GF(2)

GF(2) (also denoted ${\displaystyle \mathbb {F} _{2}}$, Z/2Z or ${\displaystyle \mathbb {Z} /2\mathbb {Z} }$) is the finite field with two elements (GF is the initialism of Galois field, another name for finite fields). Notations Z₂ and ${\displaystyle \mathbb {Z} _{2}}$ may be encountered although they can be confused with the notation of 2-adic integers.

GF(2) is the field with the smallest possible number of elements, and is unique if the additive identity and the multiplicative identity are denoted respectively 0 and 1, as usual.

The elements of GF(2) may be identified with the two possible values of a bit and to the boolean values true and false. It follows that GF(2) is fundamental and ubiquitous in computer science and its logical foundations.