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Binary data is data whose unit can take on only two possible states. These are often labelled as 0 and 1 in accordance with the binary numeral system and Boolean algebra.
Binary data occurs in many different technical and scientific fields, where it can be called by different names including bit (binary digit) in computer science, truth value in mathematical logic and related domains and binary variable in statistics.
A collection of bits may have states: see binary number for details. Number of states of a collection of discrete variables depends exponentially on the number of variables, and only as a power law on number of states of each variable. Ten bits have more () states than three (). bits are more than sufficient to represent an information (a number or anything else) that requires decimal digits, so information contained in discrete variables with 3, 4, 5, 6, 7, 8, 9, Neper... states can be ever superseded by allocating two, three, or four times more bits. So, the use of any other small number than 2 does not provide an advantage.
Moreover, Boolean algebra provides a convenient mathematical structure for collection of bits, with a semantic of a collection of propositional variables. Boolean algebra operations are known as "bitwise operations" in computer science. are also well-studied theoretically and easily implementable, either with or by so-named in digital electronics. This contributes to the use of bits to represent different data, even those originally not binary.
Often, binary data is used to represent one of two conceptually opposed values, e.g.:
However, it can also be used for data that is assumed to have only two possible values, even if they are not conceptually opposed or conceptually represent all possible values in the space. For example, binary data is often used to represent the party choices of voters in elections in the United States, i.e. Republican or Democratic. In this case, there is no inherent reason why only two political party should exist, and indeed, other parties do exist in the U.S., but they are so minor that they are generally simply ignored. Modeling continuous data (or categorical data of more than 2 categories) as a binary variable for analysis purposes is called discretization (creating a dichotomy). Like all discretization, it involves discretization error, but the goal is to learn something valuable despite the error: treating it as for the purpose at hand, but remembering that it cannot be assumed to be negligible in general.
Since there are only two possible values, this can be simplified to a single count (a scalar value) by considering one value as "success" and the other as "failure", coding a value of the success as 1 and of the failure as 0 (using only the coordinate for the "success" value, not the coordinate for the "failure" value). For example, if the value A is considered "success" (and thus B is considered "failure"), the data set A, A, B would be represented as 1, 1, 0. When this is grouped, the values are added, while the number of trial is generally tracked implicitly. For example, A, A, B would be grouped as 1 + 1 + 0 = 2 successes (out of trials). Going the other way, count data with is binary data, with the two classes being 0 (failure) or 1 (success).
Counts of i.i.d. binary variables follow a binomial distribution, with the total number of trials (points in the grouped data).
Similarly, counts of i.i.d. categorical variables with more than two categories can be modeled with a multinomial regression. Counts of non-i.i.d. binary data can be modeled by more complicated distributions, such as the beta-binomial distribution (a compound distribution). Alternatively, the relationship can be modeled without needing to explicitly model the distribution of the output variable using techniques from generalized linear models, such as quasi-likelihood and a quasibinomial model; see .
In applied computer science and in the information technology field, the term binary data is often specifically opposed to text-based data, referring to any sort of data that cannot be interpreted as text. The "text" vs. "binary" distinction can sometimes refer to the semantic content of a file (e.g. a written document vs. a digital image). However, it often refers specifically to whether the individual bytes of a file are interpretable as text (see character encoding) or cannot so be interpreted. When this last meaning is intended, the more specific terms binary format and text(ual) format are sometimes used. Semantically textual data can be represented in binary format (e.g. when compressed or in certain formats that intermix various sorts of formatting codes, as in the doc format used by Microsoft Word); contrarily, image data is sometimes represented in textual format (e.g. the X PixMap image format used in the X Window System).
1 and 0 are nothing but just two different voltage levels. You can make the computer understand 1 for higher voltage and 0 for lower voltage. There are many different ways to store two voltage levels. If you have seen floppy, then you will find a magnetic tape that has a coating of ferromagnetic material, this is a type of paramagnetic material that has domains aligned in a particular direction to give a remnant magnetic field even after removal of currents through materials or magnetic field. During loading of data in the magnetic tape, the magnetic field is passed in one direction to call the saved orientation of the domain 1 and for the magnetic field is passed in another direction, then the saved orientation of the domain is 0. In this way, generally, 1 and 0 data are stored.
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