Question

The output of the given combination gates represents :

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

Answer 1

The correct option is C

NAND Gate

Step 1: Given the figure

Step 2: Passing $A$ and $B$ to their respective gate

1. When the input $A\&B$ passed through their respective $NOR$ gate, it produces the output $\overline{A}\&\overline{B}$.

Step 3: Pass $\overline{A}\&\overline{B}$ to the NOR gate

1. When the combined input of $\overline{A}\&\overline{B}$ pass through the NOR gate, it produces the output $\overline{\overline{A}+\overline{B}}$.
2. According to DE Morgan's theorem, the sum of compliments of each term is equal to the complement of the product of all terms.
3. So, the output $\overline{\overline{A}+\overline{B}}$ can be written as $AB$.

Step 4: Determine the output of the circuit

1. When the input $AB$ is passed through the last gate, it produces the output $\overline{AB}$. The truth table of the circuit is given below:

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

The output of the truth table is equivalent to the NAND gate.

Hence, option C is the correct answer.