Mibi Mega Kibi Kilo - Decimal and Binary Prefixes

A megabit can be 1,000,000 bits or 1,048,576 bits depending on whether you using decimal or binary definitions. Standards have been defined to help - are you using the mibibyte and kibibyte in your documentation ?

The difference between binary and decimal seems small, but it can lead to very large problems. Instances of telcos providing bandwidth in decimal can cause QoS strategies to go wrong as this makes a big difference when traffic shaping.

Standards for decimal and binary prefixes

In 1999, the International Electrotechnical Commission (IEC) published a standard, which was approved in 1998, introduced the prefixes kibi-, mebi-, gibi-, tebi-, pebi-, exbi-, to be used in specifying binary multiples of a quantity. The names come from the first two letters of the original SI prefixes followed by bi which is short for "binary". It also clarifies that, from the point of view of the IEC, the SI prefixes only have their base-10 meaning and never have a base-2 meaning.

Thus kibi is a kilobyte in binary - kibi and a gibibit is a binary gigabit.

IEC standard prefixes

In 1999, the International Electrotechnical Commission (IEC) published Amendment 2 to "IEC 60027-2: Letter symbols to be used in electrical technology – Part 2: Telecommunications and electronics". This standard, which was approved in 1998, introduced the prefixes kibi-, mebi-, gibi-, tebi-, pebi-, exbi-, to be used in specifying binary multiples of a quantity. The names come from the first two letters of the original SI prefixes followed by bi which is short for "binary". It also clarifies that, from the point of view of the IEC, the SI prefixes only have their base-10 meaning and never have a base-2 meaning. It is strongly supported by many standardization bodies, including IEEE and CIPM.

Name	Symbol	Value
kibi	Ki	210 = 1,024
mebi	Mi	220 = 1,048,576
gibi	Gi	230 = 1,073,741,824
tebi	Ti	240 = 1,099,511,627,776
pebi	Pi	250 = 1,125,899,906,842,624
exbi	Ei	260 = 1,152,921,504,606,846,976

Examples

Example : 300 Gigabytes = 279.5 Gibibytes.

Decimal prefixes

Name	Symbol Value	Base 16 (Binary)
kilo	k or K	210 = 1000
mega	M	220 = 1,000,000
giga	G	230 = 1,000,000,000
tera	T	240 = 1,000,000,000,000
peta	P	250 = 1,000,000,000,000,000
exa	E	260 = 1,000,000,000,000,000,000

Why bother ?

When you are traffic shaping a 128kbps circuit, is it 128000 bits per second or is it 131072 bits per second ?

When you buy a 10 megabyte per second Internet connection, is it 10,000,000 bits per second or 10,485,760 ? That is quite a big difference isn’t it ?

By getting people to use these abbreviations, we should get this more correct int he future. To show hwo the error factor can creep into network planning, have a look at the percentage difference table below:

Approximate ratios between binary prefixes and their decimal equivalent

Name
Bin	Decimal	Bin Example	Percentage difference
kilobyte : kibibyte	1.024	0.976	100 KB = 97.6 KiB	2.4%
megabyte : mebibyte	1.049	0.954	100 MB = 95.4 MiB	4.9%
gigabyte : gibibyte	1.074	0.931	100 GB = 93.1 GiB	7.4%
terabyte : tebibyte	1.100	0.909	100 TB = 90.9 TiB	10%

Conclusion

I would like to hear what other people think ? Could this be done ? Would you do this it at work ? Or am I full of hot air ?

Reference

Wikipedia HERE