To solve this problem, we need to determine the truth table for the given logic gate configuration. The circuit involves a combination of NOT, AND, OR, and NAND gates.
Step-by-Step Solution:
Inputs: The circuit takes four inputs: A, B, C, and D.
Logic Gates: Based on the circuit:
The NOT gate inverts inputs A and B, resulting in \(\overline{A}\) and \(\overline{B}\).
The OR gate combines C and D, giving \(C + D\).
The AND gate takes \(\overline{A}\) and \(\overline{B}\), giving \(\overline{A} \cdot \overline{B}\).
A NOT gate inverts the AND gate output: \(\overline{\overline{A} \cdot \overline{B}}\).
NAND gate combines the output of the OR and the NOT gates from the previous sub-step.
Final Output: The output Y is derived based on the logic of the gates.
Evaluation of the Given Options:
By evaluating each possibility based on the logic described, we can determine what Y should be for each combination of A, B, C, and D.
A
B
C
D
Y
1
1
0
1
0
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
The correct truth table is option D as it matches the derived outputs based on the described logic.
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