sompariteit

Sompariteit, or sum parity, is a concept in mathematics and computer science that concerns the parity (evenness or oddness) of the sum of numbers or bits. In the simplest form, the parity of a1 + a2 + ... + an is even when the number of odd summands is even, and odd when that number is odd. Equivalently, modulo 2 the sum equals the XOR (exclusive OR) of the parities of the summands. This means that only whether a term is even or odd matters; the precise values of even terms do not affect the result.

Examples illustrate the idea: 2 + 3 + 4 + 5 has two odd addends (3 and 5), so the total is even. 1 + 1 + 1 equals 3, which is odd. The same principle holds for any finite collection of integers.

In computing and data transmission, sompariteit is often used in parity checks. A parity bit is added so that the total sum of bits, modulo 2, has a chosen parity (even parity or odd parity). Such schemes can detect single-bit errors and, with additional mechanisms, some multi-bit errors. Parity checks are a simple form of error detection in memory, communication protocols, and basic digital circuits.

In mathematics, sompariteit is a useful tool in parity arguments and proofs, where one counts objects by whether their defining property is even or odd. Related concepts include parity, XOR, checksums, and parity bits.