Extreme Prefixes

Most of us are familiar with the standard International System (SI) prefixes, such as kilo, mega, milli, and so forth. The prefixes are very handy and commonly used by engineers and scientists, who speak in terms of kilometer, megaton, milligrams, kilovolts, nanometers, and picoseconds. The sexier ones spill over into common language (megastar, megadose) and product names (e.g., the VTech GigaPhone). As we push the frontiers of technology and science, formerly exotic prefixes come into vogue. For example, as disk drive and other storage space has increased in capacity, the terms megabyte, gigabyte, and even terabyte, have become increasingly useful and widespread.

If you are anything like me, you might be curious what other prefixes are in store for us. It turns out that there are other, more exotic and extreme SI prefixes on the shelf, ready to be used. Most are not yet commonly known, but are fascinating to ponder. They are kind of cool. These extreme prefixes include the division prefixes atto, zepto, and yocto (I know, I know, sounds like the Marx brothers); and the multiplier prefixes exa, zetta, and yotta (sounds like the latest Shirley MacLaine book). The most extreme, and coolest, ones are the unofficial vendeko (10-33) and vendeka (1033). Wicked. We now have multi-gigabyte (GB) disk drives; soon, surely, we will speak of disk drive, or collective network, capacity, in terms of terabytes, petabytes, even exabytes. I can’t wait for vendekabytes.

The current and proposed SI prefixes are found in the table below (drawn from various sources, including link1, link2, link3, link4):

Prefixes of the International System (SI)

Divisions

 

Multiples

factor

prefix

symbol

 

factor

prefix

symbol

10-1

deci

d

 

101

deca

da

10-2

centi

c

 

102

hecto

h

10-3

milli

m

 

103

kilo

k

10-6

micro

µ

 

106

mega

M

10-9

nano

n

 

109

giga

G

10-12

pico

p

 

1012

tera

T

10-15

femto

f

 

1015

peta

P

10-18

atto

a

 

1018

exa

E

10-21

zepto

z

 

1021

zetta

Z

10-24

yocto

y

 

1024

yotta

Y

 

 

(unofficial)

 

 

10-27

xenno

x

 

1027

xenna

X

10-30

???

w

 

1030

???

W

10-33

vendeko

v

 

1033

vendeka

V

10-36

???

u

 

1036

???

U

 

As can be seen, the smaller and lesser-known division prefixes tend to end in “o”, while the larger and less-known multiplication prefixes tend to end in “a”. Also, the symbols for the larger multipliers are capital letters, while those for the division prefixes are small Roman or greek letters. This article (p. 3, footnotes * and **) provides an explanation of the origin of some of the SI and other prefixes. This article gives some examples of possible uses of some of extreme prefixes.

While Googling for this article, I discovered that the International Electrotechnical Commission (IEC) has approved a set of prefixes for binary multiples, which I had never heard of. These are for use in the computer field, for data processing and data transmission applications. Computer engineers and programmers typically express numbers in powers of two because of the use of two-valued bits for computer memory and logic (each bit can represent a 0 or a 1). A ten-bit memory register, for example, can store 210 = 1024 different binary numbers (bit combinations).

As explained here (link2), computer professionals noticed that 210 (1024) was nearly equal to 1000 and started using the SI prefix “kilo” to mean 1024, and other SI prefixes to approximate other binary quantities. This has led to confusion. For example, under the SI system, megabyte means one million (1,000,000) bytes. Most computer manufacturers, however, use the term megabyte to mean 220 = 1,048,576 bytes. Similarly, a kilobit usually refers to 210 = 1024 bits instead of 1000 bits.

The new binary prefixes defined by the IEC are designed to eliminate this confusion. For example, kibi, instead of kilo, is to be used for 210 = 1024; and mebi, instead of mega, for 220 = 1,048,576. Thus, megabyte (MB) means 1,000,000 bytes, while mebibyte (MiB) means 1,048,576 bytes. A tebibyte (TiB) denotes 240 = 1,099,511,627,776 bytes, while a terabyte indicates 1012 = 1,000,000,000,000 (a trillion) bytes. I would tell you what a gibibyte (GiB) is, but I can’t stop giggling at the name. It remains to be seen whether these binary prefixes will catch on. While they are also cool, if a little funny, and seemingly useful, I had never even heard of them until writing this article.

And speaking of confusion, it’s also interesting to note that what Americans call million (106, mega), billion (109, giga), and trillion (1012, tera), the Brits refer to as million, milliard, and billion (at least officially, if not in practice).

Incidentally, speaking of Googling, the name Google appears to be a variation of “googol,” itself an extremely large number (suggesting Google can find information from a huge number of websites, I suppose). A googol is 10100, i.e. a 1 followed by 100 zeros. (In official SI prefix terms, a googol is approximately a yotta squared, squared.) Even larger is the googolplex, which is equal to 10 to the power of a googol (10googol); this number is about the same size as the number of possible games of chess. Even larger numbers (link2, link3) have been defined, such as Skewes’ number, Graham’s number, and the Moser, which I won’t even try to describe.

May I be excused now, please? My brain — which contains approximately 100 giga-neurons — is full.

January 15, 2001