Negation

The negation or NOT of a Boolean value flips it: $0$ becomes $1$, and $1$ becomes $0$. Negating a value gives its complement.

$X$	$\overline{X}$
0	1
1	0

The corresponding hardware element is the NOT gate (inverter), drawn as a triangle with a small bubble at the output. The bubble itself stands for “invert” — that’s why a NAND gate is drawn as an AND with a bubble, and a PMOS transistor is drawn with a bubble on the gate.

Two negations cancel: $\overline{\overline{X}}=X$. This is the involution law, and in circuits it means a NOT followed by a NOT is just a wire (electrically slower, but logically equivalent).

A negation interacts with AND/OR through De Morgan’s Laws — negating a product becomes a sum of negations, and vice versa.

Notation

Several conventions:

$\neg X,\sim X,\overline{X},X^{\prime }$

Modern engineering texts predominantly use the overbar ($\overline{X}$); the prime notation ($X^{\prime }$) is older and now mostly seen in older textbooks. Programming languages typically use ! (logical NOT) or ~ (bitwise NOT).