A power of two is \(2^k\) for some non-negative integer \(k\): 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096…
Powers of two are the heartbeat of digital computing. Each bit in binary doubles the representable range; an \(n\)-bit integer holds values from 0 to \(2^n - 1\). Common limits like 256 (\(2^8\) — values per byte), 65,536 (\(2^{16}\) — UDP ports, max UInt16), and 4,294,967,296 (\(2^{32}\) — IPv4 address space) are all powers of two.
In binary, a power of two is a single 1 followed by zeros. There's a fast bit-trick to test for them: \(n\) is a power of two if and only if \(n > 0\) and \(n \\& (n-1) = 0\).