XOR calculator

Type two numbers with XOR between them: `1100 XOR 1010`, or `1100 ^ 1010`. Set Numbers are in to hex or decimal to XOR those instead, as in `F0 XOR FF` or `12 XOR 10`. The answer comes back in all three, and the working lines up the bits of both numbers and the result.

XNOR, AND, OR, NAND, NOR and NOT work the same way. For AND and OR there's also a bitwise calculator page.

Exclusive OR compares two bits and gives 1 if they're different and 0 if they're the same. 0 XOR 0 is 0, 0 XOR 1 is 1, 1 XOR 0 is 1 and 1 XOR 1 is 0. For longer numbers, it's done for each pair of bits separately, with no carries, so `1100 XOR 1010` is 0110.

Two properties make it useful. XOR with 1 flips a bit and XOR with 0 leaves it alone, so XORing with a mask flips exactly the bits you choose. And XOR undoes itself: A XOR B XOR B is A again. That's the basis of parity checks, RAID 5's recovery of a lost disk, and the oldest machine cipher there is.

In 1917 Gilbert Vernam, an engineer at AT&T, found a way to encrypt teleprinter messages automatically. Each character of the message, in five-bit Baudot code, was combined with a character from a key on paper tape using exactly this operation, built from relays. At the far end the same key tape XORed it back. His patent, US 1,310,719, was granted in 1919. With a key that's truly random, never reused and as long as the message, the scheme became the one-time pad, which is unbreakable in principle.