Bit in the context of 24-bit computing

A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method for representing numbers that uses only two symbols for the natural numbers: typically 0 (zero) and 1 (one). A binary number may also refer to a rational number that has a finite representation in the binary numeral system, that is, the quotient of an integer by a power of two.

The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit, or binary digit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices, as a preferred system of use, over various other human techniques of communication, because of the simplicity of the language and the noise immunity in physical implementation.

A file format is the way that information is encoded for storage in a computer file. It may describe the encoding at various levels of abstraction including low-level bit and byte layout as well high-level organization such as markup and tabular structure. A file format may be standarized (which can be proprietary or open) or it can be an ad hoc convention.

Some file formats are designed for very particular types of data: PNG files, for example, store bitmapped images using lossless data compression. Other file formats, however, are designed for storage of several different types of data: the Ogg format can act as a container for different types of multimedia including any combination of audio and video, with or without text (such as subtitles), and metadata. A text file can contain any stream of characters, including possible control characters, and is encoded in one of various character encoding schemes. Some file formats, such as HTML, scalable vector graphics, and the source code of computer software are text files with defined syntaxes that allow them to be used for specific purposes.

In information theory, the entropy of a random variable quantifies the average level of uncertainty or information associated with the variable's potential states or possible outcomes. This measures the expected amount of information needed to describe the state of the variable, considering the distribution of probabilities across all potential states. Given a discrete random variable ${\displaystyle X}$, which may be any member ${\displaystyle x}$ within the set ${\displaystyle {\mathcal {X}}}$ and is distributed according to ${\displaystyle p\colon {\mathcal {X}}\to [0,1]}$, the entropy is$${\displaystyle \mathrm {H} (X):=-\sum _{x\in {\mathcal {X}}}p(x)\log p(x),}$$where ${\displaystyle \Sigma }$ denotes the sum over the variable's possible values. The choice of base for ${\displaystyle \log }$, the logarithm, varies for different applications. Base 2 gives the unit of bits (or "shannons"), while base e gives "natural units" nat, and base 10 gives units of "dits", "bans", or "hartleys". An equivalent definition of entropy is the expected value of the self-information of a variable.

The concept of information entropy was introduced by Claude Shannon in his 1948 paper "A Mathematical Theory of Communication", and is also referred to as Shannon entropy. Shannon's theory defines a data communication system composed of three elements: a source of data, a communication channel, and a receiver. The "fundamental problem of communication" – as expressed by Shannon – is for the receiver to be able to identify what data was generated by the source, based on the signal it receives through the channel. Shannon considered various ways to encode, compress, and transmit messages from a data source, and proved in his source coding theorem that the entropy represents an absolute mathematical limit on how well data from the source can be losslessly compressed onto a perfectly noiseless channel. Shannon strengthened this result considerably for noisy channels in his noisy-channel coding theorem.

Hexadecimal (hex for short) is a positional numeral system for representing a numeric value as base 16. For the most common convention, a digit is represented as "0" to "9" like for decimal and as a letter of the alphabet from "A" to "F" (either upper or lower case) for the digits with decimal value 10 to 15.

As typical computer hardware is binary in nature and that hex is power of 2, the hex representation is often used in computing as a dense representation of binary information. A hex digit represents 4 contiguous bits –known as a nibble. An 8-bit byte is two hex digits, such as 2C.

In information theory, data compression, source coding, or bit-rate reduction is the process of encoding information using fewer bits than the original representation. Any particular compression is either lossy or lossless. Lossless compression reduces bits by identifying and eliminating statistical redundancy. No information is lost in lossless compression. Lossy compression reduces bits by removing unnecessary or less important information. Typically, a device that performs data compression is referred to as an encoder, and one that performs the reversal of the process (decompression) as a decoder.

The process of reducing the size of a data file is often referred to as data compression. In the context of data transmission, it is called source coding: encoding is done at the source of the data before it is stored or transmitted. Source coding should not be confused with channel coding, for error detection and correction or line coding, the means for mapping data onto a signal.

A bitstream (or bit stream), also known as binary sequence, is a sequence of bits.A bytestream is a sequence of bytes. Typically, each byte is an 8-bit quantity, and so the term octet stream is sometimes used interchangeably. An octet may be encoded as a sequence of 8 bits in multiple different ways (see bit numbering) so there is no unique and direct translation between bytestreams and bitstreams.

Bitstreams and bytestreams are used extensively in telecommunications and computing. For example, synchronous bitstreams are carried by SONET, and Transmission Control Protocol transports an asynchronous bytestream.

In telecommunications and computing, bit rate (bitrate or as a variable R) is the number of bits that are conveyed or processed per unit of time.

The bit rate is expressed in the unit bit per second (symbol: bit/s), often in conjunction with an SI prefix such as kilo (1 kbit/s = 1,000 bit/s), mega (1 Mbit/s = 1,000 kbit/s), giga (1 Gbit/s = 1,000 Mbit/s) or tera (1 Tbit/s = 1,000 Gbit/s). The non-standard abbreviation bps is often used to replace the standard symbol bit/s, so that, for example, 1 Mbps is used to mean one million bits per second.

In computing and telecommunications, a character is the encoded representation of a natural language character (including letter, numeral and punctuation), whitespace (space or tab), or a control character (controls computer hardware that consumes character-based data). A sequence of characters is called a string.

Some character encoding systems represent each character using a fixed number of bits whereas other systems use varying sizes. Various fixed-length sizes were used for now obsolete systems such as the six-bit character code, the five-bit Baudot code and even 4-bit systems (with only 16 possible values). The more modern ASCII system uses the 8-bit byte for each character. Today, the Unicode-based UTF-8 encoding uses a varying number of byte-sized code units to define a code point which combine to encode a character.

In theoretical computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor.

Since an algorithm's running time may vary among different inputs of the same size, one commonly considers the worst-case time complexity, which is the maximum amount of time required for inputs of a given size. Less common, and usually specified explicitly, is the average-case complexity, which is the average of the time taken on inputs of a given size (this makes sense because there are only a finite number of possible inputs of a given size). In both cases, the time complexity is generally expressed as a function of the size of the input. Since this function is generally difficult to compute exactly, and the running time for small inputs is usually not consequential, one commonly focuses on the behavior of the complexity when the input size increases—that is, the asymptotic behavior of the complexity. Therefore, the time complexity is commonly expressed using big O notation, typically ${\displaystyle O(n)}$, ${\displaystyle O(n\log n)}$, ${\displaystyle O(n^{\alpha })}$, ${\displaystyle O(2^{n})}$, etc., where n is the size in units of bits needed to represent the input.

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.

In digital audio using pulse-code modulation (PCM), bit depth is the number of bits of information in each sample, and it directly corresponds to the resolution of each sample. Examples of bit depth include Compact Disc Digital Audio, which uses 16 bits per sample, and DVD-Audio and Blu-ray Disc, which can support up to 24 bits per sample.

In basic implementations, variations in bit depth primarily affect the noise level from quantization error—thus the signal-to-noise ratio (SNR) and dynamic range. However, techniques such as dithering, noise shaping, and oversampling can mitigate these effects without changing the bit depth. Bit depth also affects bit rate and file size.

A binary code is the value of a data-encoding convention represented in a binary notation that usually is a sequence of 0s and 1s; sometimes called a bit string. For example, ASCII is an 8-bit text encoding that in addition to the human readable form (letters) can be represented as binary. Binary code can also refer to the mass noun code that is not human readable in nature such as machine code and bytecode.

Even though all modern computer data is binary in nature, and therefore can be represented as binary, other numerical bases may be used. Power of 2 bases (including hex and octal) are sometimes considered binary code since their power-of-2 nature makes them inherently linked to binary. Decimal is, of course, a commonly used representation. For example, ASCII characters are often represented as either decimal or hex. Some types of data such as image data is sometimes represented as hex, but rarely as decimal.

In digital logic, an inverter or NOT gate is a logic gate which implements logical negation. It outputs a bit opposite of the bit that is put into it. The bits are typically implemented as two differing voltage levels.

Color depth, also known as bit depth, is either the number of bits used to indicate the color of a single pixel, or the number of bits used for each color component of a single pixel. When referring to a pixel, the concept can be defined as bits per pixel (bpp). When referring to a color component, the concept can be defined as bits per component, bits per channel, bits per color (all three abbreviated bpc), and also bits per pixel component, bits per color channel or bits per sample. Modern standards tend to use bits per component, but historical lower-depth systems used bits per pixel more often.

Color depth is only one aspect of color representation, expressing the precision with which the amount of each primary can be expressed; the other aspect is how broad a range of colors can be expressed (the gamut). The definition of both color precision and gamut is accomplished with a color encoding specification which assigns a digital code value to a location in a color space.

The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable unit of memory in many computer architectures. To disambiguate arbitrarily sized bytes from the common 8-bit definition, network protocol documents such as the Internet Protocol (RFC 791) refer to an 8-bit byte as an octet. Those bits in an octet are usually counted with numbering from 0 to 7 or 7 to 0 depending on the bit endianness.

The size of the byte has historically been hardware-dependent and no definitive standards existed that mandated the size. Sizes from 1 to 48 bits have been used. The six-bit character code was an often-used implementation in early encoding systems, and computers using six-bit and nine-bit bytes were common in the 1960s. These systems often had memory words of 12, 18, 24, 30, 36, 48, or 60 bits, corresponding to 2, 3, 4, 5, 6, 8, or 10 six-bit bytes, and persisted, in legacy systems, into the twenty-first century. In this era, bit groupings in the instruction stream were often referred to as syllables or slab, before the term byte became common.