Question

The logic gate equivalent to the combination of logic gates shown in the figure is

• A. AND
• B. NOR
• C. OR
• D. NAND

Hint:

A NOR gate can be constructed using NOT gates followed by an OR gate, as the output $\overline{A} + \overline{B}$ matches the NOR operation $\overline{A + B}$.

Answer 1

The Correct Option is B

Let’s break this down step by step to determine the equivalent logic gate for the given combination and why option (2) is the correct answer.
Step 1: Analyze the given circuit

• Inputs A and B are fed into two separate NOT gates.
• The output of the NOT gate for A is $\overline{A}$.
• The output of the NOT gate for B is $\overline{B}$.
• These outputs ($\overline{A}$ and $\overline{B}$) are fed into an OR gate.

The output $y$ of the OR gate is:
\[ y = \overline{A} + \overline{B} \]
Step 2: Construct the truth table to find the equivalent gate
\[ \begin{array}{|c|c|c|c|c|} \hline A & B & \overline{A} & \overline{B} & y = \overline{A} + \overline{B} \\ \hline 0 & 0 & 1 & 1 & 1 \\ 0 & 1 & 1 & 0 & 1 \\ 1 & 0 & 0 & 1 & 1 \\ 1 & 1 & 0 & 0 & 0 \\ \hline \end{array} \]
Now, compare with a NOR gate ($\overline{A + B}$):
\[ \begin{array}{|c|c|c|c|} \hline A & B & A + B & \overline{A + B} \\ \hline 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 0 \\ 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 \\ \hline \end{array} \]
The truth table of $\overline{A} + \overline{B}$ matches the NOR gate’s truth table.
Step 3: Confirm the correct answer
The combination of two NOT gates followed by an OR gate ($\overline{A} + \overline{B}$) is equivalent to a NOR gate ($\overline{A + B}$), matching option (2).
Thus, the correct answer is (2) NOR.