Conversion from 25 Megaoctets to Bits

Information about the Megaoctet (Mo)

The megaoctet is a unit of digital information equal to one million octets, or eight million bits. Its symbol is Mo. It is the unit of the individual file: a photograph, a song, a document, an application download are all sized in megaoctets, which makes it the most frequently read data unit in daily life.

The typical figures are worth carrying in the head. A photograph from a phone is 2 to 5 megaoctets, a raw photograph from a system camera 25 to 50. A compressed song is 3 to 10. A minute of high-definition video is around 100. A long text document is under one. An operating system update is several thousand, which is why it is quoted in gigaoctets instead.

The megaoctet also carries the most notorious unit error in computing history. The 1.44 MB floppy disc holds neither 1.44 million octets nor 1.44 times 1,048,576. Its capacity is 1,440 kibioctets, which is 1,474,560 octets — the manufacturers multiplied a binary kilo by a decimal thousand and produced a figure that is correct in no system at all. It remains the standard illustration of why the IEC prefixes were needed.

Compact discs are cleaner: a standard disc holds about 700 megaoctets of data, or 74 to 80 minutes of audio, and that capacity was the practical limit for distributing software for a decade. Before them, distributing a program meant a box of floppies, and after them a DVD held about 4.7 gigaoctets, nearly seven times as much.

Memory sizes reached megaoctets in the early 1990s and stayed there for a decade. Four megaoctets was a comfortable amount in 1993 and inadequate by 1998, which tracks the arrival of graphical interfaces and the web. Today a single browser tab routinely holds more memory than an entire computer of that era.

The decimal-binary gap matters at this scale. A megaoctet is a million octets, but a mebioctet is 1,048,576, and a file reported as 100 MB by one program may appear as 95.4 MB in another. The difference is 4.9 per cent, small enough to overlook and large enough to cause arguments about whether a download completed correctly.

One megaoctet equals 1,000,000 octets, 1,000 kilooctets, 8 megabits, or about 0.9537 mebioctets.

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.