For given logic gate circuit choose correct truth table.
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Simplifying the Boolean expression before building the truth table can save a lot of time and reduce the chances of calculation errors. Remember key Boolean identities like the absorption law (\(A + AB = A\)) and De Morgan's theorems.
To solve this question, we need to determine the truth table for the given logic gate circuit. The circuit consists of an OR gate and a NOR gate. Let's analyze the behavior of these gates step-by-step:
Components:
An OR gate, represented by \(A + B\).
A NOR gate, which is a combination of OR gate followed by a NOT gate, represented by \(\overline{A + \text{OR output}}\).
Steps to derive the truth table:
For inputs A and B, calculate the output of the OR gate: \(Y = A + B\).
The output of the NOR gate is the negation of the OR gate's output: \(C = \overline{A + Y}\).
Now, let's fill the truth table for all combinations of inputs:
A
B
OR Output (Y = A + B)
NOR Output (C = \overline{A + Y})
0
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
The correct truth table matches with the following option:
Conclusion: The correct answer is the second option. The NOR gate output is inverted compared to the OR gate output, as seen in the truth table above.
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