▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
▾ Binary cartesian set product
▾ Binary relation
▾ Map
▾ Function
▾ Real collection function
▾ Euclidean real function
▾ Real function
▾ Rational function
▾ Integer function
▾ Natural number function
▾ Boolean function
▾ Boolean logic gate
XNOR boolean logic gate
Formulation 0
A D218: Boolean function $f : \{ 0, 1 \} \times \{ 0, 1 \} \to \{ 0, 1 \}$ is an XNOR boolean logic gate if and only if
(1) \begin{equation} f(0, 0) = 1 \end{equation}
(2) \begin{equation} f(1, 0) = 0 \end{equation}
(3) \begin{equation} f(0, 1) = 0 \end{equation}
(4) \begin{equation} f(1, 1) = 1 \end{equation}
Formulation 1
Let $\mathbb{B} = \{ 0, 1 \}$ be the D217: Set of boolean numbers.
A D218: Boolean function $f : \mathbb{B} \times \mathbb{B} \to \mathbb{B}$ is an XNOR boolean logic gate if and only if
(1) \begin{equation} f(0, 0) = 1 \end{equation}
(2) \begin{equation} f(1, 0) = 0 \end{equation}
(3) \begin{equation} f(0, 1) = 0 \end{equation}
(4) \begin{equation} f(1, 1) = 1 \end{equation}
Also known as
Biconditional boolean logic gate, Exclusive NOR boolean logic gate, Exclusive NOT OR boolean logic gate
Results
» R4091: Biconditional boolean logic gate iff complement of trivial distance function on basic boolean ordered pairs