ThmDex – An index of mathematical definitions, results, and conjectures.
Real arithmetic expressions for OR boolean logic gate
Formulation 0
Let $\text{OR} : \{ 0, 1 \} \times \{ 0, 1 \} \to \{ 0, 1 \}$ be an D3555: OR boolean logic gate.
Let $x, y \in \{ 0, 1 \}$ each be a D1043: Boolean number.
Then
(1) \begin{equation} \text{OR}(x, y) = \max(x, y) \end{equation}
(2) \begin{equation} \text{OR}(x, y) = \frac{x + y + |x - y|}{2} \end{equation}
(3) \begin{equation} \text{OR}(x, y) = \text{XOR}(x, y) + \text{AND}(x, y) \end{equation}
(4) \begin{equation} \text{OR}(x, y) = 1 - \text{NOR}(x, y) \end{equation}
(5) \begin{equation} \text{OR}(x, y) = \text{NOT}(\text{NOR}(x, y)) \end{equation}