Units of information.html

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

1 Primary units
2 Units derived from bit
3 Terminology
- 3.1 What is "byte"?
- 3.2 SI vs. Binary prefixes
4 References

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.

We can represent small amount of information just as logarithm of number of states, which have equal probability (see Logarithm#Science). 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 multiples

Decimal
Value	SI
1000	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
1024	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:

the typical sector of a hard disk: 512 bytes = ½ KiB
the classical block size in UNIX filesystems: 1024 bytes = 1 KiB
a CD-ROM sector: 2048 bytes = 2 KiB
a memory page in x86 (since Intel 80386): 4096 bytes = 4 KiB

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.

Please help improve this section by expanding it. Further information might be found on the talk page or at requests for expansion. (June 2008)

Gigabyte

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

Please help improve this section by expanding it. Further information might be found on the talk page or at requests for expansion. (June 2008)

Terminology

What is "byte"?

Main article: Byte

The word "byte" has two closely related meanings:

A contiguous sequence of a fixed number of bits (binary digits).
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

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

Representation of numerical values and SI units in character strings for information interchanges

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