XORs, swizzling, and reductions

Sun, 11 Oct 2026 00:00:00 +0000

One way to think about XOR is as a bit flip: XORing a bit with $0$ is a no-op, while XORing it with $1$ flips it. The same idea extends to bitwise XOR: to compute $x \oplus y$ , flip each bit of $x$ wherever the corresponding bit of $y$ is $1$ .

The rule is straightforward, but I never had a good intuition for what bitwise XOR does to a number. That changed when I visualized what XOR does to a sequence.

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XORs, swizzling, and reductions