Conversion from Pebioctets per second to Mebioctets per second

Information about the Pebioctet per second (Pio/s)

The pebioctet per second is a unit of data transfer rate equal to 1,024 tebioctets per second, or two to the fiftieth power octets per second. Its symbol is Pio/s. It is the binary counterpart of the petaoctet per second, and the two differ by 12.6 per cent.

The rate exists only as a total. The aggregate memory bandwidth of a whole supercomputer, or the summed capacity of the network fabric joining its cabinets, reaches this range, and both are sums over tens of thousands of components, each of which moves a few hundred gibioctets per second on its own.

Whether such a total means anything depends on the calculation being run. A problem that divides so that each node works mostly on its own data can use the full aggregate. A problem where every node must constantly consult every other cannot, and the machine's effective bandwidth falls to what the slowest shared path allows. Most of the art of parallel programming lies in getting problems into the first category.

In octets a pebioctet per second is 1,125,899,906,842,624, and in decimal terms about 1.126 petaoctets per second. The 12.6 per cent difference is the accumulated effect of five multiplications by 1.024, and it is now large enough that no report can leave the convention unstated without introducing real uncertainty.

The unit also appears in descriptions of parallel filesystems at the largest facilities, where a storage system spread across tens of thousands of drives delivers a few pebioctets per second to a compute cluster. That number determines how quickly the machine can checkpoint its state, which in turn determines how much work is lost when a component fails — and in a machine of that size, something is always failing.

For a converter the requirement is simply that the arithmetic be exact and the label preserved. Multiplying by 1,024 five times is not difficult; silently substituting the decimal prefix is the error to avoid.

One pebioctet per second equals 1,024 tebioctets per second, 1,125,899,906,842,624 octets per second, or about 1.126 petaoctets per second.

Information about the Mebioctet per second (Mio/s)

The mebioctet per second is a unit of data transfer rate equal to 1,048,576 octets per second, which is 1,024 kibioctets per second. Its symbol is Mio/s. It is the unit that disc benchmarks, copy tools and backup programs report in, and one of the few binary units most people see regularly without noticing.

Storage measurement produces it naturally. A benchmark writes and reads blocks whose size is a power of two, times the operation, and divides. The result is a binary rate, and reporting it as such preserves the arithmetic. A tool that converted to decimal megaoctets would introduce a 4.9 per cent adjustment for no purpose other than to match a marketing convention.

That five per cent is exactly where the two conventions diverge visibly for consumers. A drive advertised at 550 megaoctets per second and measured at 524 mebioctets per second is performing precisely as claimed; the numbers differ only because one is decimal and the other binary. A great deal of complaint about storage performance is this arithmetic misread as a shortfall.

For everyday sizes, one mebioctet per second copies a photograph in three seconds and a two-gigaoctet film in about half an hour. Modern drives run hundreds or thousands of times faster, so the unit is now the resolution at which small differences are reported rather than the scale of the whole figure.

The unit also appears in memory and cache measurements, in database throughput reports and in the output of the low-level commands that write disc images. All of these count in binary blocks because the underlying structures are binary, and all of them report in mebioctets per second because that is what the count divided by the time actually gives.

The habit of writing the lowercase i is worth keeping. It costs one character and it tells a later reader which of two conventions produced the number, which is information that cannot be recovered from context once it has been left out.

One mebioctet per second equals 1,048,576 octets per second, 1,024 kibioctets per second, or about 1.049 megaoctets per second.