The circuit consists of an AND gate, a NOT gate, and an OR gate. The output \(Y\) is determined as follows:
The output of the AND gate is \(A \cdot B\).
The output of the NOT gate is \(\overline{A \cdot B}\).
The output \(Y\) is the OR of \(\overline{A \cdot B}\) and \(B\):
\[ Y = \overline{A \cdot B} + B \]
Step-by-Step Evaluation of Truth Table:
A
B
A · B
A · B
Y = A · B + B
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
0
1
Thus, the correct truth table is represented in Option (2).
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Approach Solution -2
To determine the correct truth table for the given logic circuit, we need to analyze the circuit step by step. The circuit consists of an OR gate followed by a NOT gate and then an AND gate. Let's go through each component:
The inputs to the circuit are A and B.
The first gate is an OR gate. The output of the OR gate (\(Z\)) is given by: \(Z = A + B\) where \(+\) represents the OR operation.
The output of the OR gate is then passed through a NOT gate, producing: \(\overline{Z} = \overline{A + B}\) where \(\overline{}\) denotes the NOT operation.
The final gate is an AND gate that takes inputs from the output of the NOT gate and the original input \(B\). The final output (\(Y\)) is: \(Y = \overline{Z} \cdot B = \overline{A + B} \cdot B\)
Now, let's create a truth table for the circuit:
A
B
Z = A + B
\(\overline{Z}\)
Y = \(\overline{Z} \cdot B\)
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
Based on this analysis, the correct truth table is depicted in the following image:
This matches the correct truth table for the given logic circuit.
