Conversion from 3 Mebibits per second to Tebibits per second

Information about the Mebibit per second (Mibit/s)

The mebibit per second is a unit of data transfer rate equal to 1,048,576 bits per second. Its symbol is Mibit/s. It is the binary counterpart of the megabit per second, and the two differ by 4.9 per cent — small, but large enough to change a headline figure.

That five per cent is where the unit starts to matter. A connection advertised at 100 megabits per second and a connection at 100 mebibits per second differ by about five megabits, which is a whole high-definition video stream. In a specification, a contract or a benchmark report, quoting one and delivering the other is a real discrepancy rather than a rounding difference.

In practice the confusion is rare in networking, because network equipment is always specified in decimal. What produces mebibit figures is measurement software: a tool that counts a transfer in mebioctets and divides by elapsed seconds is reporting a binary rate, and multiplying by eight makes it mebibits per second. A person comparing that reading with an advertised rate must convert twice, once for the base and once for the factor of eight.

Where a genuine binary rate does arise is inside a machine. A memory bus transfers a fixed number of bits per clock cycle, and the width is a power of two — sixty-four bits at a time, for instance — so the quantity moved per cycle is binary even though the clock frequency is not. Rates derived from such a structure are naturally expressed with binary prefixes.

For scale, a mebibit per second is 131,072 octets per second, or about 128 kibioctets per second. That is roughly a photograph every two seconds, or a plain-text novel every four. It is a rate at which the modern web is slow but usable, which puts it in the range that mobile networks fall to when congested.

The correct symbol has the lowercase i, and its presence is the only reliable way to tell the two conventions apart. A document writing Mbit/s in a context where the underlying figure came from a binary computation has misstated its own measurement by five per cent.

One mebibit per second equals 1,048,576 bits per second, 131,072 octets per second, or about 1.049 megabits per second.

Information about the Tebibit per second (Tibit/s)

The tebibit per second is a unit of data transfer rate equal to 1,099,511,627,776 bits per second, which is 1,024 gibibits per second. Its symbol is Tibit/s. It is the binary counterpart of the terabit per second, and the two differ by 10 per cent.

Ten per cent is the point at which the distinction becomes a matter of money rather than of pedantry. A supplier quoting a system at a hundred terabits per second and a customer measuring a hundred tebibits per second are not describing the same performance, and the difference is ten terabits — more than most organisations' entire external connectivity.

The rate belongs to the interior of very large machines. The aggregate memory bandwidth of a rack of accelerators, or the internal switching capacity of a large network chip, reaches this range, and both are built from power-of-two structures: memory channels of fixed binary width, switch ports in powers of two, buffers sized in binary. Expressing their totals with binary prefixes preserves the arithmetic that produced them.

In octets a tebibit per second is 137,438,953,472, or 128 gibioctets per second. That is more than any single storage device can supply and more than any external cable carries. It is a figure that describes something happening inside a cabinet, between chips connected by short traces on a board, where the physical distance is measured in centimetres.

Optical research also brushes this range. A laboratory demonstration carrying a petabit per second down one fibre is a thousand times higher, but individual wavelength channels and the electronics driving them work at tebibit-scale aggregates, and papers reporting them often state the binary figure because the underlying frame sizes are binary.

The habit of writing the lowercase i is worth keeping even where the reader is unlikely to check. A number written unambiguously can be converted correctly by anyone who reads it later; one written ambiguously cannot be repaired, and at ten per cent the ambiguity is no longer harmless.

One tebibit per second equals 1,024 gibibits per second, 137,438,953,472 octets per second, or about 1.100 terabits per second.