Conversion from 2 Mebioctets to Bits

Information about the Mebioctet (Mio)

The mebioctet is a unit of digital information equal to 1,048,576 octets, which is 1,024 kibioctets. Its symbol is Mio. It is the binary counterpart of the megaoctet, and the two differ by 4.9 per cent — the point at which a careful writer starts distinguishing them.

The unit's most visible home is the processor cache. The fast memory built into a processor to hold recently used data is sized in binary, and modern chips carry caches measured in mebioctets: a few hundred kibioctets at the second level and tens of mebioctets at the third. Those figures are exact powers of two because the cache is addressed by dividing an address into fixed bit fields.

Block sizes and buffers follow the same logic. Filesystems allocate in blocks, database engines read in pages, compression tools work in windows, and all of these are powers of two, most often a few mebioctets. A tool that offers a buffer of 16 megaoctets almost always means 16 mebioctets, because the underlying allocation is a shift rather than a multiplication.

The distinction has become visible to ordinary users through the discrepancy between what a download claims and what a file manager reports. A file described as 100 megaoctets on a website is often 100 mebioctets on disc, or the reverse, and the resulting 4.9 per cent difference is enough to make a progress bar look wrong without anything actually being wrong.

For scale, a mebioctet holds a million characters of unaccented text — roughly a long novel, or five hundred pages. It is also a single photograph from a modest camera, or eight seconds of high-definition video. The same unit therefore describes both a very large amount of text and a very small amount of video, which says a good deal about the relative cost of representing the two.

The IEC notation Mio is used in technical documentation, in the Linux kernel, in filesystem tools and in standards. It remains rare in consumer software, where MB is written for both quantities. When a figure matters, the safest habit is to compute in octets and convert once at the end.

One mebioctet equals 1,048,576 octets, 1,024 kibioctets, 8 mebibits, or about 1.049 megaoctets.

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.