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Decimal vs Binary, base 10 values vs base 2 values. (by Jack B. Korten)

When you purchase a 1 terabyte hard drive, you will find that it holds only 931 gigabytes. What happened to the missing 69 gigabytes?

The prefixes kilo, mega, giga, tera etc.. belong to the International System of Units (SI) which uses a decimal system with base 10 values.

kilo       10³      from Greek "chilioi" meaning 'thousand' (1000¹)

mega   10⁶      from Greek "megas" meaning 'great', 'large'

giga     10⁹      from Greek "gigas" meaning ‘giant’.

tera      10¹²    from Greek "teras", meaning 'monster'.

peta     10¹⁵    from Greek "penta" meaning five (1000⁵)

exa      10¹⁸    from Greek "hex" meaning ‘six’.

zetta    10²¹ from Latin "septem" meaning seven, p dropped, first letter changed to z

yotta    10²⁴    from Latin "octo" meaning eight, y added, c dropped.

Computers use a binary system with a base value of 2. The prefixes kilo, mega, giga, etc. are decimal prefixes and are out of step with binary values. Hard drive manufacturers take advantage of this ambiguity, so they inflate the sizes of their hard drives.

The difference between the two systems has always been an annoyance, but now the discrepancies have become difficult to ignore, because of today's enormous hard drives.

In December 1998, the IEC (International Electrotechnical Commission) addressed this problem by creating prefixes such as kibi, mebi, gibi, etc., denoting powers of 1024. Thus the kibibyte, symbol KiB, represents 2¹⁰ = 1024 bytes.

These prefixes are now part of the International System of Quantities.

Below, a comparison of the two systems:

 

kilobyte           KB       10³      1000                           kibibyte           KiB      2¹⁰       1024

megabyte        MB       10⁶      1000²                         mebibyte         MiB      2²⁰       1024²

gigabyte          GB       10⁹      1000³                         gibibyte           GiB      2³⁰       1024³

terabyte          TB       10¹²        1000⁴                        tebibyte           TiB       2⁴⁰       1024⁴

petabyte         PB       10¹⁵    1000⁵                           pebibyte          PiB       2⁵⁰       1024⁵

exabyte          EB       10¹⁸     1000⁶                          exbibyte          EiB       2⁶⁰       1024⁶

zettabyte        ZB       10²¹        1000⁷                         zebibyte          ZiB      2⁷⁰       1024⁷

yottabyte        YB       10²⁴     1000⁸                           yobibyte          YiB      2⁸⁰       1024⁸