OpenStax-CNX module: m13081 1 Prefixes for binary multiples* Rick Simpson This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 2.0 1 Prexes Almost all digital computers these days are binary, meaning that they deal with numbers expressed in binary rather than decimal. This means that memory addresses, and thus memory sizes, are also expressed in binary. Memory sizes are almost always nice, round numbers in binary, but not in decimal. Thus a computer with a 16-bit wide address can have up to 216 bytes of memory, which is 10,000,000,000,000,000 in binary and 65,536 in decimal. Early on it was observed that 210, which is 10,000,000,000 in binary, is 1024 in decimal. This isn't too far o from 1000 ("only" 2.4% o). Not only that, but 220 is close to a million, being equal to 1,048,576 in decimal. It became common to refer to "kilobytes" and "megabytes", where a "kilobyte" was really 1024 bytes and a "megabyte" was really 1,048,576 bytes. To those in scientic and technical disciplines other than computer science and computer engineering, though, "kilo" means 1000 and "mega" means 1,000,000. They don't mean about 1000 or approximately 1,000,000. Properly, all the SI prexes1 such as "kilo" and "mega" refer to powers of 10, not powers of 2. Lately the disparity caused by using power-of-ten names for power-of-two quantities has gotten worse because the numbers have gotten bigger. We now have even laptop computers with "gigabytes" of memory, and large server computers can have "terabytes" of disk space. How far o are we? When we say but mean we're this far o 1 kilobyte 210 bytes 2.4% 1 megabyte 220 bytes 4.9% 1 gigabyte 230 bytes 7.4% 1 terabyte 240 bytes 10.0% 1 petabyte 250 bytes 12.6% 1 exabyte 260 bytes 15.3% Table 1 *Version 1.1: Oct 21, 2005 10:52 pm -0500 http://creativecommons.org/licenses/by/2.0/ 1http://physics.nist.gov/cuu/Units/prexes.html http://cnx.org/content/m13081/1.1/ OpenStax-CNX module: m13081 2 Being o by 15% when talking about an "exabyte" means being o by about 1:5 × 1017 bytes, or 150 petabytes. To eliminate this imprecision and confusion, a set of prexes for binary multiples2 that closely parallel those for powers of 10 has been adopted as a standard by the International Electrotechnical Commission (IEC3 ). SI (Metric) Prexes Factor Name Symbol 103 kilo k 106 mega M 109 giga G 1012 tera T 1015 peta P 1018 exa E 1021 zetta Z 1024 yotta Y (a) IEC Binary Prexes Factor Name Symbol 210 kibi Ki 220 mebi Mi 230 gibi Gi 240 tebi Ti 250 pebi Pi 260 exbi Ei 270 280 (b) Figure 1: (a) Powers of 10 (b) Powers of 2 The binary symbols are just the SI symbols with an "i" for binary appended. The binary table only goes through 260, which is enough to handle the largest number in a 64-bit computer. There is even suggested pronounciation4 for the names: "KIH-bee" and "MEH-bee" for kibi and mebi, and similarly for the others. This standard was published by the IEC in 2000, but it appears to have had very little publicity and is almost certainly unknown to most people who deal with computers. Adoption of the new prexes and 2http://physics.nist.gov/cuu/Units/binary.html 3http://www.iec.ch 4http://physics.nist.gov/cuu/Units/binary.html http://cnx.org/content/m13081/1.1/ OpenStax-CNX module: m13081 3 names by the general population is likely to be slow in coming. Getting people to say "mebi bytes" and "gebi bytes" with a straight face may take even longer. 2 Links SI stands for le Système International d'Unités, or International System of Units, commonly called "the metric system" in English-speaking countries. The Bureau international des poids et mesures (BIPM)5 in Paris has a good description on their web site (in French and English). In the US, the National Institute of Standards and Technology (NIST)6 has web pages that describe the SI names and prexes7 and the binary names and prexes8 . 5http://www.bipm.fr/noash.html 6http://www.nist.gov 7http://physics.nist.gov/cuu/Units/prexes.html 8http://physics.nist.gov/cuu/Units/binary.html http://cnx.org/content/m13081/1.1/.