Boolean Algebra & Logic Circuits – Detailed Explanation for NEET 2024
📌 NEET 2024 Physics Question
A logic circuit provides the output Y as per the following truth table:
| A | B | Y |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
The expression for the output Y is:
📝 Given Options:
- $A.B+\overline{A}$
- $A.\overline{B} + \overline{A}$
- $\overline{B}$ ✅
- $B$
Step 1: Observing the Truth Table
The given truth table is:
| A | B | Y |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
- The output $Y$ is 1 when $B = 0$.
- The output $Y$ is 0 when $B = 1$.
- This suggests that $Y$ depends only on $B$, not on $A$.
Step 2: Identifying the Boolean Expression
To derive the Boolean expression, we analyze when $Y = 1$ :
- For (A=0, B=0) → Y=1
- For (A=1, B=0) → Y=1
- For (A=0, B=1) → Y=0
- For (A=1, B=1) → Y=0
Clearly, Y is 1 whenever B = 0, and 0 whenever B = 1.
This is the definition of the NOT gate, where: $Y = \overline{B}$
Thus, the Boolean expression for Y is : $\boxed{\overline{B}}$
Step 3: Verifying the Options
Now, let’s check which option matches our derived expression:
- $A.B+\overline{A}$ ❌
- This expression is too complex and does not match the truth table.
- $A.\overline{B} + \overline{A}$ ❌
- This involves A, but we saw that Y is independent of A.
- $\overline{B}$ ✅
- Correct! The output follows the NOT operation on B.
- B ❌
- Incorrect! The truth table shows that Y = 1 when B = 0, meaning Y is NOT B but rather $B‾\overline{B}$.
Thus, the correct answer is: (3) $B‾\boxed{(3) \ \overline{B}}$
🎯 Understanding the Logic Gate Representation
The Boolean expression $Y = \overline{B}$ corresponds to a NOT gate.
Truth Table for NOT Gate
| Input ($B$) | Output $Y = \overline{B}$ |
|---|---|
| 0 | 1 |
| 1 | 0 |
This confirms that our derived expression is correct.
Circuit Diagram
A NOT gate takes a single input BB and inverts it:
B →──|>o──→ Y
If B = 0, the NOT gate outputs 1.
If B = 1, the NOT gate outputs 0.
📊 Summary Table of Logic Operations
| Operation | Symbol | Expression | Function |
|---|---|---|---|
| AND | . | A.B | Outputs 1 if both A and B are 1 |
| OR | + | A + B | Outputs 1 if either A or B is 1 |
| NOT | $\overline{}$ | $\overline{A}$ | Inverts the input |
| NAND | — | $\overline{A.B}$ | Opposite of AND |
| NOR | — | $\overline{A+B}$ | Opposite of OR |
📝 Key Takeaways
✔️ Boolean algebra helps simplify logic circuits.
✔️ Truth tables provide a systematic way to determine circuit outputs.
✔️ The output Y depends only on B, meaning it is $\overline{B}$.
✔️ NOT gate inverts the input signal.
🧩 Practice Questions
💡 Question 1:
A logic circuit provides the following truth table. Find the correct Boolean expression for YY:
| A | B | Y |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
(A) A + B
(B) A.B
(C) B
(D) $\overline{B}$
💡 Question 2:
Which of the following gates produces an output of 1 only when at least one of the inputs is 1?
(A) AND Gate
(B) OR Gate
(C) NOT Gate
(D) NAND Gate
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