2.3 Scales of Magnitude

Mass storage devices and memories are very large and thus measured with units that have names different from those used in everyday life. While we use the colloquial word grand to refer to $1,000, for amounts greater than $1,000 we use the names of the decimal system, such as million. These are not universally used—in the United States, one thousand million is called billion; in Europe it is called milliard. There is, however, an agreed upon nomenclature for powers of 10 so that one thousand is called kilo, one million is called Mega, and so on (see Table 2-1). Note the lowercase in kilo, the uppercase in Mega, and all that follow. This comes from the fact that the letter K is reserved, in the decimal nomenclature, for the designation of the absolute temperature measure (degrees in Kelvin).^[1]

The computer is not based on the radix 10; it is based on the radix 2. Inasmuch as 2¹⁰ equals 1,024, which is close to 10³, it became customary in the past to refer to 2¹⁰ as kilo. Thus, one kilobyte was approximately one thousand bytes, and the discrepancy was small. When we move from a kilobyte to a megabyte, which now stands for 2²⁰ bytes, the discrepancy between 10⁶ and 2²⁰ is significant, as 10⁶ = 1,000,000 and 2²⁰ = 1,048,576. This is not a small difference and cannot be ignored. Obviously, as we move toward larger scales, the discrepancy in sizes expressed as decimal names for binary-based quantities is increased, causing confusion and inconsistency in reporting sizes.

For that reason, as of 2005, there is a standard that introduces new names for quantities expressed as powers of 2 and retains the familiar names for quantities expressed as powers of 10. Table 2-1 has names, sizes, and observations about the real meaning of the sizes, starting with megabyte for the decimal meaning of the size in bytes and mebibytes for the binary meaning. As of the time of this writing (2013), sizes of mass storage devices are usually quoted in the decimal meanings, and sizes of RAM are quoted in the binary meaning, both using the decimal nomenclature. This confusion, well exploited in advertising, will hopefully disappear as the binary nomenclature becomes better used, or if the community will decide to report correctly when decimal nomenclature is used.

Please refer to Table 2-1 to make sense of what you just read. The binary prefixes were first proposed by the IEC (International Electrotechnical Commission) in January 1999 and expanded in 2005 to include all binary equivalents to the accepted decimal prefixes. All binary prefixes and names were codified by the IEEE (Institute of Electrical and Electronics Engineers) as a standard in 2005 (IEEE 1541-2002).