• i. Bit Tricks and XOR: Bitwise operations act on every bit independently, with no carries.
• ii. Gray Code: An ordering of all $2^n$ bit strings where consecutive strings differ in exactly one bit.
• iii. Submasks, Supermasks and SOS DP: Iterating over subsets of subsets costs $3^n$.
• iv. Bitwise Convolutions: XOR, AND and OR convolutions on arrays of size $2^n$ all follow the same recipe as FFT:
• v. XOR Basis: Integers are vectors over ${\mathbb{F}}_2$ and XOR is vector addition.
• vi. Bitset: Pack 64 booleans into a machine word and operate on all of them at once.
• vii. Bitset and Word-Level Parallelism: A machine word holds $w=64$ booleans, and one instruction processes all of them.