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 |
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