The number of binary bits necessary to represent a number, given explicitly by

where is the ceiling function, is the floor function, and is lg, the logarithm to base 2. For , 1, 2, ..., the sequence of bit lengths is given by 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, ... (OEIS A029837). The function is given by the Wolfram Language function BitLength[n].

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References

Sloane, N. J. A. Sequence A029837 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Bit Length

Cite this as:

Weisstein, Eric W. "Bit Length." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BitLength.html

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