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Binary entropy function - Wikipedia

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In information theory, the binary entropy function, denoted H ⁡ ( 𝑝 ) or H b ⁡ ( 𝑝 ) , is defined as the entropy of a Bernoulli process (i.i.d. binary variable) with probability 𝑝 of one of two values, and is given by the formula: The base of the logarithm corresponds to the choice of units of information; base e corresponds to nats and is mathematically convenient, while base 2 (binary logarithm) corresponds to shannons and is conventional (as shown in the graph); explicitly: Note that the values at 0 and 1 are given by the limit 0 log ⁡ 0 := lim 𝑥 → 0 + 𝑥 log ⁡ 𝑥 = 0 (by L'Hôpital's rule); and that "binary" refers to two possible values for the variable, not the units of information. When 𝑝 = 1 / 2 , the binary entropy function attains its maximum value, 1 shannon (1 binary unit of information); this is the case of an unbiased coin flip. When 𝑝 = 0 or 𝑝 = 1 , the binary entropy is 0 (in any units), corresponding to no information, since there is no uncertainty in

Binary entropy function - Wikipedia Jump to content From Wikipedia, the free encyclopedia Entropy of a process with only two probable values This article has multiple issues. Please help improve it or discuss these issues on the talk page . ( Learn how and when to remove these messages ) This article needs additional or more specific categories . Please help out by adding categories to it so that it can be listed with similar articles. ( November 2025 ) This article needs more citations . Please help improve this article by adding citations to reliable sources . Unsourced material may be chall

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