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When both inputs of a 2-input NAND gate are connected together, the gate functions as a:
AND gate
OR gate
NOT gate
NOR gate
NOT gate
Remember the rule: When inputs of a NAND gate or a NOR gate are shorted together, they effectively reduce the gate to an INVERTER (NOT gate).
A 2-input NAND gate where both input terminals A and B are connected to a single source terminal X.
Y=AтЛЕB
Remember the rule: When inputs of a NAND gate or a NOR gate are shorted together, they effectively reduce the gate to an INVERTER (NOT gate).
Students often assume that shorting inputs makes it behave like an AND gate, forgetting that the NAND gate has an inherent inversion (bubble) at the output.
Define the NAND logic
The Boolean expression for a 2-input NAND gate is Y=AтЛЕB.
Y=AтЛЕB
Apply input constraint
Since both inputs are connected together, we have A=B=X.
A=B=X
Substitute and simplify
Substitute A and B with X in the Boolean expression to get Y=XтЛЕX. By the Idempotent law of Boolean algebra, XтЛЕX=X.
Y=XтЛЕX=X
Identify the operation
The resulting expression Y=X is the definition of a NOT gate operation.
Y=X
C is correct because the shorted input NAND gate produces an output that is the inverse of the input, which is the definition of a NOT gate.
This concept is a precursor to universal gates; remember that both NAND and NOR gates can be used to construct any other logic gate, including the NOT gate.