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Two bits of entropy: In the case of two fair coin tosses, the information entropy in bits is the base-2 logarithm of the number of possible outcomes — with two coins there are four possible outcomes, and two bits of entropy. Generally, information entropy is the average amount of information conveyed by an event, when considering all ...
Entropy of a Bernoulli trial (in shannons) as a function of binary outcome probability, called the binary entropy function.. In information theory, the binary entropy function, denoted or (), is defined as the entropy of a Bernoulli process (i.i.d. binary variable) with probability of one of two values, and is given by the formula:
The physical entropy may be on a "per quantity" basis (h) which is called "intensive" entropy instead of the usual total entropy which is called "extensive" entropy. The "shannons" of a message ( Η ) are its total "extensive" information entropy and is h times the number of bits in the message.
Shannon entropy (information entropy), being the expected value of the information of an event, is inherently a quantity of the same type and with a unit of information. The International System of Units, by assigning the same unit (joule per kelvin) both to heat capacity and to thermodynamic entropy implicitly treats information entropy as a quantity of dimension one, with 1 nat = 1.
Bits are transmitted one at a time in serial transmission. By contrast, multiple bits are transmitted simultaneously in a parallel transmission. A serial computer processes information in either a bit-serial or a byte-serial fashion. From the standpoint of data communications, a byte-serial transmission is an 8-way parallel transmission with ...
The minimum number of bits of entropy needed for a password depends on the threat model for the given application. If key stretching is not used, passwords with more entropy are needed. RFC 4086, "Randomness Requirements for Security", published June 2005, presents some example threat models and how to calculate the entropy desired for each one ...
The entropy at the output for a given and fixed input symbol ((| =)) equals the binary entropy function, which leads to the third line and this can be further simplified. In the last line, only the first term H ( Y ) {\displaystyle H(Y)} depends on the input distribution p X ( x ) {\displaystyle p_{X}(x)} .
The basic measures of discrete entropy have been extended by analogy to continuous spaces by replacing sums with integrals and probability mass functions with probability density functions. Although, in both cases, mutual information expresses the number of bits of information common to the two sources in question, the analogy does not imply ...