The logic operations performed by the given digital circuit is...

As shown in the figure the various logic gates have been mentioned.

Let the output before the $NOT$ gate be $Z$.

Using the expression for the logic gates, it can be written

$Z = \left(A + B\right) \cdot ( A \cdot B )$

Hence, the output $Y$ is

$Y = Z = \left(A + B\right) \cdot ( A \cdot B ) ⇒ Y = A \cdot B$

Hence the digital circuit is equivalent to an $AND$ gate.