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Units of information 

Units of information are a way of measuring a quantity of information or an entropy.

Contents

Primary units

Comparison of units of information: bit, trit, nat, ban. Quantity of informations is the height of bars. Dark green level is the "Nat" unit.
Comparison of units of information: bit, trit, nat, ban. Quantity of informations is the height of bars. Dark green level is the "Nat" unit.

Small amount of information just as logarithm of number of states. According to Shannon, The choice of a logarithmic base corresponds to the choice of a unit for measuring information.

The minimal integer, whose logarithm is positive, is 2. The unit, corresponding to it is bit. Bit is the base of information measurement in modern information technologies. The unit, corresponding to the number 3 is trit, which is equal to \ \log_{2} 3 \approx 1.585 bit. The unit, corresponding to the number 10: ban = \ \log_{2} 10 \approx 3.322 bit.

Since the base of natural logarithm is not an integer, such unit as Nat is usually not applied to digital information, but is well known in theory.

Units derived from bit

There have been some attempts to construct unambiguous terms for bit blocks of some sizes.[1] Terms in italic are strictly jargon, not serve as units (in the proper sense) and not very common.

  • 2 bits: crumb, quad, quarter, tayste, tydbit
  • 4 bits: nibble, nybble, sometimes "half-byte"
  • 5 bits: nickel, nyckle
  • 8 bits: byte, octet
  • 10 bits: deckle
  • 16 bits: plate, playte, chomp, chawmp (on a 32-bit machine)
  • 18 bits: chomp, chawmp (on a 36-bit machine)
  • 32 bits: dinner, dynner, gawble (on a 32-bit machine)
  • 48 bits: gobble, gawble (under circumstances that remain obscure)

The following therms allows precise meaning on bits quantities:

  • 1 bit is binary digit
  • 8 bits: byte or octet, 1B(yte) = 8b(its)
  • 16 bits: doublet
  • 32 bits: quadlet
  • 64 bits: octlet

Byte

Prefixes for bit and byte
Decimal
Value SI
10001 k kilo-
10002 M mega-
10003 G giga-
10004 T tera-
10005 P peta-
10006 E exa-
10007 Z zetta-
10008 Y yotta-
Binary
Value IEC JEDEC
10241 Ki kibi- K kilo-
10242 Mi mebi- M mega-
10243 Gi gibi- G giga-
10244 Ti tebi-
10245 Pi pebi-
10246 Ei exbi-
10247 Zi zebi-
10248 Yi yobi-
Main article: Octet (computing)

Large amounts of information are almost always counted in bytes rather than bits, and it is generally used as an atomic unit when addressing memory. See below a clarification of the term byte.

Kilobyte

Whether used to denote 1024 bytes (a kibibyte, or KiB), or more correctly, 1000 bytes (kB), this is a convenient order of magnitude to express:

Megabyte

Units megabyte MB = 1000000 bytes and mebibyte MiB = 1024 KiB = 1048576 bytes.

Electronic memory is commonly measured in mebibytes, but hard disks are (or were) measured mainly in megabytes.


Gigabyte

Units gigabyte GB = 109 bytes and gibibyte GiB = 1024 MiB = 230 bytes.


Terminology

What is "byte"?

Main article: Byte

The word "byte" has two closely related meanings:

  1. A contiguous sequence of a fixed number of bits (binary digits).
  2. A contiguous sequence of bits within a binary computer that comprises the smallest addressable sub-field of the computer's natural word-size.

In modern computing, the use of a byte to mean 8 bits has become nearly ubiquitous in both senses. The term octet is used in very strict speech (such as RFCs) to avoid any ambiguity.

SI vs. Binary prefixes

Main article: Binary prefix

The prefixes historically used for byte measurements are usually the same as the SI prefixes used for other measurements, but have slightly different values. The former are based on powers of 1,024 (210), a convenient binary number, while the SI prefixes are based on powers of 1,000 (103), a convenient decimal number. The table below illustrates these differences.

Prefix Name SI Meaning Binary meaning Size difference
k kilo 103   = 10001 210 = 10241 2.40%
M mega 106   = 10002 220 = 10242 4.86%
G giga 109   = 10003 230 = 10243 7.37%
T tera 1012 = 10004 240 = 10244 9.95%
P peta 1015 = 10005 250 = 10245 12.59%
E exa 1018 = 10006 260 = 10246 15.29%
Z zetta 1021 = 10007 270 = 10247 18.67%

Sometimes "K" is used instead of "k". The use of "K" as a prefix has no meanings for the SI.

In 1998, the IEC, then the IEEE, published a new standard describing binary prefixes:

Prefix Name
kibi binary kilo 1 kibibyte (KiB) 210 bytes 1024 B
mebi binary mega 1 mebibyte (MiB) 220 bytes 1024 KiB
gibi binary giga 1 gibibyte (GiB) 230 bytes 1024 MiB
tebi binary tera 1 tebibyte (TiB) 240 bytes 1024 GiB
pebi binary peta 1 pebibyte (PiB) 250 bytes 1024 TiB
exbi binary exa 1 exbibyte (EiB) 260 bytes 1024 PiB

References

  1. ^ nybble reference.com sourced from Jargon File 4.2.0, accessed 2007-08-12
  1. ^ nybble reference.com sourced from Jargon File 4.2.0, accessed 2007-08-12
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