| Bits (bit) | Exbioctets (Eio) |
|---|---|
| 1 Bit | 1.08420217249 × 10-19 Eio |
| 2 Bits | 2.16840434497 × 10-19 Eio |
| 3 Bits | 3.25260651746 × 10-19 Eio |
| 4 Bits | 4.33680868994 × 10-19 Eio |
| 5 Bits | 5.42101086243 × 10-19 Eio |
| 10 Bits | 1.08420217249 × 10-18 Eio |
| 20 Bits | 2.16840434497 × 10-18 Eio |
| 25 Bits | 2.71050543121 × 10-18 Eio |
| 50 Bits | 5.42101086243 × 10-18 Eio |
| 100 Bits | 1.08420217249 × 10-17 Eio |
| Reference | Bits (bit) | Exbioctets (Eio) |
|---|---|---|
| A plain text message (160 characters) | 1280 bit | 1.38778 × 10-16 Eio |
| A three-minute MP3 | 24000000 bit | 2.60209 × 10-12 Eio |
| A smartphone photo | 32000000 bit | 3.46945 × 10-12 Eio |
| A high-definition film | 3.2 × 1010 bit | 0.00000000346945 Eio |
| A dual-layer Blu-ray disc | 4 × 1011 bit | 0.0000000433681 Eio |
The bit is the fundamental unit of information. Its symbol is bit, and its name is a contraction of binary digit, coined by the statistician John Tukey and put into print by Claude Shannon in his 1948 paper A Mathematical Theory of Communication, the work that founded information theory.
A bit is the amount of information carried by a single choice between two equally likely possibilities. A coin landing heads or tails, a switch open or closed, a voltage high or low: each of those settles one bit. That definition is what makes the bit a unit rather than a mere convention of notation. It measures how much uncertainty an answer removes, and it does so in a way that is independent of what the question was about.
Shannon's insight was that this could be counted. A message drawn from an alphabet of thirty-two equally likely symbols carries five bits per symbol, because thirty-two is two to the fifth. If the symbols are not equally likely — as letters in English are not — the average drops, and that gap between the naive count and the true average is exactly what compression exploits. A well-compressed file is one from which the redundant bits have been removed.
In hardware the bit is a physical state: a charge trapped on a floating gate in flash memory, the direction of magnetisation of a domain on a hard disc platter, a pit or land on an optical disc, a pulse of light present or absent in a fibre. All of these encode the same abstract quantity, which is why data can move between them without loss.
Bits are almost never counted singly in storage. They are grouped into octets of eight, and storage capacity is quoted in octets or their multiples. Transmission is different: network and interface speeds are quoted in bits per second, so a connection described as 100 megabits per second delivers about 12.5 megaoctets per second. Confusing the two is the commonest arithmetic error in the whole field.
Where single bits do get counted is in specifications of precision and range. A colour channel with 8 bits holds 256 levels; one with 10 bits holds 1,024. Audio at 16 bits per sample has about 96 decibels of dynamic range, and at 24 bits about 144. A 64-bit address can name about 18 quintillion locations. In every case, each added bit doubles what can be distinguished.
One bit equals 0.125 octets, 0.001 kilobits, or about 0.0009766 kibibits.
The exbioctet is a unit of digital information equal to two to the sixtieth power octets, which is 1,024 pebioctets. Its symbol is Eio. It is the binary counterpart of the exaoctet, and the two differ by 15.3 per cent.
One number involving this unit is quoted more than any other: sixteen exbioctets, the size of the address space a 64-bit processor can reach. Two to the sixty-fourth octets is 16 EiB, and that figure is the theoretical ceiling on the memory of every machine built on the architecture that has dominated computing since the mid-2000s.
The same limit reappears in filesystems. A filesystem that numbers its blocks with 64-bit values can address 16 exbioctets of blocks, and several modern designs state exactly that as their maximum volume size. Others state 8 exbioctets, having reserved one bit for a sign or a flag — a detail that halves the limit and is worth knowing when reading a specification.
Nothing approaches these sizes in practice. The largest storage systems in the world hold exaoctets, and the total of all data held by humanity is a few hundred zettaoctets, which is tens of thousands of exbioctets. The 64-bit ceiling was chosen precisely so that it would not be reached, and the transition from 32 bits, whose four-gibioctet limit was reached within a decade, is why the designers left so much room.
An exbioctet is 1,152,921,504,606,846,976 bits and 128 pebioctets. It is a quantity that exists in specifications, in address arithmetic and in the design documents of large systems, and nowhere else. Describing it in terms of photographs or films is not useful, because no collection of either comes close.
The symbol Eio and its decimal sibling Eo differ by more than an eighth, which is far too much to leave to inference. When a document writes EB in the context of an address space, it almost certainly means EiB, because address spaces are powers of two by construction; when it writes EB about stored data, it almost certainly means the decimal unit.
One exbioctet equals 1,024 pebioctets, 1,152,921,504,606,846,976 octets, 8 exbibits, or about 1.153 exaoctets.