Why Isn't a Kilobyte 1,000 Bytes?

Date: 03/29/2001 at 10:06:47
From: Gerry England
Subject: Computer systems - Metric numbers

Question: If the following is true, how is it correct?

A nibble is 2^2, or 4 bits; a byte is 2^3, or 8 bits; a word is 2^4, 
or 16 bits. Thus one kilobyte, which ought to be 1000 bytes, is 
actually 1024 bytes (2^10 bytes).

The computer counts by twos instead of by tens, but how does this 
work? 10^2 is not 2^10, which equals 1024.

Thanks
Gerry England

Date: 03/29/2001 at 13:44:13
From: Doctor TWE
Subject: Re: Computer systems - Metric numbers

Hi Gerry - thanks for writing to Dr. Math.

You are correct that the term kilobyte refers to 1024 bytes, whereas 
kilometer refers to 1000 meters. You are also correct in your 
statement that this is due to the fact that computers use binary 
("counts in twos") instead of decimal (base 10).

When computer scientists wanted prefixes to describe large numbers of 
bytes, they decided to "borrow" the prefixes used in the metric 
system. But metric prefixes were based on the decimal system, not the 
binary system. One thousand is 1111101000 in binary, which is not a 
convenient group size to use. (This would be the equivalent of using 
1 km = 976 m in the decimal system - not very helpful.)

However, since 1024 = 2^10 is very close to 1000 = 10^3, those 
scientists decided to call 1024 bytes a "kilobyte" and to describe it 
as being "about 1000 bytes." Further confusion was caused when even 
larger prefixes were introduced, because they weren't used 
consistently. The term "megabyte," for example, sometimes means 
1,048,576 (= 1024*1024) bytes, sometimes means 1,024,000 (= 1000*1024) 
bytes, and sometimes means 1,000,000 (= 1000*1000) bytes; depending on 
who's using the term!

To clarify the confusion and multiple definitions, in 1998 the 
International Electrotechnical Commission (IEC) proposed a different 
set of prefixes for the binary multiples. Instead of "kilobytes" we'd 
use "kibibytes," instead of "megabytes" we'd use "mebibytes," and so 
on. Unfortunately, because of the widespread use of kilobytes, 
megabytes, etc. in the industry and in popular culture, the IEC's 
proposals have not caught on and are not in common use. 

For more information on the IEC binary prefix system, visit NIST's 
"Prefixes for binary multiples" Web page at:

   http://physics.nist.gov/cuu/Units/binary.html   

I hope this helps. If you have any more questions, write back.

- Doctor TWE, The Math Forum
  http://mathforum.org/dr.math/   

Date: 04/06/2001 at 11:10:32
From: Gerry G England
Subject: Re: Computer systems - Metric numbers

Thank you Dr. Math,

I have used your service before and have found it to be a great help.

Gerry England