Bool Operation

Multi-input-XOR

an $N$-input XOR produces TRUE when an odd number of inputs are TRUE. Example: $N=3$

Normal Forms

Note that AND is represented as Sum, OR is represented as Product. The reason for this deep connection is that $\{0,1\}$ forms a semiring under the bool operation, where AND acts like $\otimes$ and OR acts like $\oplus$.

• Product-of-Sums Form $\simeq$ CNF (Conjunctive Normal Form)
• Sum of Products Form $\simeq$ DNF (Disjunctive Normal Form)
  • $e$.$g$. $F(A,B)=\sum (m_1,m_3)$