| Bits (bit) | Tebioctets (Tio) |
|---|---|
| 1 Bit | 1.13686837722 × 10-13 Tio |
| 2 Bits | 2.27373675443 × 10-13 Tio |
| 3 Bits | 3.41060513165 × 10-13 Tio |
| 4 Bits | 4.54747350886 × 10-13 Tio |
| 5 Bits | 5.68434188608 × 10-13 Tio |
| 10 Bits | 1.13686837722 × 10-12 Tio |
| 20 Bits | 2.27373675443 × 10-12 Tio |
| 25 Bits | 2.84217094304 × 10-12 Tio |
| 50 Bits | 5.68434188608 × 10-12 Tio |
| 100 Bits | 1.13686837722 × 10-11 Tio |
| Reference | Bits (bit) | Tebioctets (Tio) |
|---|---|---|
| A plain text message (160 characters) | 1280 bit | 1.45519 × 10-10 Tio |
| A three-minute MP3 | 24000000 bit | 0.00000272848 Tio |
| A smartphone photo | 32000000 bit | 0.00000363798 Tio |
| A high-definition film | 3.2 × 1010 bit | 0.00363798 Tio |
| A dual-layer Blu-ray disc | 4 × 1011 bit | 0.0454747 Tio |
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 tebioctet is a unit of digital information equal to 1,099,511,627,776 octets, which is 1,024 gibioctets. Its symbol is Tio. It is the binary counterpart of the teraoctet, and at this level the two differ by 10 per cent — the gap that produces the most familiar complaint in consumer computing.
That complaint runs as follows. A drive is sold as one teraoctet, holds exactly one million million octets, and the operating system reports 931 gigaoctets. What it is actually reporting is 0.909 tebioctets, expressed with the wrong label. Nothing is missing from the drive; the number has simply been divided by 1,024 three times and then written with a decimal prefix.
Storage administration lives in this unit. Volume sizes, RAID array capacities, snapshot reserves and quota limits are all quoted in tebioctets by the tools that manage them, because the underlying allocation units are powers of two. A filesystem asked to create a 10-teraoctet volume and one asked to create a 10-tebioctet volume will produce visibly different results.
The difference matters commercially as well as technically. Cloud storage priced per teraoctet and cloud storage priced per tebioctet differ by a tenth in the quantity delivered for the same price, and a contract that does not say which is being used is genuinely ambiguous. Careful procurement documents specify the unit explicitly for exactly this reason.
A tebioctet holds around a quarter of a million photographs, two hundred hours of high-definition video, or the complete text of every book in a large public library many times over. In a household it is more storage than a lifetime of ordinary files will use; in a video production company it is a few days of work.
The correct symbol Tio appears in filesystem tools, in storage array documentation and in standards, and it is worth using even when the audience is unlikely to notice. A figure written with a binary prefix can be converted correctly by anyone who reads it later; one written ambiguously cannot be repaired.
One tebioctet equals 1,099,511,627,776 octets, 1,024 gibioctets, 8 tebibits, or about 1.100 teraoctets.