1. What is Information Entropy?

Information entropy is a measure of uncertainty or randomness in a probability distribution. Introduced by Claude Shannon, it quantifies the expected value of the information contained in a message.

2. How Does the Calculator Work?

The calculator uses the Shannon entropy formula:

Where:

• \( H \) — Information entropy in bits
• \( p_i \) — Probability of event i (must be between 0 and 1)
• \( \log_2 \) — Logarithm base 2

Explanation: The formula sums the product of each probability with its log probability. Events with higher uncertainty contribute more to the total entropy.

3. Importance of Entropy Calculation

Details: Entropy is fundamental in information theory, data compression, cryptography, and machine learning. It helps quantify information content and system uncertainty.

4. Using the Calculator

Tips: Enter probabilities as comma-separated values between 0 and 1. The probabilities must sum to 1. Example: 0.5,0.3,0.2

5. Frequently Asked Questions (FAQ)

Q1: What does entropy of 0 mean?
A: An entropy of 0 indicates a completely predictable system with no uncertainty (one outcome has probability 1).

Q2: What's the maximum possible entropy?
A: For n outcomes, maximum entropy is log₂(n) bits, achieved when all outcomes are equally likely.

Q3: Why use base 2 logarithms?
A: Base 2 gives entropy in bits, the fundamental unit of information. Other bases can be used but bits are standard.

Q4: How is entropy used in data compression?
A: Entropy sets the theoretical limit on lossless compression - you can't compress below the entropy rate.

Q5: What's the difference between entropy and variance?
A: Variance measures spread of numerical values, while entropy measures uncertainty in outcomes regardless of their numerical values.