 Bit-length

For a positive integer $n$, its bit length is the number of binary digits in its usual representation:Equivalently, $\ell (n)$ is the unique positive integer satisfying $2^{\ell (n)-1}\le n<2^{\ell (n)}$. For example, $13=1101_2$ has bit length four, and $8=1000_2$ has bit length four too. The inequalities provide an exact characterization without a floating-point logarithm.

Many integer programming interfaces define the bit length of zero as zero. That convention counts no significant one-bit; it differs from the written binary numeral $0$, which has one character. A fixed-width machine word can also contain leading zero bits that do not contribute to the value's bit length.

Bit-length, often referred to in the context of binary numbers or digital data, is the number of bits required to represent a given value in binary form. It indicates how many binary digits (0s and 1s) are needed to express a number. For example: - The decimal number `5` is represented in binary as `101`, which has a bit-length of 3.