XOR Logic Gate Notes

[Literal] Post summarizes exclusive OR (XOR) for cryptography and parity. [AI Synthesis] Treat XOR as the bridge between bitwise ops and modular arithmetic.

Key points

• [Literal] XOR lets you flip bits with a mask in a reversible operation—useful in cryptography.
• [Literal] p₁ ⊕ p₂ ⊕ … ⊕ pₙ is true when an odd number of inputs are 1 (associative).
• [Literal] XOR equals addition modulo 2; only 1-bits contribute to the sum.
• [Literal] Parity check uses XOR as a checksum to detect flipped bits.

Patterns / reminders

• [AI Synthesis] When you need reversible masking or even/odd detection, reach for XOR before inventing custom logic.

Sources

• (Source: raw/_posts/2015-10-07-logicgate.md)