---
tag: 1JP7127DA5
kind: concept
name: Zhegalkin algebra
sources:
  - wikipedia: en:75604189@r1288379270
    locator: Zhegalkin algebra
    note: adopted
    mention: wikipedia://en/75604189
    sections: [Summary]
same_as:
  wikidata: Q12077567
  wikipedia: Zhegalkin algebra
inventory: [8F8MEP493M]
---

## Summary

In mathematics, **Zhegalkin algebra** is a set of Boolean functions defined by the nullary operation taking the value $1$, use of the binary operation of [[conjunction|025YZN3VJW]] $\land$, and use of the binary sum operation for modulo 2 $\oplus$. The constant $0$ is introduced as $1 \oplus 1 = 0$. The negation operation is introduced by the relation $\neg x = x \oplus 1$. The disjunction operation follows from the identity $x \lor y = x \land y \oplus x \oplus y$.