log₂(256)
- Input
- x=256, base=2
- Expected output
- log₂(256) = 8
2⁸ = 256, one byte.
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binary logarithm base 2
log₂(x) = number of bits needed to represent x distinct values. log₂(1024) = 10 (2¹⁰ = 1024).
2⁸ = 256, one byte.
20 bits for ~1 million values.
log_b(x) = y means b^y = x, so a logarithm is simply an exponent, the power the base must be raised to. It is the inverse operation of exponentiation. For example, log₂(8) = 3 because 2³ = 8, and log₁₀(100) = 2 because 10² = 100.
ceil(log₂(1000)) = ceil(9.97) = 10 bits (2¹⁰ = 1024 > 1000).
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