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Units of information

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Units of information

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 information contents or entropy of random variables.

The most common units are the bit, the capacity of a system which can exist in 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 (binary power prefixes). Information capacity is a dimensionless quantity.

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,[1] which was further formalized by Claude Shannon in 1945: the information that can be stored in a system is proportional to the logarithm logb N of the number N of possible states of that system. Changing the basis 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 logc N = (logc b) logb N. Therefore, the choice of the basis 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 b possible states.

When b is 2, the unit is the shannon, equal to the information content of one "bit" (a contraction 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:

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 sometimes 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 the integers 0 to 255, or -128 to 127. The IEEE 1541-2002 standard specifies "B" (upper case) as the symbol for byte. 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.[6]

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 8, 24, 32, 36, 56, 64, 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 Page (computer memory)s.

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 misused 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 disks), 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:[7]
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
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.[8]

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 MB - 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
  • 15 GB - amount of storage Google offers for free.[9]
  • 8/16 GB - size of a normal flash drive
  • 4 TB - The size of a $150 hard disk (as of late 2014)
  • 966 EB - prediction of the volume of the whole internet in 2015

Obsolete and unusual units

Several other units of information storage have been named.[6]

  • 1 bit: sniff.
  • 2 bits: crumb,[10] quad, quarter, tayste, tydbit, semi-nibble.
  • 3 bits: triad, triade[11][12]
  • 5 bits: nickel, nyckle.
  • 6 bits: byte (in early IBM machines using BCD alphamerics).
  • 10 bits: decle,[13] deckle, dyme.
  • 16 bits: wyde,[14] doublet,[15] plate, playte, chomp, chawmp (on a 32-bit machine).
  • 18 bits: chomp, chawmp (on a 36-bit machine).
  • 32 bits: quadlet,[16] dinner, dynner, gawble (on a 32-bit machine).
  • 48 bits: gobble, gawble (under circumstances that remain obscure).
  • 64 bits: octlet.[17]
  • 128 bits: hexlet.[18]
  • 16 bytes: paragraph.
  • 6 trits: tryte [19]

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

References

  1. ^ a b c Norman Abramson (1963), Information theory and coding. McGraw-Hill.
  2. ^ Donald E. Knuth, The Art of Computer Programming, vol.2: Seminumerical algorithms.
  3. ^ Shanmugam (2006), Digital and Analog Computer Systems.
  4. ^ Gregg Jaeger (2007), [1]Quantum information: an overview'
  5. ^ I. Ravi Kumar (2001), Comprehensive Statistical Theory of Communication.
  6. ^ a b Nybble at dictionary reference.com; sourced from Jargon File 4.2.0, accessed 2007-08-12
  7. ^ ISO/IEC standard is ISO/IEC 80000-13:2008. Not publicly available. This standard cancels and replaces subclauses 3.8 and 3.9 of IEC 60027-2:2005. The only significant change is the addition of explicit definitions for some quantities. ISO Online Catalogue
  8. ^
  9. ^
  10. ^
  11. ^
  12. ^
  13. ^
  14. ^
  15. ^
  16. ^
  17. ^
  18. ^
  19. ^

External links

  • Representation of numerical values and SI units in character strings for information interchanges
  • Bit Calculator - Convert between bit, byte, kilobit, kilobyte, megabit, megabyte, gigabit, gigabyte
  • Paper on standardized units for use in information technology
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