To derive the truth table for the provided circuit, a step-by-step analysis of its logic gates is required. The circuit comprises two XOR gates feeding into an OR gate.
Circuit breakdown:
The initial XOR gate accepts inputs A and B, producing an output according to the rule: \(A \oplus B = \overline{A}B + A\overline{B}\).
The second XOR gate also accepts inputs A and B, yielding the same output: \(A \oplus B = \overline{A}B + A\overline{B}\).
The outputs from both XOR gates are then connected to an OR gate. The OR gate operation is: \((A \oplus B) \lor (A \oplus B)\).
Given that the outputs are identical, this simplifies to \(A \oplus B\).
As both XOR gates share identical functionality and inputs, the OR gate’s output is dictated by the XOR condition itself. The truth table is constructed as follows:
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
The resulting truth table for the circuit is presented above. Option 2 accurately reflects this derived truth table.
