Brainy Figuring -- 5/29/99

Möbius in the Playground -- 5/22/99

Coloring Penrose Tiles -- 5/15/99

Counting by Twos

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

The problem started 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 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 several years ago started to work on finding 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 ½ 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 absolutely always, means 8 bits.

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

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. The new binary standard is discussed at http://www.iec.ch/tclet6.pdf.

Comments are welcome. Please send messages to Ivars Peterson at ip@sciserv.org.

Ivars Peterson is the mathematics/computers writer and online editor at Science News. He is the author of *The Mathematical Tourist, Islands of Truth, Newton's Clock, Fatal Defect, and The Jungles of Randomness. His current work in progress is Fragments of Infinity: A Kaleidoscope of Mathematics and Art (to be published in 1999 by Wiley).

MATHEMUSEMENTS: Look for math-related articles by Ivars Peterson every month in the children's general-interest magazine Muse (http://www.musemag.com) from the publishers of Cricket and Smithsonian magazine.

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