1. What is Shannon Entropy?

Shannon entropy measures the uncertainty or information content in a probability distribution. It was introduced by Claude Shannon in 1948 and is fundamental to information theory.

2. How Does the Calculator Work?

The calculator uses the Shannon entropy formula:

Where:

• \( H \) — Shannon entropy in bits
• \( p_i \) — Probability of event i
• \( n \) — Number of possible events

Explanation: The equation quantifies the average information produced by a stochastic source of data.

3. Importance of Entropy Calculation

Details: Shannon entropy is crucial for data compression, cryptography, machine learning, and understanding information systems.

4. Using the Calculator

Tips: Enter probabilities as comma-separated values (e.g., 0.5,0.3,0.2). Probabilities must sum to 1 and each must be between 0 and 1.

5. Frequently Asked Questions (FAQ)

Q1: What does higher entropy mean?
A: Higher entropy indicates greater uncertainty or more information content in the distribution.

Q2: What's the maximum possible entropy?
A: For n events, maximum entropy is log₂n bits, achieved with uniform distribution.

Q3: How is entropy related to compression?
A: Entropy sets a lower bound on lossless compression of data from that source.

Q4: Why use base 2 logarithm?
A: Base 2 gives entropy in bits, the fundamental unit of information.

Q5: Can entropy be negative?
A: No, entropy is always non-negative since probabilities are between 0 and 1.