Conversion from 3 Kibibits to Bits

Information about the Kibibit (Kibit)

The kibibit is a unit of digital information equal to 1,024 bits. Its symbol is Kibit. It is the first of the binary prefixes, a set of units defined by the International Electrotechnical Commission in 1998 to end a confusion that had run through computing since the 1960s.

The problem was straightforward. Computers address memory in powers of two, so memory came in chunks of 1,024 rather than 1,000. Engineers borrowed the metric prefix kilo for that quantity because 1,024 is close to 1,000, and for small numbers the approximation was harmless. But storage and transmission counted in true thousands, so the same prefix meant two different things depending on which part of the machine was being described.

The IEC's solution was to coin new names. Kibi is a contraction of kilo binary, and the pattern continues with mebi, gibi, tebi, pebi, exbi, zebi and yobi. Each is 1,024 times the one below, and each symbol takes the form of a capital letter followed by a lowercase i: Ki, Mi, Gi, Ti and so on. The kilobit then means one thousand bits and nothing else.

A kibibit is 128 octets, and the gap from a kilobit is 2.4 per cent. That small difference is why the two were confused for so long: at this scale nobody notices. The error compounds by 2.4 per cent at every step, reaching 5 per cent at the mebibit, 7 per cent at the gibibit and 21 per cent by the yobibit, which is where the ambiguity became genuinely expensive.

Adoption has been partial and uneven. Standards bodies, the Linux kernel and most technical documentation use the IEC prefixes correctly. Consumer software largely does not, and many programs still write KB while dividing by 1,024. The result is that a reader must often infer from context which convention a number follows, which is exactly what the standard was written to prevent.

In practice the kibibit itself appears mainly in the specifications of small memory chips, in serial memory used by embedded systems, and in protocol documents where an exact power of two matters. Anywhere the number 1,024 is meant rather than 1,000, this is the correct unit.

One kibibit equals 1,024 bits, 128 octets, or 1.024 kilobits.

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.