This calculator returns the entropy \(H(X)\) of the random variable \(X \sim \text{Bernoulli}(p)\) in bits.
Result:
\(H(X) = \) 1 bit per channel use.
Formula Used:
\begin{equation} H(X) = -p\log_2(p) - (1 - p)\log_2(1-p) \end{equation}
Notes on limits:
\begin{equation} \lim_{p \to 0} p \log_2(p) = 0 \end{equation}
Reference (Courtesy of Claude E. Shannon):
A Mathematical Theory of Communication, Part I-6