gate

Step 1: Given digram

Step 2: Passing inputs$A\&B$ to their respective gate

1. When the input $A$ is passed to $NAND$ gate, it becomes $\overline{A}$.
2. Similarly, when the input $B$ passed to $NAND$ gate, it becomes $\overline{B}$.

Step 3: Passing Both the input together in the third gate

1. According to Demorgan's theorem, the complement of the product of all terms is equal to the complement of each term added together.
2. Now $\overline{A}$ and $\overline{B}$ passed as an input to $NAND$ gate$\left(3^{rd}gate\right)$ that produces the output $\overline{\overline{A}\overline{B}}$ which is equivalent to $\overline{\overline{A}+\overline{B}}$.

Step 4: Passing the input to the last gate

1. When the $\overline{\overline{A}+\overline{B}}$ is passed as an input to the last gate, it produces the output $\overline{A}+\overline{B}$ .
2. So, it can be said that the $Y$ is equivalent to $\overline{A}+\overline{B}$. Its truth table is given below.

$A$	$B$	$Y$
$0$	$0$	$1$
$0$	$1$	$1$
$1$	$0$	$1$
$1$	$1$	$0$

So, the truth table of the given logic gate is equivalent to the NOR gate.

Hence, option A is the correct answer.