Bit
Non-system unit · quantity: amount of information
01 · Definition
Claude Shannon showed in 1948 that information can be measured, and proposed counting it in binary digits. The word «bit» was coined by John Tukey as a contraction of binary digit, and Shannon adopted it in his paper.
One bit is the amount of information in a choice between two equally likely outcomes. A tossed coin gives exactly a bit, a die 2.585 bits, a letter of the Russian alphabet about five. The unit is logarithmic: to tell N variants apart you need the binary logarithm of N, and so every added bit doubles the number of distinguishable states. The bit is not part of the SI and never has been: it is defined by a separate standard, IEC 80000-13, and its prefixes come in two incompatible sets, decimal and binary.
A lower-case b is a bit, a capital B is a byte, and the difference is eightfold. Channel speed is given in bits, file size in bytes, so «100 Mbit/s» yields about 12 MB per second, not a hundred.
02 · Conversion
Enter a volume — the sheet will convert it
The bit has two systems of prefixes. The decimal one takes a thousand: a kilobyte is 1000 bytes. The binary one, introduced by the IEC in 1998, takes 1024 and is written with an «i»: kibibyte, mebibyte, gibibyte. Drive makers count in decimal ones, operating systems in binary ones — hence the «missing» gigabytes.
At the kilobyte the discrepancy is only 2.4 per cent, but it accumulates: a terabyte drive is shown by the operating system as 931 GiB. Neither side is wrong — they simply count in different prefixes.
| Unit | Name | Value | Where it is met |
|---|---|---|---|
| bit | bit, the unit of information | 8 | the basis of counting |
| B | byte, eight bits | 1 | file size |
| kbit | kilobit, 1000 bits | 0.008 | channel speed |
| kB | kilobyte, 1000 bytes | 0.001 | decimal prefix |
| MB | megabyte, 10⁶ bytes | 1·10⁻⁶ | drives, storage devices |
| GB | gigabyte, 10⁹ bytes | 1·10⁻⁹ | media, tariffs |
| TB | terabyte, 10¹² bytes | 1·10⁻¹² | drive capacity |
| KiB | kibibyte, 1024 bytes | 9.766·10⁻⁴ | IEC 80000-13, 1998 |
| MiB | mebibyte, 1024 kibibytes | 9.537·10⁻⁷ | memory, file systems |
| GiB | gibibyte, 1024 mebibytes | 9.313·10⁻¹⁰ | operating systems |
| nat | nat, the natural logarithm | 5.55 | statistics, physics |
| Hart | hartley, the decimal logarithm | 2.41 | early communication theory |
| bit | bit | 8 | the present-day unit |
The nat and the hartley are the same bits, but with the logarithm to a different base: natural and decimal. One nat is 1.4427 bits, one hartley 3.3219. In communication theory one counts in bits, in statistics more often in nats.
03 · Orders of magnitude
from a coin to all the world’s dataAES-256 key
04 · Measuring instruments
What bits are measured with
It drives a known sequence down the channel and counts the corrupted bits. The norm for optics is one erroneous bit in 10¹².
It lays thousands of bit intervals on top of one another: the opening of the «eye» shows how confidently the receiver tells a one from a zero. A closed eye means errors.
It records the states of dozens of lines at once and decodes the protocol: bits become a picture in which a missing pulse or a shifted front is visible.
A random number generator is tested statistically: how many true bits of entropy there are per output bit. A generator that yields less than one is unfit for keys.
05 · Writing rules
b — bit, B — byte, Ki — 1024
Case carries meaning: 100 Mb/s and 100 MB/s differ eightfold. Binary prefixes are written with an «i» and a capital first letter: KiB, MiB, GiB — the capital K is lawful here, unlike the decimal kB. The full spelling «bit» is preferable wherever «b» could be taken for a byte.
In Russian the abbreviated name takes no case ending: one writes 8 bit, never the plural form, in technical texts. The byte behaves the same way in the singular and the plural: 512 byte.
06 · Neighbouring units
The bit is a binary measure, but the logarithm may be taken to any base. The nat takes the natural logarithm and is used in statistics and physics, the hartley the decimal one. The second beside it gives the rate of transfer, and the joule links information to thermodynamics through the Landauer limit.
log₂
1 nat = 1.443 bit
communication channel
The Landauer limit: erasing one bit at room temperature requires at least 2.9·10⁻²¹ joules. That is the lower bound set by thermodynamics itself — information turns out to have a physical price.
07 · Historical section
What information was measured with before the bit
The logarithm to base ten: the unit of information of one decimal digit. Under the names dit and ban it was used in early communication theory and in cryptanalysis at Bletchley Park.
The natural logarithm. Convenient in theory and physics: entropy in nats is directly linked to thermodynamic entropy through the Boltzmann constant.
The ternary digit of the Setun machine: three states instead of two. The only production ternary computer in the world, built at Moscow University in 1959.
Before the standard a byte was six, seven or nine bits depending on the machine. The eight-bit byte was fixed by the IBM System/360.
The only unit whose prefix «kilo» means two different numbers
In 1998 the IEC introduced the binary prefixes — Ki, Mi, Gi — to separate a thousand from 1024. The standard was adopted, but the industry split: makers of storage devices count in decimal gigabytes, Windows shows binary ones and calls them by the same name, macOS and Linux moved to decimal. As a result a terabyte drive honestly holds 10¹² bytes while the system writes «931 GB», and the seven per cent difference has been irritating buyers for a quarter of a century.
Catalogue · units of measurement
A passport for every quantity
Seven SI base units, twenty-two derived ones with their own names, and non-system units alongside them. Each has its own sheet: definition, dimension, conversion, instruments, rules of writing. In 14 languages.