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Find the Boolean expression for the given logic gate circuit diagram where inputs are A and B. Diagram

A + B

A ⊕ B

A ⊙ B

Correct Answer

⚙️ TE • Technical Concept & PrincipleTechnicalDigital Electronics

Option B

Quick Summary:

The given circuit consists of two NAND gates feeding into a NOR gate. Analyzing the logic: the top NAND output is $\overline{A \cdot B}$ and the bottom NAND output is $\overline{A \cdot B}$ , which are then combined by a NOR gate to yield $Y = \overline{(\overline{A \cdot B}) + (\overline{A \cdot B})}$ . By applying DeMorgan's laws and Boolean simplification, this expression simplifies to $A \cdot B$ .

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🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of this as two identical security checks (NAND gates) that only let a signal pass if specific criteria are met, followed by a final filter (NOR gate) that effectively 'negates the negation', acting like a double-negative returning the signal to its original logic state.

🧠 Memory Mnemonic / Shortcut Aid

NAND followed by NOR with common inputs = AND gate functionality.

🔢 Key Formulas

$Y = \overline{\overline{A \cdot B} + \overline{A \cdot B}} = A \cdot B$ — The final simplified Boolean expression.

$X + X = X$ — Idempotent law used for simplification.

⚙️ Working Principle

The circuit functions by first processing the inputs $A$ and $B$ through two NAND gates, resulting in the intermediate signals $\overline{A \cdot B}$ . These two identical signals are then input into a NOR gate. According to the Boolean property of idempotent laws ( $X + X = X$ ), the NOR gate output is $\overline{\overline{A \cdot B} + \overline{A \cdot B}} = \overline{\overline{A \cdot B}} = A \cdot B$ .

📌 Key Points

▸
NAND gate logic: $Y = \overline{A \cdot B}$
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NOR gate logic: $Y = \overline{A + B}$
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Double negation rule: $\overline{\overline{X}} = X$

✅ Advantages

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Standard implementation of an AND gate using universal gates.

❌ Disadvantages / Limitations

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Uses three gates instead of a single AND gate, increasing component count.

🛠️ Applications / Uses

▸
Digital electronics
▸
Integrated circuit design

📄 Additional Information

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The circuit essentially acts as an AND gate.
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Option A ( $\overline{AB}$ ) is the NAND function.
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Option C ( $\overline{A+B}$ ) is the NOR function.
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Option D ( $A+B$ ) is the OR function.

📊 Diagram / Illustration

✅

B is correct — The circuit simplifies mathematically to the AND function represented by AB.

Core Concepts Used

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Boolean Algebra Universal Logic Gates De Morgan's Laws

💡 EXAM TIP

Whenever you see universal gates (NAND/NOR) connected to themselves or each other, always simplify the expression using Boolean laws before choosing the answer.

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