1. What is Binary Entropy?

Binary entropy measures the uncertainty in a binary (two-outcome) random variable. It quantifies the average information content or uncertainty associated with the possible outcomes.

2. How Does the Calculator Work?

The calculator uses the binary entropy equation:

Where:

• \( p \) — Probability of the first outcome (0 ≤ p ≤ 1)
• \( 1-p \) — Probability of the second outcome
• \( \log_2 \) — Logarithm base 2 (gives result in bits)

Explanation: The function reaches its maximum (1 bit) when p = 0.5 (maximum uncertainty) and minimum (0 bits) when p = 0 or 1 (complete certainty).

3. Importance of Binary Entropy

Details: Binary entropy is fundamental in information theory, data compression, cryptography, and machine learning. It sets bounds on how much information can be reliably transmitted through communication channels.

4. Using the Calculator

Tips: Enter a probability value between 0 and 1. The calculator will compute the entropy in bits. Valid inputs are 0 ≤ p ≤ 1.

5. Frequently Asked Questions (FAQ)

Q1: What does 0 bits of entropy mean?
A: It means there's no uncertainty - the outcome is completely predictable (p=0 or p=1).

Q2: Why is entropy measured in bits?
A: Using base-2 logarithm gives the number of bits needed to represent the information, which is fundamental in digital systems.

Q3: What's the maximum possible binary entropy?
A: 1 bit, which occurs when p = 0.5 (both outcomes equally likely).

Q4: Can binary entropy be negative?
A: No, entropy is always non-negative (0 ≤ H ≤ 1 for binary variables).

Q5: How is this related to Shannon entropy?
A: Binary entropy is a special case of Shannon entropy for systems with exactly two possible outcomes.