ThmDex – An index of mathematical definitions, results, and conjectures.

Biconditional boolean logic gate iff complement of trivial distance function on basic boolean ordered pairs

Formulation 0

Let $f : \{ 0, 1 \} \times \{ 0, 1 \} \to \{ 0, 1 \}$ be a D5402: Boolean logic gate.

Then $f$ is a D3553: XNOR boolean logic gate if and only if \begin{equation} \forall \, x, y \in \{ 0, 1 \} : f(x, y) = 1 - |x - y| \end{equation}