The bit (a portmanteau of binary digit)
The two values of a binary digit can also be interpreted as Truth value (true/false, yes/no), algebraic signed number (+/−), activation states (on/off), or any other two-valued attribute. The correspondence between these values and the physical states of the underlying storage or computing device is a matter of convention, and different assignments may be used even within the same device or computer program. The length of a binary number may be referred to as its bit-length.
In information theory, one bit is typically defined as the information entropy of a binary random variable that is 0 or 1 with equal probability,John B. Anderson, Rolf Johnnesson (2006) Understanding Information Transmission. or the information that is gained when the value of such a variable becomes known.Simon Haykin (2006), Digital CommunicationsIEEE Std 260.1-2004
Confusion often arises because the words bit and binary digit are used interchangeably. But, within Claude Shannon's information theory, a bit and a binary digit are fundamentally different types of entities. A binary digit is a number that can adopt one of two possible values (0 or 1), whereas a bit is the maximum amount of Self-information that can be conveyed by a binary digit (when Expected value over both of its states). By analogy, just as a pint-sized bottle can contain between zero and one pint, so a binary digit can convey between zero and one bit of information. A less confusing terminology is to refer to bits as shannons (see below).
In quantum computing, a quantum bit or qubit is a quantum system that can exist in superposition of two classical (i.e., non-quantum) bit values; see also two-state quantum system.
The symbol for binary digit is either simply bit (recommended by the IEC 80000-13:2008 standard) or lowercase b (recommended by the IEEE 1541-2002 and IEEE Std 260.1-2004 standards). A group of eight binary digits is commonly called one byte, but historically the size of the byte is not strictly defined.
As a unit of information in information theory, the bit has alternatively been called a shannon, named after Claude Shannon, the founder of information theory. This usage distinguishes the quantity of information from the form of the state variables used to represent it. When the logical values are not equally probable or when a signal is not conveyed perfectly through a communication system, a binary digit in the representation of the information will convey less than one bit of information. However, the shannon unit terminology is uncommon in practice.
Ralph Hartley suggested the use of a logarithmic measure of information in 1928.Norman Abramson (1963), Information theory and coding. McGraw-Hill. Claude E. Shannon first used the word bit in his seminal 1948 paper A Mathematical Theory of Communication. He attributed its origin to John W. Tukey, who had written a Bell Labs memo on 9 January 1947 in which he contracted "binary information digit" to simply "bit". Vannevar Bush had written in 1936 of "bits of information" that could be stored on the used in the mechanical computers of that time. The first programmable computer, built by Konrad Zuse, used binary notation for numbers.
Bits can be implemented in several forms. In most modern computing devices, a bit is usually represented by an Electricity voltage or Electric current pulse, or by the electrical state of a flip-flop circuit.
For devices using positive logic, a digit value of 1 (or a logical value of true) is represented by a more positive voltage relative to the representation of 0. The specific voltages are different for different logic families and variations are permitted to allow for component aging and noise immunity. For example, in transistor–transistor logic (TTL) and compatible circuits, digit values 0 and 1 at the output of a device are represented by no higher than 0.4 volts and no lower than 2.6 volts, respectively; while TTL inputs are specified to recognize 0.8 volts or below as 0 and 2.2 volts or above as 1.
In the 1950s and 1960s, these methods were largely supplanted by magnetic storage devices such as magnetic core memory, , magnetic drum, and Disk storage, where a bit was represented by the polarity of magnetism of a certain area of a ferromagnetic film, or by a change in polarity from one direction to the other. The same principle was later used in the magnetic bubble memory developed in the 1980s, and is still found in various magnetic strip items such as Rapid transit tickets and some .
In modern semiconductor memory, such as dynamic random-access memory, the two values of a bit may be represented by two levels of electric charge stored in a capacitor. In certain types of programmable logic arrays and read-only memory, a bit may be represented by the presence or absence of a conducting path at a certain point of a circuit. In , a bit is encoded as the presence or absence of a microscopic pit on a reflective surface. In one-dimensional , bits are encoded as the thickness of alternating black and white lines.
Computers usually manipulate bits in groups of a fixed size, conventionally named "words". Like the byte, the number of bits in a word also varies with the hardware design, and is typically between 8 and 80 bits, or even more in some specialized computers. In the 21st century, retail personal or server computers have a word size of 32 or 64 bits.
The International System of Units defines a series of decimal prefixes for multiples of standardized units which are commonly also used with the bit and the byte. The prefixes kilo- (103) through yotta- (1024) increment by multiples of 1000, and the corresponding units are the kilobit (kbit) through the yottabit (Ybit).
For example, it is estimated that the combined technological capacity of the world to store information provides 1,300 exabytes of hardware digits in 2007. However, when this storage space is filled and the corresponding content is optimally compressed, this only represents 295 exabytes of information. "The World's Technological Capacity to Store, Communicate, and Compute Information" , especially Supporting online material , Martin Hilbert and Priscila López (2011), Science, 332(6025), 60-65; free access to the article through here: martinhilbert.net/WorldInfoCapacity.html When optimally compressed, the resulting carrying capacity approaches Shannon information or information entropy.
In the 1980s, when computer displays became popular, some computers provided specialized bitblt ("bitblt" or "blit") instructions to set or copy the bits that corresponded to a given rectangular area on the screen.
In most computers and programming languages, when a bit within a group of bits, such as a byte or word, is referred to, it is usually specified by a number from 0 upwards corresponding to its position within the byte or word. However, 0 can refer to either the most or least significant bit depending on the context.
Other units of information, sometimes used in information theory, include the natural digit also called a nat or nit and defined as logarithm2 e (≈ 1.443) bits, where e is the base of the natural logarithms; and the dit, ban, or hartley, defined as log2 10 (≈ 3.322) bits. This value, slightly less than 10/3, may be understood because 103 = 1000 ≈ 1024 = 210: three decimal digits are slightly less information than ten binary digits, so one decimal digit is slightly less than 10/3 binary digits. Conversely, one bit of information corresponds to about ln 2 (≈ 0.693) nats, or log10 2 (≈ 0.301) hartleys. As with the inverse ratio, this value, approximately 3/10, but slightly more, corresponds to the fact that 210 = 1024 ~ 1000 = 103: ten binary digits are slightly more information than three decimal digits, so one binary digit is slightly more than 3/10 decimal digits. Some authors also define a binit as an arbitrary information unit equivalent to some fixed but unspecified number of bits.