Logic Gate Question Every JEE Student Should Solve! 🔥 | Find When Y = 0

 

❓ Question

The output Y = 0 when:

1. A = 1 and B = 1

2. A = 0 and B = 1

3. A = 1 and B = 0

4. A = 0 and B = 0

(Which logic gate does this condition represent?)

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🖼️ Question Image

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✍️ Short Solution

To find the correct answer, we analyze when the output becomes 0 for different input combinations.

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Step 1 — Recall common two-input logic gates

Gate	Expression	Output (Y) = 0 occurs when…
AND	Y = A·B	When A = 0 or B = 0
OR	Y = A + B	When A = 0 and B = 0
NAND	Y = ¬(A·B)	When A = 1 and B = 1
NOR	Y = ¬(A + B)	When A = 1 or B = 1
XOR	Y = A ⊕ B	When A = B (both 0 or both 1)
XNOR	Y = ¬(A ⊕ B)	When A ≠ B (0,1 or 1,0)

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Step 2 — Given condition

The question states that Y = 0 when A = 1 and B = 1.

Let’s check which gate satisfies this.

1. For AND gate:
   A=1, B=1 → Y=1·1=1 → Y≠0 ❌

2. For OR gate:
   A=1, B=1 → Y=1+1=1 → Y≠0 ❌

3. For NAND gate:
   A=1, B=1 → Y=¬(1·1)=¬1=0 ✅

That’s the correct condition!

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Step 3 — Verify other inputs (optional cross-check)

Let’s create the full truth table for NAND:

A	B	A·B	Y = ¬(A·B)
0	0	0	1
0	1	0	1
1	0	0	1
1	1	1	0

✅ The output Y=0 only when A=1 and B=1, which matches perfectly with the question.

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🧮 Image Solution

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✅ Conclusion & Concept Recap

✅ Final Answer:

$$\boxed{{\displaystyle \text{Y = 0 when A = 1 and B = 1 → NAND Gate}}}$$

🔹 Key Points:

• NAND gate = NOT + AND combined.

• Boolean expression: $Y = \overline{A·B}$.

• Only gives 0 when both inputs are 1.

• In all other cases, output is 1.