gen-define-bits-versus-nats-and-give-one-short-worked-example-5582

Define bits versus nats and give one short worked example.

# Bits vs Nats **Bits** and **nats** are units for measuring information, differing only in the logarithm base used: - **Bits**: Information measured using log base 2 (log₂) - **Nats**: Information measured using natural log (ln or logₑ) The information content of an event with probability *p* is: - In bits: -log₂(p) - In nats: -ln(p) **Conversion**: 1 nat = log₂(e) ≈ 1.443 bits ## Worked Example **Question**: What is the information content of flipping heads on a fair coin? **Solution**: - Probability: p = 0.5 *In bits*: - I = -log₂(0.5) = -log₂(2⁻¹) = 1 bit *In nats*: - I = -ln(0.5) = -ln(e⁻⁰·⁶⁹³) ≈ 0.693 nats **Check**: 0.693 nats × 1.443 ≈ 1 bit ✓ The answer "1 bit" makes intuitive sense—a fair coin flip provides exactly one binary digit of information.