NorVNorW

NorVNorW is a composite boolean operator used in theoretical discussions of logic circuits. It is defined for two boolean inputs, V and W, as the NOR of V and the NOR of W, written as Nor(V, Nor(W)). This construction illustrates how nesting NOR operations can produce other logical functions.

Formally, since Nor(x,y) = ¬(x ∨ y), NorVNorW equals ¬(V ∨ ¬W). By De Morgan’s laws, this is equivalent to ¬V ∧ W. Some authors may adopt alternative bracketing, such as Nor(Nor(V), W), which yields ¬(¬V ∨ W) = V ∧ ¬W. Both variants show how nested NORs can realize simpler conjunction-like behavior depending on parentheses.

Truth table wise, the operator is true only when V is false and W is true; in all other input combinations, the result is false. Concretely, for V and W in {0,1}, NorVNorW is 1 only for (V=0, W=1) and 0 otherwise. This makes NorVNorW equivalent to the function ¬V ∧ W.

In practical terms, NorVNorW can be used to demonstrate how NOR gates compose to realize specific logic functions without introducing additional gate types. It also serves as an example in boolean algebra of how operator nesting affects outcome and how equivalent forms can be derived through logical identities.

See also: NOR gate, boolean algebra, logic circuits, De Morgan’s laws.

There are no widely cited standard references specific to NorVNorW; it appears primarily as a teaching construct to illustrate nested NOR behavior in introductory logic discussions.