XNOR gate ($\neg (a\oplus b)$)

A two-input logic gate whose output is one exactly when its two input bits agree. Its Boolean function is $(a\wedge b)\vee (\neg a\wedge \neg b)$, equivalently $(a\vee \neg b)\wedge (\neg a\vee b)$. This follows by considering the two cases in which inputs are equal. It implements logical equivalence of the input truth values.