Singlesetbits

Singlesetbits refers to integers that have exactly one bit set in their binary representation. In common terminology, these numbers are the powers of two: 1, 2, 4, 8, 16, 32, and so on. The concept is widely used in low-level programming and digital logic, where bit patterns encode discrete resources or states.

A nonnegative integer n is a singlesetbit number if n > 0 and n & (n - 1) = 0. This condition holds precisely for powers of two, because a single 1 bit followed by zeros remains after subtracting 1 and performing the bitwise AND. Equivalently, the binary representation of such numbers is a 1 in some position and 0s elsewhere.

Examples include 1 (2^0), 2 (2^1), 4 (2^2), 8 (2^3), and so on. In contrast, numbers with more than one set bit, such as 3 (11 in binary) or 5 (101), do not satisfy the condition.

Common uses and properties come from their role as cleanly separable bit patterns. They enable fast tests for power-of-two status, efficient bitwise operations such as isolating the least significant set bit with x & -x, and simple indexing schemes in bitsets and memory allocation schemes. The index of the single set bit equals the position of the 1 in the binary form, often obtainable via logarithms or language-specific bit-length utilities.

See also: power of two, bit manipulation, population count, bit scan.