NOTAND

NOTAND refers to the logical operation that yields the negation of the conjunction of its operands. For two inputs A and B, NOTAND equals ¬(A ∧ B), which is commonly known as NAND.

Notation and synonyms: The operation is often written as A NAND B, or with symbols such as ↑ (the Sheffer stroke) or ⊼ in some texts. In boolean algebra, it is equivalent to the negation of AND, and it is functionally complete, meaning any boolean function can be constructed using only NOTAND operations.

Truth table: For two inputs, A and B, A NAND B is true in all cases except when both A and B are true. Specifically: 0 0 -> 1, 0 1 -> 1, 1 0 -> 1, 1 1 -> 0. This can be generalized to any number of inputs: NOTAND of n inputs equals ¬(A1 ∧ A2 ∧ ... ∧ An); it evaluates to 1 unless all inputs are 1.

General properties: NOTAND is a commutative and associative operator only in the limited sense of producing the same result under certain input permutations; its primary practical property is functional completeness, allowing construction of any boolean function when used with itself.

Applications and history: The concept traces to the Sheffer stroke, introduced by Henry M. Sheffer in the early 20th century. In digital electronics, NAND gates implement the NOTAND function directly, and their prevalence stems from their simplicity and universality for implementing logic circuits.