The circuit shown in the image consists of logic gates that process the inputs \( A \) and \( B \) to produce the output \( Y \). We need to identify the logical expression for \( Y \) based on the given combination.
Examine the Gates:
The circuit involves NOT gates (inverters) which invert the input signals.
Two AND gates combine inputs, and an OR gate at the end provides the final output.
Analyze the Inputs for Each Gate:
The first inverter negates \( A \), giving \(\overline{A}\).
The second inverter negates \( B \), giving \(\overline{B}\).
Operation of AND Gates:
The top AND gate receives \( A \) and \(\overline{B}\) and outputs \( A.\overline{B} \).
The bottom AND gate receives \(\overline{A}\) and \( B \) and outputs \(\overline{A}.B \).
OR Gate Combination:
The OR gate combines the outputs of both AND gates: \( A.\overline{B} + \overline{A}.B \).
Final Output:
The expression \( A.\overline{B} + \overline{A}.B \) is known as the XOR operation.
Thus, the output \( Y \) can be written in terms of inputs \( A \) and \( B \) as \( A.\overline{B} + \overline{A}.B \).
Therefore, the correct option is A.\overline{B}+\overline{A}.B, corresponding to the XOR logic gate operation.
