NOToperations

NOT operations are unary operators that invert values. In logic, the NOT operation, or negation, maps true to false and false to true. In computing there are two main variants: logical NOT that operates on Boolean values, and bitwise NOT that inverts every bit in an integer’s binary representation.

Logical NOT is defined by a simple truth table: NOT true equals false, and NOT false equals true. Bitwise NOT yields the bitwise complement: every 0 becomes 1 and every 1 becomes 0 in the target word. On two’s complement machines, the bitwise NOT of x equals -x minus 1. De Morgan’s laws relate negation to conjunction and disjunction: NOT (A AND B) equals (NOT A) OR (NOT B), and NOT (A OR B) equals (NOT A) AND (NOT B).

In programming languages, the syntax and behavior vary. Logical NOT is typically written as not in Python and as ! in C-like languages; bitwise NOT uses ~ in C, C++, Java, and JavaScript. NOT is usually unary and binds tightly; applying it to non-Boolean values is language-specific, often yielding a Boolean result or a bitwise complement after type coercion.

Applications of NOT include negating conditions in control flow and forming logical expressions via De Morgan transformations. Bitwise NOT is useful for masking, flipping bits, and implementing complements in low-level arithmetic or bit-twiddling tasks.

Historically, NOT is a fundamental operation in Boolean algebra, formalized by George Boole, and realized in hardware as an inverter or NOT gate in digital circuits. It forms the basis for building more complex logic functions together with AND and OR.