# GF(2)

## Finite field of two elements / From Wikipedia, the free encyclopedia

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GF(2) (also denoted $\mathbb {F} _{2}$, **Z**/2**Z** or $\mathbb {Z} /2\mathbb {Z}$) is the finite field with two elements[1] (GF is the initialism of *Galois field*, another name for finite fields). Notations **Z**_{2} and $\mathbb {Z} _{2}$ 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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