Appendix F / F.1 / F.1.1

F.1.1 Example: GF(2)

The simplest Galois Field is GF(2), which contains only two elements: {0, 1}. The arithmetic is performed modulo 2 (see Appendix E). For example 0 + 0 = 0, 0 + 1 + 1, and 1 + 0 = 1 (mod 2) because the answer remains in the field {0, 1}, but 1 + 1 = 0 (mod 2).

Addition therefore in GF(2) behaves like the logical exclusive-OR (XOR) operation, and multiplication corresponds to the logical AND operation.