Extreme Prefixes

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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

Stephan
Kinsella [send him mail]
practices patent law in Houston. His website is www.stephankinsella.com.

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