Write the truth table for a $NAND$ gate connected as given in the figure. Hence,identify the exact logic operation carried out by this circuit.

(N/A) In the given circuit,the input $A$ is connected to both inputs of the $NAND$ gate. Let the inputs be $A_1 = A$ and $A_2 = A$. The output $Y$ of a $NAND$ gate is given by $Y = \overline{A_1 \cdot A_2}$.
Substituting the inputs,we get:
$Y = \overline{A \cdot A}$
Using the Boolean identity $A \cdot A = A$,we have:
$Y = \overline{A}$
The truth table for this operation is:

$A$	$Y = \overline{A}$
$0$	$1$
$1$	$0$

Since the output $Y$ is the complement of the input $A$,this circuit functions as a $NOT$ gate.