log₂(256)
- Input
- x=256, base=2
- Expected output
- log₂(256) = 8
2⁸ = 256 — one byte.
binary logarithm base 2
Calculate Base-2 Logarithm (log₂)
log₂(x) = number of bits needed to represent x distinct values. log₂(1024) = 10 (2¹⁰ = 1024).
log₂ in computer science
- Binary search halves the problem each step — complexity is O(log₂ n). Huffman coding and Shannon entropy also use log₂.
Examples
log₂(1000000)
- Input
- x=1000000, base=2
- Expected output
- log₂(1000000) ≈ 19.93
20 bits for ~1 million values.
Full tool FAQ
log_b(x) = y means b^y = x. It is the inverse of exponentiation. Example: log₂(8) = 3 because 2³ = 8.
Frequently asked questions
How many bits do I need for 1000 values?
ceil(log₂(1000)) = ceil(9.97) = 10 bits (2¹⁰ = 1024 > 1000).
Does this page replace official or professional review?
No. It helps explain the scenario and use the tool more safely, but real decisions should consider official sources, full context and qualified guidance when needed.