Question

Combination of NAND gates is shown in the figure. It is equivalent to

Choose the correct answer from the options given below

• A. AND gate
• B. NOR gate
• C. OR gate
• D. X-OR gate

Hint:

Memorize this standard shorthand combination for entrance exams:
NOTs before a NAND $\implies$ OR gate.
NOTs before a NOR $\implies$ AND gate.
Recognizing these standard gate configurations saves you from drawing full truth tables under time pressure!

Answer 1

The Correct Option is C

Step 1: Understand the question.
A combination of NAND gates is given, and we must find which single basic gate it behaves like. The method is to write the output of each NAND step using Boolean algebra.
Step 2: Recall the NAND operation.
A NAND gate gives the AND of its inputs, then inverts it. With one input $A$ tied together, a NAND acts as a NOT gate: its output is $\overline{A}$.
Step 3: Invert each input first.
In the standard two-input arrangement, each input $A$ and $B$ is first sent into a NAND used as a NOT, giving $\overline{A}$ and $\overline{B}$.
Step 4: Combine with a final NAND.
The two results $\overline{A}$ and $\overline{B}$ go into a final NAND gate. Its output is \[ \overline{\overline{A}\cdot\overline{B}}. \]
Step 5: Apply De Morgan's law.
De Morgan's law says $\overline{\overline{A}\cdot\overline{B}} = A + B$.
Step 6: Identify the gate.
The output $A + B$ is exactly the OR operation, so the circuit acts as an OR gate. \[ \boxed{\text{OR gate}} \]