Find the Boolean expression for the logic circuit shown below: (1-NAND gate,…
2018
Find the Boolean expression for the logic circuit shown below:
(1-NAND gate, 2-NOR gate, 3-NOR gate)
- A.
AB
- B.
AB'
- C.
A'B
- D.
A'B'
Attempted by 60 students.
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Correct answer: A
1. Analyze the gates: The top gate is a NAND with inputs A and B, outputting (AB)'. The bottom gate is a NOR with inputs A and NOT B, outputting (A + B')'. The final gate is a NOR combining these outputs.
2. Simplify the bottom output: Using De Morgan's laws, (A + B')' simplifies to A'B.
3. Combine and simplify: The final output is ((AB)' + A'B)'. Substituting (AB)' with A' + B', we get ((A' + B') + A'B)'. Since A' absorbs A'B, this becomes (A' + B')', which simplifies to AB.