# Shannon entropy

Definition from Wiktionary, the free dictionary

## English[edit]

### Etymology[edit]

Named after Claude Shannon, the "father of information theory".

### Noun[edit]

**Shannon entropy** (*countable and uncountable*, *plural* **Shannon entropies**)

- information entropy
**Shannon entropy***H*is given by the formula where*p*_{i}is the probability of character number*i*showing up in a stream of characters of the given "script".- Consider a simple digital circuit which has a two-bit input (
*X*,*Y*) and a two-bit output (*X*and*Y*,*X*or*Y*). Assuming that the two input bits*X*and*Y*have mutually independent chances of 50% of being HIGH, then the input combinations (0,0), (0,1), (1,0), and (1,1) each have a 1/4 chance of occurring, so the circuit's**Shannon entropy**on the input side is . Then the possible output combinations are (0,0), (0,1), and (1,1) with respective chances of 1/4, 1/2, and 1/4 of occurring, so the circuit's**Shannon entropy**on the output side is , so the circuit reduces (or "orders") the information going through it by half a bit of**Shannon entropy**due to its logical irreversibility.