Conversion from 2 Teraoctets to Bits

Information about the Teraoctet (To)

The teraoctet is a unit of digital information equal to one million million octets, or a thousand gigaoctets. Its symbol is To. It is the unit of the modern hard drive, and the point at which personal storage stopped being something anyone needed to manage carefully.

A teraoctet holds roughly two hundred and fifty thousand photographs from a phone, or two hundred hours of high-definition video, or a quarter of a million songs. For a person who is not a professional photographer or video editor, a single teraoctet is more storage than a lifetime of ordinary files will fill.

Consumer hard drives crossed one teraoctet in 2007 and now reach twenty or more. Solid-state drives arrived at the same capacities more slowly and at higher cost, but with far greater speed, and the two technologies now divide the market between capacity and performance rather than competing directly.

The teraoctet is where the decimal-binary discrepancy becomes visible enough to annoy. A drive sold as one teraoctet holds a million million octets exactly; the operating system divides by 1,024 four times and reports 0.909 tebioctets, which it usually labels as 931 gigaoctets. The shortfall appears to be 7 per cent, though nothing has actually been lost. At the petaoctet the same arithmetic produces a 12 per cent gap.

Backup and archiving live at this scale. A household's complete collection of photographs, documents and video typically fits in a few teraoctets, which is why external drives are sold in exactly that range. Cloud storage services price in teraoctets too, and the economics of keeping a second copy of everything only work because the unit price of storage has fallen faster than the quantity has grown.

In professional work the teraoctet is a daily quantity rather than a milestone. A day of filming in high resolution produces several teraoctets of raw footage. A genome sequencing run produces a few hundred gigaoctets, so a modest laboratory generates teraoctets a week. Both fields have had to build workflows around moving data that will not fit on any network in reasonable time.

One teraoctet equals 1,000,000,000,000 octets, 1,000 gigaoctets, 8 terabits, or about 0.9095 tebioctets.

Information about the Bit (bit)

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.