The bit is also a unit of measurement, the information capacity of one binary digit. It has the symbol bit, or b (see discussion below).
A bit of storage can be either on (1) or off (0). A single bit is a one or a zero, a true or a false, a "flag" which is "on" or "off", or in general, the quantity of information required to distinguish two mutually exclusive equally probable states from each other. Gregory Bateson defined a bit as "a difference that makes a difference".
It is important to differentiate between the use of "bit" in referring to a discrete storage unit and the use of "bit" in referring to a statistical unit of information. The bit, as a discrete storage unit, can by definition store only 0 or 1. A statistical bit is the amount of information that, on average, can be stored in a discrete bit. It is thus the amount of information carried by a choice between two equally likely outcomes. One bit corresponds to about 0.693 nats (ln(2)), or 0.301 hartleys (log10(2)).
Consider, for example, a computer file with one thousand 0s and 1s which can be losslessly compressed to a file of five hundred 0s and 1s (on average, over all files of that kind). The original file, although having 1,000 bits of storage, has at most 500 bits of information entropy, since information is not destroyed by lossless compression. A file can have no more information theoretical bits than it has storage bits. If these two ideas need to be distinguished, sometimes the name bit is used when discussing data storage while shannon is used for the statistical bit. However, most of the time, the meaning is clear from the context.
The other commonly-quoted relevant standard, IEEE 1541, specifies "b" to be the unit symbol for bit and "B" to be that for byte. This convention is also widely used in computing, but has so far not been considered acceptable internationally for several reasons:
The unit bel is rarely used by itself (only as decibel, "dB", which is unlikely to be confused with a decibyte), so the chances of conflict with "B" for byte are quite small, even though both units are very commonly used in the same fields (e.g., telecommunication).
"Word" is a term for a slightly larger group of bits, but it has no standard size. It represents the size of one register in a Computer-CPU. In the IA-32 architecture more commonly known as x86-32, 16 bits are called a "word" (with 32 bits being a double word or dword), but other architectures have word sizes of 8, 32, 64, 80 or others.
Terms for large quantities of bits can be formed using the standard range of SI prefixes, e.g., kilobit (kbit), megabit (Mbit) and gigabit (Gbit). Note that much confusion exists regarding these units and their abbreviations (see above).
When a bit within a group of bits such as a byte or word is to be referred to, it is usually specified by a number from 0 (not 1) upwards corresponding to its position within the byte or word. However, 0 can refer to either the most significant bit or to the least significant bit depending on the context, so the convention being used must be known.
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