We use a Binary number system (long post) was: [plug] honeymoon is over - Telstra introduces traffic cap on freedom ADSL

[Michael Hunt]

Some time today alan howard [mailto:alanh at wn.com.au] wrote:

> actually its probably the computer industry thats wrong here.
> as kilo, mega etc are part of the metric system and SI.
> Kilo means one thousand not 1024 etc.
>
> On Wednesday 06 June 2001 17:28, Paul Day wrote:
>
> > And the other assumption to make is that Telstra have defined a gigabyte
> > (incorrectly) as 1,000,000 bytes, as it seems that's what all the
> > bandwidth providers do.

Alan,

I'd like to quote the quantifiers section of the Jargon file as to why the
computer industry is justified in stating that 1024 bytes is equal to a
kilobyte.

(Sorry about posting the whole section but I only have it available in
offline mode and couldn't find a URL to quote. Besides it gets the point
across quite concisely)

Quantifiers

In techspeak and jargon, the standard metric prefixes used in the SI
(Système International) conventions for scientific measurement have dual
uses. With units of time or things that come in powers of 10, such as money,
they retain their usual meanings of multiplication by powers of 1000 = 10^3.
But when used with bytes or other things that naturally come in powers of 2,
they usually denote multiplication by powers of 1024 = 2^(10).

Here are the SI magnifying prefixes, along with the corresponding binary
interpretations in common use:

prefix  decimal  binary
kilo-   1000^1   1024^1 = 2^10 = 1,024
mega-   1000^2   1024^2 = 2^20 = 1,048,576
giga-   1000^3   1024^3 = 2^30 = 1,073,741,824
tera-   1000^4   1024^4 = 2^40 = 1,099,511,627,776
peta-   1000^5   1024^5 = 2^50 = 1,125,899,906,842,624
exa-    1000^6   1024^6 = 2^60 = 1,152,921,504,606,846,976
zetta-  1000^7   1024^7 = 2^70 = 1,180,591,620,717,411,303,424
yotta-  1000^8   1024^8 = 2^80 = 1,208,925,819,614,629,174,706,176

Here are the SI fractional prefixes:

prefix  decimal     jargon usage
milli-  1000^-1     (seldom used in jargon)
micro-  1000^-2     small or human-scale (see micro-)
nano-   1000^-3     even smaller (see nano-)
pico-   1000^-4     even smaller yet (see pico-)
femto-  1000^-5     (not used in jargon---yet)
atto-   1000^-6     (not used in jargon---yet)
zepto-  1000^-7     (not used in jargon---yet)
yocto-  1000^-8     (not used in jargon---yet)

The prefixes zetta-, yotta-, zepto-, and yocto- have been included in these
tables purely for completeness and giggle value; they were adopted in 1990
by the `19th Conference Generale des Poids et Mesures'. The binary peta- and
exa- loadings, though well established, are not in jargon use either -- yet.
The prefix milli-, denoting multiplication by 1/1000, has always been rare
in jargon (there is, however, a standard joke about the `millihelen' --
notionally, the amount of beauty required to launch one ship). See the
entries on micro-, pico-, and nano- for more information on connotative
jargon use of these terms. `Femto' and `atto' (which, interestingly, derive
not from Greek but from Danish) have not yet acquired jargon loadings,
though it is easy to predict what those will be once computing technology
enters the required realms of magnitude (however, see attoparsec).

There are, of course, some standard unit prefixes for powers of 10. In the
following table, the `prefix' column is the international standard suffix
for the appropriate power of ten; the `binary' column lists jargon
abbreviations and words for the corresponding power of 2. The B-suffixed
forms are commonly used for byte quantities; the words `meg' and `gig' are
nouns that may (but do not always) pluralize with `s'.

prefix   decimal   binary       pronunciation
kilo-       k      K, KB,       /kay/
mega-       M      M, MB, meg   /meg/
giga-       G      G, GB, gig   /gig/,/jig/

Confusingly, hackers often use K or M as though they were suffix or numeric
multipliers rather than a prefix; thus "2K dollars", "2M of disk space".
This is also true (though less commonly) of G.

Note that the formal SI metric prefix for 1000 is `k'; some use this
strictly, reserving `K' for multiplication by 1024 (KB is thus `kilobytes').

K, M, and G used alone refer to quantities of bytes; thus, 64G is 64
gigabytes and `a K' is a kilobyte (compare mainstream use of `a G' as short
for `a grand', that is, $1000). Whether one pronounces `gig' with hard or
soft `g' depends on what one thinks the proper pronunciation of `giga-' is.

Confusing 1000 and 1024 (or other powers of 2 and 10 close in magnitude) --
for example, describing a memory in units of 500K or 524K instead of 512K --
is a sure sign of the marketroid. One example of this: it is common to refer
to the capacity of 3.5" microfloppies as `1.44 MB' In fact, this is a
completely bogus number. The correct size is 1440 KB, that is, 1440 * 1024 =
1474560 bytes. So the `mega' in `1.44 MB' is compounded of two `kilos', one
of which is 1024 and the other of which is 1000. The correct number of
megabytes would of course be 1440 / 1024 = 1.40625. Alas, this fine point is
probably lost on the world forever.

[1993 update: hacker Morgan Burke has proposed, to general approval on
Usenet, the following additional prefixes:

	groucho 	10^(-30)
	harpo 	10^(-27)
	harpi 	10^(27)
	grouchi 	10^(30)

We observe that this would leave the prefixes zeppo-, gummo-, and chico-
available for future expansion. Sadly, there is little immediate prospect
that Mr. Burke's eminently sensible proposal will be ratified.]

[1999 upate: there is an IEC proposal for binary multipliers, but no
evidence that any of its proposals are in live use.]

Michael Hunt
An Aussie in Africa

"Toto I don't think we are using decimal anymore"

	-- Quote from a 6502 Assembly Guide --