The parity function on bits returns whether an odd number of them are one:For example, , and flipping any single input flips the output. A chain of exclusive or gates computes it with gates and linear depth; a balanced binary tree of such gates has logarithmic depth and still linear size.
Appending a parity bit to make the total even detects every single-bit error in a transmitted binary string. It misses any even number of flipped bits, because their changes cancel modulo two. This simple example separates error detection from error correction: detecting an odd number of changes does not identify which positions changed.
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The term "parity function" can refer to different concepts depending on the context in which it's used, particularly in computer science, mathematics, and digital logic. Here are a few interpretations of the parity function: 1. **Mathematics**: In a mathematical context, the parity function typically refers to a function that determines whether a given integer is even or odd.