Conversion from 2 Kilooctets to Bits

Information about the Kilooctet (ko)

The kilooctet is a unit of digital information equal to one thousand octets, and therefore to eight thousand bits. Its symbol is ko. It is the smallest of the everyday storage units, and for two decades it was the unit in which the whole capacity of a computer was described.

A kilooctet holds a thousand characters of unaccented text, which is about two hundred words, or a third of a page. The plain-text file of a short letter is a few kilooctets. Almost nothing else in modern computing is this small: an empty document from a word processor is already tens of kilooctets, because the file format carries formatting, fonts and metadata around the text.

The historical importance of the unit is hard to overstate. The Apple II shipped with 4 kilooctets of memory, the Commodore 64 was named for its 64, and the first IBM personal computer could address 640. Programs of real complexity — spreadsheets, word processors, games with graphics and sound — were written to fit inside those numbers, which required a discipline that has largely disappeared.

The kilooctet is also where the decimal and binary confusion began. Memory came in 1,024-octet units because addressing is binary, and everyone called that a kilooctet. Disc manufacturers counted in true thousands. The two conventions differ by 2.4 per cent, which was negligible at this scale, but the same error compounds at each step upward and reaches 10 per cent by the teraoctet.

The IEC resolved the ambiguity in 1998 by defining the kibioctet as 1,024 octets and leaving the kilooctet at exactly 1,000. Operating systems have adopted this unevenly: some report file sizes in true kilooctets, others still divide by 1,024 while writing ko, and a few now write Kio correctly.

Where the unit still appears daily is in network protocols and in the sizes of small resources on the web. A web page's stylesheet, an icon, a certificate, a configuration file, a database index page — all of these are measured in kilooctets, and the standard memory page on most processors is 4 kibioctets, close enough to 4 kilooctets for casual conversation but not for arithmetic.

One kilooctet equals 1,000 octets, 8,000 bits, 8 kilobits, or about 0.9766 kibioctets.

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.