| Bits (bit) | Yobioctets (Yio) |
|---|---|
| 1 Bit | 1.03397576569 × 10-25 Yio |
| 2 Bits | 2.06795153138 × 10-25 Yio |
| 3 Bits | 3.10192729707 × 10-25 Yio |
| 4 Bits | 4.13590306277 × 10-25 Yio |
| 5 Bits | 5.16987882846 × 10-25 Yio |
| 10 Bits | 1.03397576569 × 10-24 Yio |
| 20 Bits | 2.06795153138 × 10-24 Yio |
| 25 Bits | 2.58493941423 × 10-24 Yio |
| 50 Bits | 5.16987882846 × 10-24 Yio |
| 100 Bits | 1.03397576569 × 10-23 Yio |
| Reference | Bits (bit) | Yobioctets (Yio) |
|---|---|---|
| A plain text message (160 characters) | 1280 bit | 1.32349 × 10-22 Yio |
| A three-minute MP3 | 24000000 bit | 2.48154 × 10-18 Yio |
| A smartphone photo | 32000000 bit | 3.30872 × 10-18 Yio |
| A high-definition film | 3.2 × 1010 bit | 3.30872 × 10-15 Yio |
| A dual-layer Blu-ray disc | 4 × 1011 bit | 4.1359 × 10-14 Yio |
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 yobioctet is a unit of digital information equal to two to the eightieth power octets, which is 1,024 zebioctets. Its symbol is Yio. It is the largest binary unit the International Electrotechnical Commission has named, and the binary counterpart of the yottaoctet.
At this final step the binary and decimal conventions differ by 20.9 per cent. That is the end of the argument the IEC prefixes were created to settle: a difference that began as a harmless 2.4 per cent at the kibioctet has grown, by eight successive multiplications of 1.024, into a discrepancy of more than a fifth. No system of measurement can carry an ambiguity that large.
A yobioctet is 1,208,925,819,614,629,174,706,176 octets. The entire quantity of data held by humanity is a few hundred zettaoctets, which is a fraction of a per cent of this. Nothing of this size has been built, and current manufacturing rates would need to continue for many centuries to accumulate one.
The binary series stops at yobi because the decimal series stopped at yotta when the IEC standard was written in 1998. When ronna and quetta were added to the metric system in 2022, no matching binary names were defined, so a quantity of two to the ninetieth octets has no accepted short form. That gap will presumably be filled if it is ever needed.
The value of defining the top of a ladder nobody has climbed is the same as the value of defining the bottom. A measurement system whose names run out forces its users to improvise, and improvised extensions conflict. Both the metric and the IEC series were written out in full so that the rule, rather than a table of exceptions, is all anyone has to learn.
For any reader of technical material, the lesson of the whole series is one character. Kio, Mio, Gio, Tio, Pio, Eio, Zio and Yio are binary; ko, Mo, Go, To, Po, Eo, Zo and Yo are decimal; and the difference between them widens from a rounding error to a fifth as you climb. That lowercase i is the only thing in a document that says which was meant.
One yobioctet equals 1,024 zebioctets, 1,208,925,819,614,629,174,706,176 octets, 8 yobibits, or about 1.209 yottaoctets.