Units of information

From Wikipedia, the free encyclopedia

 

In computing and telecommunications, a unit of information is the capacity of some standard data storage system or communication channel, used to measure the capacities of other systems and channels. In information theory, units of information are also used to measure the entropy of random variables and information contained in messages.

The most commonly used units of data storage capacity are the bit, the capacity of a system that has only two states, and the byte (or octet), which is equivalent to eight bits. Multiples of these units can be formed from these with the SI prefixes (power-of-ten prefixes) or the newer IEC binary prefixes (power-of-two prefixes).

Primary units

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

 

In 1928, Ralph Hartley observed a fundamental storage principle, which was further formalized by Claude Shannon in 1945: the information that can be stored in a system is proportional to the logarithm of N possible states of that system, denoted log_b N. Changing the base of the logarithm from b to a different number c has the effect of multiplying the value of the logarithm by a fixed constant, namely log_c N = (log_c b) log_b N. Therefore, the choice of the base b determines the unit used to measure information. In particular, if b is a positive integer, then the unit is the amount of information that can be stored in a system with N possible states.

When b is 2, the unit is the shannon, equal to the information content of one "bit" (a portmanteau of binary digit). A system with 8 possible states, for example, can store up to log₂8 = 3 bits of information. Other units that have been named include:

• Base b = 3: the unit is called "trit", and is equal to log₂ 3 (≈ 1.585) bits.

Units of information

shannon or bit (base 2) nat (base e) trit (base 3) hartley, ban or dit (base 10) qubit (quantum)

• Base b = 10: the unit is called decimal digit, hartley, ban, decit, or dit, and is equal to log₂ 10 (≈ 3.322) bits.
• Base b = e, the base of natural logarithms: the unit is called a nat, nit, or nepit (from Neperian), and is worth log₂ e (≈ 1.443) bits.

The trit, ban, and nat are rarely used to measure storage capacity; but the nat, in particular, is often used in information theory, because natural logarithms are mathematically more convenient than logarithms in other bases.

Units derived from bit

Several conventional names are used for collections or groups of bits.

Byte

Historically, a byte was the number of bits used to encode a character of text in the computer, which depended on computer hardware architecture; but today it almost always means eight bits – that is, an octet. A byte can represent 256 (2⁸) distinct values, such as non-negative integers from 0 to 255, or signed integers from −128 to 127. The IEEE 1541-2002 standard specifies "B" (upper case) as the symbol for byte (IEC 80000-13 uses "o" for octet in French, but also allows "B" in English, which is what is actually being used). Bytes, or multiples thereof, are almost always used to specify the sizes of computer files and the capacity of storage units. Most modern computers and peripheral devices are designed to manipulate data in whole bytes or groups of bytes, rather than individual bits.

Nibble

A group of four bits, or half a byte, is sometimes called a nibble or nybble. This unit is most often used in the context of hexadecimal number representations, since a nibble has the same amount of information as one hexadecimal digit.

Crumb

A pair of two bits or a quarter byte was called a crumb, often used in early 8-bit computing. It is now largely defunct.

Word, block, and page

Computers usually manipulate bits in groups of a fixed size, conventionally called words. The number of bits in a word is usually defined by the size of the registers in the computer's CPU, or by the number of data bits that are fetched from its main memory in a single operation. In the IA-32 architecture more commonly known as x86-32, a word is 16 bits, but other past and current architectures use words with 4, 8, 9, 12, 13, 16, 18, 20, 21, 22, 24, 25, 26, 29, 30, 31, 32, 33, 35, 36, 38, 39, 40, 42, 44, 48, 50, 52, 54, 56, 60, 64, 72, 80 bits or others. 

Some machine instructions and computer number formats use two words (a "double word" or "dword"), or four words (a "quad word" or "quad"). 

Computer memory caches usually operate on blocks of memory that consist of several consecutive words. These units are customarily called cache blocks, or, in CPU caches, cache lines. 

Virtual memory systems partition the computer's main storage into even larger units, traditionally called pages.

Systematic multiples

Terms for large quantities of bits can be formed using the standard range of SI prefixes for powers of 10, e.g., kilo = 10³ = 1000 (as in kilobit or kbit), mega- = 10⁶ = 1000000 (as in megabit or Mbit) and giga = 10⁹ = 1000000000 (as in gigabit or Gbit). These prefixes are more often used for multiples of bytes, as in kilobyte (1 kB = 8000 bit), megabyte (1 MB = 8000000bit), and gigabyte (1 GB = 8000000000bit). 

However, for technical reasons, the capacities of computer memories and some storage units are often multiples of some large power of two, such as 2²⁸ = 268435456 bytes. To avoid such unwieldy numbers, people have often repurposed the SI prefixes to mean the nearest power of two, e.g., using the prefix kilo for 2¹⁰ = 1024, mega for 2²⁰ = 1048576, and giga for 2³⁰ = 1073741824, and so on. For example, a random access memory chip with a capacity of 2²⁸ bytes would be referred to as a 256-megabyte chip. The table below illustrates these differences.

Multiples of bits
Decimal Value SI 1000 103 kbit kilobit 10002 106 Mbit megabit 10003 109 Gbit gigabit 10004 1012 Tbit terabit 10005 1015 Pbit petabit 10006 1018 Ebit exabit 10007 1021 Zbit zettabit 10008 1024 Ybit yottabit	Binary Value IEC JEDEC 1024 210 Kibit kibibit Kbit kilobit 10242 220 Mibit mebibit Mbit megabit 10243 230 Gibit gibibit Gbit gigabit 10244 240 Tibit tebibit - 10245 250 Pibit pebibit - 10246 260 Eibit exbibit - 10247 270 Zibit zebibit - 10248 280 Yibit yobibit -

Symbol	Prefix	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	18.06%
Y	yotta	1024 = 10008	280 = 10248	20.89%

In the past, uppercase K has been used instead of lowercase k to indicate 1024 instead of 1000. However, this usage was never consistently applied.

On the other hand, for external storage systems (such as optical discs), the SI prefixes were commonly used with their decimal values (powers of 10). There have been many attempts to resolve the confusion by providing alternative notations for power-of-two multiples. In 1998 the International Electrotechnical Commission (IEC) issued a standard for this purpose, namely a series of binary prefixes that use 1024 instead of 1000 as the main radix:

Multiples of bytes
Decimal Value Metric 1000 kB kilobyte 10002 MB megabyte 10003 GB gigabyte 10004 TB terabyte 10005 PB petabyte 10006 EB exabyte 10007 ZB zettabyte 10008 YB yottabyte	Binary Value IEC JEDEC 1024 KiB kibibyte KB kilobyte 10242 MiB mebibyte MB megabyte 10243 GiB gibibyte GB gigabyte 10244 TiB tebibyte – 10245 PiB pebibyte – 10246 EiB exbibyte – 10247 ZiB zebibyte – 10248 YiB yobibyte –
Orders of magnitude of data

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

The JEDEC memory standards however define uppercase K, M, and G for the binary powers 2¹⁰, 2²⁰ and 2³⁰ to reflect common usage.

Size examples

• 1 bit – answer to a yes/no question.
• 1 byte – a number from 0 to 255.
• 90 bytes: enough to store a typical line of text from a book.
• 512 bytes = ½ KiB: the typical sector of a hard disk.
• 1024 bytes = 1 KiB: the classical block size in UNIX filesystems.
• 2048 bytes = 2 KiB: a CD-ROM sector.
• 4096 bytes = 4 KiB: a memory page in x86 (since Intel 80386).
• 4 kB: about one page of text from a novel.
• 120 kB: the text of a typical pocket book.
• 1 MiB – a 1024×1024 pixel bitmap image with 256 colors (8 bpp color depth).
• 3 MB – a three-minute song (133 kbit/s).
• 650–900 MB – a CD-ROM.
• 1 GB – 114 minutes of uncompressed CD-quality audio at 1.4 Mbit/s.
• 8/16 GB – two common sizes of USB flash drives.
• 4 TB – the size of a $100 hard disk (as of early 2018).
• 12 TB Largest hard disk drive (as of early 2018)
• 16 TB Largest commercially available solid state drive (as of early 2018)
• 100 TB Largest solid state drive constructed (as of early 2018)
• 1.3 ZB – prediction of the volume of the whole internet in 2016.

Obsolete and unusual units

Several other units of information storage have been named:

• 1 bit: unibit, sniff.
• 2 bits: dibit, crumb, quad, quarter, taste, tayste, tidbit, tydbit, lick, lyck, semi-nibble.
• 3 bits: tribit, triad, triade, tribble.
• 5 bits: pentad, pentade, nickel, nyckle.
• 6 bits: byte (in early IBM machines using BCD alphamerics), hexad, hexade, sextet.
• 7 bits: heptad, heptade.
• 8 bits: octet, now usually called byte
• 10 bits: declet, decle, deckle, dyme.
• 12 bits: slab.
• 15 bits: parcel (on CDC 6600 and CDC 7600).
• 16 bits: doublet, wyde, parcel (on Cray-1), plate, playte, chomp, chawmp (on a 32-bit machine).
• 18 bits: chomp, chawmp (on a 36-bit machine).
• 32 bits: quadlet, tetra, dinner, dynner, gawble (on a 32-bit machine).
• 48 bits: gobble, gawble (under circumstances that remain obscure).
• 64 bits: octlet, octa.
• 96 bits: bentobox (in ITRON OS)
• 128 bits: hexlet.
• 16 bytes: paragraph (on Intel x86 processors).
• 6 trits: tryte.
• combit, comword.

Some of these names are jargon, obsolete, or used only in very restricted contexts.