If, like me, you get confused between entropy in terms of information content, and entropy in the medium/signal transmission, Harish Joe can help 🙂

The entropy (information content) can be affected by the entropy in the medium. 😄

This is one of the reasons I stopped thinking of entropy in terms of order/disorder paradigm.
— Harish Jose (@harish_josev) November 10, 2020

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Online calculator: Shannon Entropy

Shannon Entropy

This online calculator computes Shannon entropy for a given event probability table and for a given messageperson_outlineTimurschedule7 years ago

In information theory, entropy is a measure of the uncertainty in a random variable. In this context, the term usually refers to the Shannon entropy, which quantifies the expected value of the message’s information.
Claude E. Shannon introduced the formula for entropy in his 1948 paper “A Mathematical Theory of Communication.”

H(X) = - \sum_{i=1}^np(x_i)\log_b p(x_i)

Minus is used because for values less than 1, and logarithm is negative. However, since

$-\log a = \log \frac{1}{a}$ ,

formula can be expressed as

H(X)= \sum_{i=1}^np(x_i)\log_b \frac{1}{p(x_i)}

Expression
$\log_b \frac{1}{p(x_i)}$
is also called an uncertainty or surprise, the lower the probability $p(x_i)$ , i.e. $p(x_i)$ → 0, the higher the uncertainty or the potential surprise, i.e. $u_i$ → ∞, for the outcome $x_i$ .

In this case, the formula expresses the mathematical expectation of uncertainty, which is why information entropy and information uncertainty can be used interchangeably.

This calculator computes Shannon entropy for given probabilities of events