| Bits (bit) | Pebioctets (Pio) |
|---|---|
| 1 Bit | 1.11022302463 × 10-16 Pio |
| 2 Bits | 2.22044604925 × 10-16 Pio |
| 3 Bits | 3.33066907388 × 10-16 Pio |
| 4 Bits | 4.4408920985 × 10-16 Pio |
| 5 Bits | 5.55111512313 × 10-16 Pio |
| 10 Bits | 1.11022302463 × 10-15 Pio |
| 20 Bits | 2.22044604925 × 10-15 Pio |
| 25 Bits | 2.77555756156 × 10-15 Pio |
| 50 Bits | 5.55111512313 × 10-15 Pio |
| 100 Bits | 1.11022302463 × 10-14 Pio |
| Reference | Bits (bit) | Pebioctets (Pio) |
|---|---|---|
| A plain text message (160 characters) | 1280 bit | 1.42109 × 10-13 Pio |
| A three-minute MP3 | 24000000 bit | 0.00000000266454 Pio |
| A smartphone photo | 32000000 bit | 0.00000000355271 Pio |
| A high-definition film | 3.2 × 1010 bit | 0.00000355271 Pio |
| A dual-layer Blu-ray disc | 4 × 1011 bit | 0.0000444089 Pio |
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 pebioctet is a unit of digital information equal to 1,125,899,906,842,624 octets, which is 1,024 tebioctets. Its symbol is Pio. It is the binary counterpart of the petaoctet, and the two now differ by 12.6 per cent.
This is the unit in which filesystem limits are written. Several widely deployed filesystems have maximum file or volume sizes that are exact powers of two, and those limits fall in this range: sixteen tebioctets for one, a pebioctet for another, eight pebioctets for a third. The numbers are not choices made by anyone; they follow from how many bits the filesystem uses to number its blocks.
Large scientific and commercial storage systems are also sized here. A research computing centre may run a filesystem of several pebioctets across thousands of drives, and the tools that manage it report in pebioctets because the underlying allocation is binary throughout. Converting those figures to decimal units for a report introduces an error of an eighth for no benefit.
A pebioctet is roughly a thousand large consumer hard drives, or the complete video output of a broadcaster over many years. It is also close to the size of the largest single scientific archives, though those are typically stated in petaoctets by press offices and in pebioctets by the engineers who run them, which produces two different numbers for the same building.
Distinguishing the two is not pedantry at this level. A twelve per cent difference on a purchase of many pebioctets is a large sum of money, and a capacity plan built on the wrong unit will be wrong by more than the margin most plans allow. This is precisely the situation the IEC prefixes were introduced to prevent.
The symbol Pio is used in filesystem documentation, in storage system manuals and in standards. Where a source writes PB without saying which it means, the difference is an eighth, and the honest thing for a reader to do is treat the figure as approximate rather than assume one convention or the other.
One pebioctet equals 1,024 tebioctets, 1,125,899,906,842,624 octets, 8 pebibits, or about 1.126 petaoctets.