Binary arithmetic | Finite fields

GF(2)

GF(2) (also denoted , Z/2Z or ) is the finite field of two elements (GF is the initialism of Galois field, another name for finite fields). Notations Z2 and 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. (Wikipedia).

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Quotient ring | Coding theory | Vector space | Finite field | Ideal (ring theory) | Ring of integers | Boolean domain | Fermat's little theorem | Group (mathematics) | Identity element | BCH code | Linear code | Rational number | Additive identity | Polynomial ring | Cryptography | Matrix ring | Characteristic (algebra) | Field (mathematics) | Real number | Involution (mathematics) | Bit | Polynomial code | Basis (linear algebra) | Even number | Irreducible polynomial | Distributive property | Mathematical logic | Nimber | Field with one element | Abelian group | Bitwise operation | Advanced Encryption Standard | Boolean algebra (structure)