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Identify the Boolean expression from the given options, which is equivalent to the Logic Circuit Diagram.
Question

Identify the Boolean expression from the given options, which is equivalent to the Logic Circuit Diagram.

A.

(A + B') · C' + D

B.

A · B' + C' · D

C.

A + B' · C' + D

D.

(A · B' + C') · D

Correct option is A

The circuit contains four inputs: A, B, C and D. We analyze the circuit sequentially from left to right.
Step 1: First Logic Gate

  • The first gate is an OR gate.
  • Input A enters directly.
  • Input B first passes through a NOT gate, producing B′.

Therefore, the output of the first gate is:

[A + B']

Step 2: Inversion of Input C

  • Input C passes through a NOT gate.

Hence,

[C']

Step 3: Second Logic Gate (AND Gate)

  • The output ((A + B')) and (C') are applied to an AND gate.

Output becomes:

[(A+B)C][(A + B') \cdot C']​​

Step 4: Final Logic Gate (OR Gate)

  • The output from the AND gate is ORed with input D.

Thus, the final output expression is:

[(A + B')C' + D]

Final Boolean Expression

​​​(A+B)C+D\boxed{(A + B')C' + D}​​

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