# Prefixes for decimal and binary multiples powers of ten

Note that, for consistency with the others, the simbol for kibi- is "Ki" and not "ki". With these prefixes is thus possible to indicate binary multipliers and preserve the decimal meaning of the SI prefixes, avoiding ambiguity. A common mistake is to think that the correct thing to do now that the binary prefixes have their own symbols, is to just use them everywhere.

Even thought using the right binary prefix is certantly better than misusing the decimal ones, there's no real reasons to use binary prefixes in most of the cases. Working with powers of 10 is easier, therefore , if the quantities we are dealing are not exact powers of 2, decimal powers should be preferred.

Let's see a few examples of quantities that should be indicated using decimal and binary prefixes:. File sizes are probably the quantities that are most frequently found while working with PCs. File sizes are not powers of 2. For example, this document is now bytes, and it's easier to express this as With decimal prefixes it's also a lot easier to add and subtract values with different prefixes.

For example assume that we have a 4. Let's do the same calculation again, but assuming that the sizes of the files are instead expressed with binary prefixes. The sizes are expressed with binary prefixes so it's more difficult to convert them to MiB: Our DVD uses decimal prefixes and its size is 4.

After several conversion we finally found out that the exact size of all the files is 5. Even though it's now clear how using decimal prefixes greatly simplifies calculations, several applications still prefers to use binary prefixes. The main reason is that decimal prefixes were and are often misused e.

Using MiB avoids ambiguity and clarifies that the quantity is equal to 1 bytes, but on the other hand it makes the calculations more difficult. A better approach would be to use decimal prefixes with their correct meaning of course , and possibly specify the exact size in bytes or add a note to clarify that the application is using decimal prefixes. As noted by the IT specialist, the difference between 1 kB bytes and 1 KiB bytes is not so much, but it grows with the larger prefixes.

This table and graph show the differences between decimal and binary prefixes. For example, 1 GB is equal to 0. The following table and graph, instead, show the differences between binary and decimal prefixes. For example, 1 GiB is equal to 1. Finally, this table combines the two previous tables and summarizes the differences between the prefixes, showing their exact value in bytes.

As we said at the beginning of this paragraph, the difference between 1 kB and 1 KiB is only 24 bytes, but between 1 TB and 1 TiB is about Between a YB and a YiB is even greater: It's quite clear that the difference will keep increasing as long as the technology will evolve, and that small errors will become huge. Nowadays we already use gigabytes and terabytes and these differences are already noticeable.

We will now analize how these prefixes are used to specify the size of mass-storage devices, memories and the speed of processors. The size of the hard disks is probably one of the well-known cases where the differences between the prefixes leads to confusion. Due to the high number of bytes that a modern hard disk can store, it's easy to see the divergence between what you read on the package and what your operative system may see.

In most contexts only a few, the most common, combinations are established. For example, prefixes for multiples greater than one thousand are rarely applied to the gram or metre. Some prefixes used in older versions of the metric system are no longer used. The prefix " myrio- " was an alternative spelling variant for " myria- ", as proposed by Thomas Young.

A binary prefix indicates multiplication by a power of two. This has prompted the use of the metric prefixes kilo , mega , and giga to also denote the powers of which is common in information technology with the unit of digital information, the byte.

Units of information are not covered in the International System of Units. Computer professionals have historically used the same spelling, pronunciation and symbols for the binary series in the description of computer memory , although the symbol for kilo is often capitalised.

In the specifications of hard disk drive capacities and network transmission bit rates , on the other hand, decimal prefixes, consistent with the metric system, are used. For example, a gigabyte hard drive holds billion bytes, and a megabit-per-second Ethernet connection transfers data at million bits per second. The ambiguity has led to some confusion and even of lawsuits from purchasers who were expecting 2 20 or 2 30 and considered themselves shortchanged by the seller.

Western Digital Corporation and Cho v. The symbols are the decimal symbol, always capitalised, followed by the letter "i". According to these standards, kilo , mega , giga et seq. Their adoption in popular publications remains limited. Many personal, and sometimes facetious, proposals for additional metric prefixes have been formulated.

In , an online petition sought to establish hella as the SI prefix for 10 27 , a movement that began on the campus of UC Davis. On page 23 of the 7 th edition of the SI brochure , published in , there is a marginal note that, referring to the decimal prefixes, says:. They should not be used to indicate powers of 2 for example, one kilobit represents bits and not bits. Letter symbols to be used in electrical technology specifically in Part 2: In the following table are listed all the binary prefixes defined in these standards:.

The names of the new prefixes are formed adding the letters "bi" for binary after the first two letters of the corresponding SI prefix e. Their symbols are formed adding a "i" to the SI symbol e. Note that, for consistency with the others, the simbol for kibi- is "Ki" and not "ki". With these prefixes is thus possible to indicate binary multipliers and preserve the decimal meaning of the SI prefixes, avoiding ambiguity. A common mistake is to think that the correct thing to do now that the binary prefixes have their own symbols, is to just use them everywhere.

Even thought using the right binary prefix is certantly better than misusing the decimal ones, there's no real reasons to use binary prefixes in most of the cases. Working with powers of 10 is easier, therefore , if the quantities we are dealing are not exact powers of 2, decimal powers should be preferred.

Let's see a few examples of quantities that should be indicated using decimal and binary prefixes:. File sizes are probably the quantities that are most frequently found while working with PCs.

File sizes are not powers of 2. For example, this document is now bytes, and it's easier to express this as With decimal prefixes it's also a lot easier to add and subtract values with different prefixes. For example assume that we have a 4. Let's do the same calculation again, but assuming that the sizes of the files are instead expressed with binary prefixes. The sizes are expressed with binary prefixes so it's more difficult to convert them to MiB: Our DVD uses decimal prefixes and its size is 4.

After several conversion we finally found out that the exact size of all the files is 5. Even though it's now clear how using decimal prefixes greatly simplifies calculations, several applications still prefers to use binary prefixes. The main reason is that decimal prefixes were and are often misused e. Using MiB avoids ambiguity and clarifies that the quantity is equal to 1 bytes, but on the other hand it makes the calculations more difficult.

A better approach would be to use decimal prefixes with their correct meaning of course , and possibly specify the exact size in bytes or add a note to clarify that the application is using decimal prefixes. As noted by the IT specialist, the difference between 1 kB bytes and 1 KiB bytes is not so much, but it grows with the larger prefixes. This table and graph show the differences between decimal and binary prefixes. For example, 1 GB is equal to 0. The following table and graph, instead, show the differences between binary and decimal prefixes.

For example, 1 GiB is equal to 1. Finally, this table combines the two previous tables and summarizes the differences between the prefixes, showing their exact value in bytes.

As we said at the beginning of this paragraph, the difference between 1 kB and 1 KiB is only 24 bytes, but between 1 TB and 1 TiB is about