The truth table of the given circuit diagram is :
The Correct Option is B
Approach Solution - 1
To determine the truth table for the given circuit, we need to analyze the logic gates step-by-step. The circuit consists of two XOR gates whose outputs are fed into an OR gate.
Let’s break down the circuit:
- The first XOR gate takes inputs A and B. The XOR gate produces an output according to the rule: \(A \oplus B = \overline{A}B + A\overline{B}\).
- The second XOR gate also takes inputs A and B and similarly produces: \(A \oplus B = \overline{A}B + A\overline{B}\).
- The outputs from the two XOR gates are then fed into an OR gate. The OR gate performs: \((A \oplus B) \lor (A \oplus B)\).
- However, since the outputs are identical, this is essentially \(A \oplus B\).
Since both XOR gates have the same functionality and inputs, the output of the OR gate is determined by the XOR condition itself. Let's construct the truth table:
| A | B | First XOR: A ⊕ B | Second XOR: A ⊕ B | Y = (A ⊕ B) OR (A ⊕ B) |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 0 |
Thus, the truth table for the circuit is:
The correct answer is Option 2, which matches the truth table derived above.
Approach Solution -2
The given circuit diagram is equivalent to an XOR gate, which outputs a value of 1 if and only if the inputs are different.
| A | B | Y = A ⊕ B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
This matches the truth table given in option (2).
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