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What logic function is produced by adding an inverter to each input and the output of an AND gate?
Answer & Solution
Correct Answer:
Option
C
Let inputs be A and B.
Inverting each input gives A′ and B′ to the AND gate.
The AND gate outputs A′ · B′.
Now, the output inverter changes A′ · B′ into (A′ · B′)′.
By De Morgan’s law: (A′ · B′)′ = A + B.
A + B is the OR function, not NOR.
The NOR function would be (A + B)′, which is not what we have here.
Therefore: Adding inverters to each input and the output of an AND gate produces an OR gate.
Inverting each input gives A′ and B′ to the AND gate.
The AND gate outputs A′ · B′.
Now, the output inverter changes A′ · B′ into (A′ · B′)′.
By De Morgan’s law: (A′ · B′)′ = A + B.
A + B is the OR function, not NOR.
The NOR function would be (A + B)′, which is not what we have here.
Therefore: Adding inverters to each input and the output of an AND gate produces an OR gate.
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