gf

GF(2) (also denoted





F


2




{\displaystyle \mathbb {F} _{2}}
, Z/2Z or




Z


/

2

Z



{\displaystyle \mathbb {Z} /2\mathbb {Z} }
) is the finite field of two elements (GF is the initialism of Galois field, another name for finite fields). Notations Z2 and





Z


2




{\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.

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