The base-2 logarithm, common in computer science for bits, binary search depth, and data-doubling problems.
How it works
The base-2 logarithm asks “2 raised to what power gives this number,” computed directly using the natural-log change-of-base relationship.
What this does not include
This does not include other logarithm bases — this calculator is specifically for base 2.
How to use this calculator
- Enter a positive number.
Frequently asked questions
Why is base 2 especially useful in computer science?
Binary computing is built on powers of 2, so log base 2 directly answers questions like “how many bits are needed to represent this many values” or “how many times can this be halved.”
What is log base 2 of a number less than 1?
It’s negative — for example, log base 2 of 0.5 is −1, since 2⁻¹ equals 0.5.
Is log base 2 of 1 always zero?
Yes — any number raised to the power of zero equals 1, which is why the logarithm of 1, in any base, is always zero.
