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In particular, if b is a positive integer, then the unit is the amount of information that can be stored in a system with b possible states. When b is 2, the unit is the shannon, equal to the information content of one "bit" (a portmanteau of binary digit [2]). A system with 8 possible states, for example, can store up to log 2 8 = 3 bits of ...
Orders of magnitude (data) An order of magnitude is usually a factor of ten. Thus, four orders of magnitude is a factor of 10,000 or 10 4. This article presents a list of multiples, sorted by orders of magnitude, for units of information measured in bits and bytes. The byte is a common unit of measurement of information (kilobyte, kibibyte ...
the mutual information, and the channel capacity of a noisy channel, including the promise of perfect loss-free communication given by the noisy-channel coding theorem; the practical result of the Shannon–Hartley law for the channel capacity of a Gaussian channel; as well as; the bit—a new way of seeing the most fundamental unit of information.
The bit is the most basic unit of information in computing and digital communication. The name is a portmanteau of binary digit. [1] The bit represents a logical state with one of two possible values. These values are most commonly represented as either "1" or "0", but other representations such as true / false, yes / no, on / off, or + / − ...
Channel capacity is additive over independent channels. [4] It means that using two independent channels in a combined manner provides the same theoretical capacity as using them independently. More formally, let and be two independent channels modelled as above; having an input alphabet and an output alphabet .
The mathematical theory of information is based on probability theory and statistics, and measures information with several quantities of information. The choice of logarithmic base in the following formulae determines the unit of information entropy that is used. The most common unit of information is the bit, or more correctly the shannon, [2 ...
Just as the shannon describes the maximum possible information capacity of a binary symbol, the hartley describes the information that can be contained in a 10-ary symbol, that is, a digit value in the range 0 to 9 when the a priori probability of each value is 1 / 10 . The conversion factor quoted above is given by log 10 (2).
It leads to a maximal rate of information of 10 6 log 2 (1 + 10 −3) = 1443 bit/s. These values are typical of the received ranging signals of the GPS, where the navigation message is sent at 50 bit/s (below the channel capacity for the given S/N), and whose bandwidth is spread to around 1 MHz by a pseudo-noise multiplication before transmission.