1. What is Binary Logarithm?

The binary logarithm (log₂) is the logarithm to the base 2. It answers the question "To what power must 2 be raised to get this number?" It's widely used in computer science and information theory.

2. How Does the Calculator Work?

The calculator uses the change of base formula:

Where:

• \( x \) — Positive real number
• \( \ln \) — Natural logarithm (base e)

Explanation: The formula converts the base from 2 to e (Euler's number) using the mathematical identity for logarithm base conversion.

3. Applications of Binary Logarithm

Details: Binary logarithms are essential in computer science (binary trees, algorithm complexity), information theory (bits required to represent numbers), and digital signal processing.

4. Using the Calculator

Tips: Enter any positive real number. The calculator will compute its binary logarithm. Invalid inputs (zero or negative numbers) will be rejected.

5. Frequently Asked Questions (FAQ)

Q1: Why is binary logarithm important in computing?
A: Because computers use binary (base-2) number systems, binary logarithms naturally describe many computational processes.

Q2: What's the relationship between binary and natural logarithms?
A: They differ by a constant factor: log₂(x) ≈ 1.442695 × ln(x).

Q3: What's the binary log of 1?
A: log₂(1) = 0, since 2⁰ = 1.

Q4: What's the binary log of 2?
A: log₂(2) = 1, since 2¹ = 2.

Q5: How is binary log used in algorithm analysis?
A: It describes the depth of binary trees and appears in O(log n) time complexity calculations.