re: Cluster size survey, check your computer now!
Wednesday, July 14, 2004 at 4:37 pm
Windows Me Annoyances Discussion Forum
Posted by Cam
(4178 messages posted)
Free MS Update CD
"None of this has ANY relationship to the "binary" formula you are still trying to
justify!"
Binary vs. Decimal Measurements
"One of the most confusing problems regarding PC statistics and measurements is the
fact that the computing world has two different definitions for most of its measurement
terms. :^) Capacity measurements are usually expressed in kilobytes (thousands of
bytes), in megabytes (millions of bytes), or gigabytes (billions of bytes). Due to
a mathematical coincidence, however, there are two different meanings for each of
these measures.
Computers are digital and store data using binary numbers, or powers of two, while
humans normally use decimal numbers, expressed as powers of ten. As it turns out,
two to the tenth power, 2^10, is 1,024, which is very close in value to 1,000 (10^3).
Similarly, 2^20 is 1,048,576, which is approximately 1,000,000 (10^6), and 2^30
is 1,073,741,824, close to 1,000,000,000 (10^9). When computers and binary numbers
first began to be used regularly, computer scientists noticed this similarity, and
for convenience, "hijacked" the abbreviations normally used for decimal numbers and
began applying them to binary numbers. Thus, 2^10 was given the prefix "kilo", 2^20
was called "mega", and 2^30 "giga".
This shorthand worked fairly well when used only by technicians who worked regularly
with computers; they knew what they were talking about, and nobody else really cared.
Over the years however, computers have become mainstream, and the dual notation has
led to quite a bit of confusion and inconsistency. In many areas of the PC, only
binary measures are used. For example, "64 MB of system RAM" always means 64 times
1,048,576 bytes of RAM, never 64,000,000. In other areas, only decimal measures are
found--a "28.8K modem" works at a maximum speed of 28,800 bits per second, not 29,491.
Storage devices however are where the real confusion comes in. Some companies and
software packages use binary megabytes and gigabytes, and some use decimal megabytes
and gigabytes. What's worse is that the percentage discrepancy between the decimal
and binary measures increases as the numbers get larger: there is only a 2.4% difference
between a decimal and a binary kilobyte, which isn't that big of a deal. However,
this increases to around a 5% difference for megabytes, and around 7.5% for gigabytes,
which is actually fairly significant. This is why with today's larger hard disks,
more people are starting to notice the difference between the two measures. Hard
disk capacities are always stated in decimal gigabytes, while most software uses
binary. So, someone will buy a "30 GB hard disk", partition and format it, and then
be told by Windows that the disk is "27.94 gigabytes" and wonder "where the other
2 gigabytes went". Well, the disk is 27.94 gigabytes--27.94 binary gigabytes. The
2 gigabytes didn't go anywhere.
Another thing to be careful of is converting between binary gigabytes and binary
megabytes. Decimal gigabytes and megabytes differ by a factor of 1,000 but of course
the binary measures differ by 1,024. So this same 30 GB hard disk is 30,000 MB in
decimal terms. But its 27.94 binary gigabytes are equal to 28,610 binary megabytes
(27.94 times 1,024).
One final "gotcha" in this area is related to arithmetic done between units that
have different definitions of "mega" or "giga". For example: most people would say
that the PCI bus has a maximum theoretical bandwidth of 133.3 Mbytes/second, because
it is 4 bytes wide and runs at 33.3 MHz. The problem here is that the "M" in "MHz"
is 1,000,000; but the "M" in "Mbytes/second" is 1,048,576. So the bandwidth of the
PCI bus is more properly stated as 127.2 Mbytes/second (4 times 33,333,333 divided
by 1,048,576).
There's potential good news regarding this whole binary/decimal conundrum. The IEEE
has proposed a new naming convention for the binary numbers, to hopefully eliminate
some of the confusion. Under this proposal, for binary numbers the third and fourth
letters in the prefix are changed to "bi", so "mega" becomes "mebi" for example.
Thus, one megabyte would be 10^6 bytes, but one mebibyte would be 2^20 bytes. The
abbreviation would become "1 MiB" instead of "1 MB". "Mebibyte" sounds goofy, but
hey, I'm sure "byte" did too, 30 years ago."
Good site this and well worth taking the time to read up on.
Mac
WINDOWS HELP RAM
|
All messages in this thread [show all]
 |  | | | | | | | | | | | | | |  | re: Cluster size survey, check your computer now! (Cam: Wed, Jul 14, 2004, 4:37 pm) |
| |
| |
Return to the Windows Me Discussion Forum
|
|
