Ivars Peterson's MathTrek

June 7, 1999

Counting by Twos

How much is a megabyte? Many people don't really know.

The problem originated decades ago when computer professionals noticed that 210 is very nearly equal to 1,000, and they began using the metric prefix "kilo" to mean 1,024. That was okay when computers were solely the domain of an elite group of high priests. Physicists, engineers, and ordinary folk could continue to use the prefix to mean 103 without worrying about what the computer gurus were up to. A kilogram remained 1,000 grams.

Now, nearly everyone uses computers, and even the computer world can't agree on what the prefixes actually mean.

When describing computer memory, most manufacturers use the term megabyte to mean 220, or 1,048,576 bytes of data. A few storage-device makers, however, insist on using the term to mean 1,000,000 bytes.

Similarly, some designers of local-area networks use megabit per second to mean a transmission rate of 1,048,576 bits per second, but telecommunications engineers use it to mean 106 bits per second.

The confusion stems from the use of prefixes designating powers of 10 for quantities expressed in powers of 2. The discrepancy mounts as you go to prefixes denoting higher powers.

To remove that nagging ambiguity, several international organizations began looking for acceptable names for prefixes related to powers of 2. Last December, the International Electrotechnical Commission voted to introduce the new prefixes kibi (Ki), mebi (Mi), gibi (Gi), tebi (Ti), pebi (Pi), and exbi (Ei), each one derived from the corresponding metric prefix and the word "binary."

So a gibibyte would be 230 bytes, and a gigabyte would be 109 bytes. Your handy 90-millimeter (3-inch) diskette would be formatted for 1440 KiB. However, that doesn't resolve ambiguities in the use of the term "byte," which normally, but not always, means 8 bits.

What about the Y2K problem? Changing the meaning of "K" from kilo to kibi postpones the number crunch to the year 2048!

Copyright 1999 by Ivars Peterson

References:

Barrow, B. 1997. A lesson in megabytes. IEEE Standards Bearer (January):5. Available at http://physics.nist.gov/cuu/Units/binary.html.

Holden, C. 1999. Computer gibirish. Science 283(March 12):1631.

Information about the International Electrotechnical Commission can be found at http://www.iec.ch.


Comments are welcome. Please send messages to Ivars Peterson at ipeterson@maa.org.