Log Base 2 Calculator
Calculate binary logarithms with step-by-step solutions and antilog conversions
Expression:
log₂() 2 ⌈log₂()⌉ = bits
log₂() 2 Bits needed for values
bits
Step-by-Step Solution
Natural Log (ln)
ln()
Log Base 10
log₁₀()
Bits Needed
⌈log₂()⌉
Logarithm Properties Reference
| Property | Formula |
|---|---|
Common Binary Logarithms
Computing Applications
Memory Sizes (Powers of 2)
If you like this calculator
Please help us simply by sharing it. It will help us a lot!
Related Calculators
Other calculators you might find useful.
Average Rate of Change Calculator
Calculate the average rate of change between two points on a function
Gamma Function Calculator
Calculate the gamma function Γ(z) for real numbers with step-by-step solutions
Rational Zeros Calculator
Find all possible and actual rational zeros of a polynomial using the Rational Root Theorem
Pythagorean Theorem Calculator
Calculate any side of a right triangle using the Pythagorean theorem a² + b² = c²
Area Calculator
Calculate the area of rectangles, circles, triangles, and other 2D shapes instantly
Proportion Calculator
Solve proportions using cross-multiplication, find missing values, and verify if ratios are proportional
About Log Base 2 Calculator
What is Log Base 2?
The binary logarithm (log base 2) is the power to which 2 must be raised to obtain a given number. If log₂(x) = y, then 2^y = x. The binary logarithm is fundamental in computer science, information theory, and digital systems.
How to Use This Calculator
- Select your calculation mode: Choose from Calculate Log₂, Antilog (2^x), or find number of bits
- Enter your value: Input the number you want to calculate
- View instant results: See the result with step-by-step explanation
- Explore properties: Learn logarithm rules and applications
Key Formulas
Logarithm Definition
- If 2^y = x, then log₂(x) = y
- Example: log₂(8) = 3 because 2³ = 8
Antilogarithm (Inverse)
- If log₂(x) = y, then x = 2^y
- Example: antilog₂(4) = 2⁴ = 16
Conversion from Other Bases
- log₂(x) = ln(x) / ln(2) = log₁₀(x) / log₁₀(2)
Logarithm Properties
Product Rule
log₂(xy) = log₂(x) + log₂(y)
Quotient Rule
log₂(x/y) = log₂(x) - log₂(y)
Power Rule
log₂(x^n) = n × log₂(x)
Change of Base
log_b(x) = log₂(x) / log₂(b)
Applications in Computing
Binary Representation
The number of bits needed to represent n values is ⌈log₂(n)⌉.
Algorithm Complexity
Binary search has O(log₂ n) time complexity. Many divide-and-conquer algorithms involve log₂.
Information Theory
Entropy and information content are measured in bits using log₂.
Data Storage
Memory sizes (KB, MB, GB) are powers of 2: 2¹⁰ = 1024 bytes = 1 KB.
Common Values
| x | log₂(x) | Description |
|---|---|---|
| 1 | 0 | 2⁰ = 1 |
| 2 | 1 | 2¹ = 2 |
| 4 | 2 | 2² = 4 |
| 8 | 3 | 2³ = 8 |
| 16 | 4 | 2⁴ = 16 |
| 32 | 5 | 2⁵ = 32 |
| 64 | 6 | 2⁶ = 64 |
| 128 | 7 | 2⁷ = 128 |
| 256 | 8 | 1 byte |
| 1024 | 10 | 1 KB |
| 1048576 | 20 | 1 MB |
| 1073741824 | 30 | 1 GB |
Note: Logarithms are only defined for positive numbers. log₂(0) and log₂(negative) are undefined in real numbers.