Units of information

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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.

Contents

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. Units of information.svg
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 of N possible states of that system, denoted logbN. 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 logcN = (logcb) logbN. 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 [2] ). 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 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, [nb 1] 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, nybble or nyble. 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. [7]

Crumb

A pair of two bits or a quarter byte was called a crumb, [8] often used in early 8-bit computing (see Atari 2600, ZX Spectrum).[ citation needed ] 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, [9] 8, [9] 9, [9] 12, [9] 13, [9] 16, [9] 18, [9] 20, [9] 21, [9] 22, [9] 24, [9] 25, [9] 26, 29, [9] 30, [9] 31, [9] 32, [9] 33, [9] 35, [9] 36, [9] 38, [9] 39, [9] 40, [9] 42, [9] 44, [9] 48, [9] 50, [9] 52, [9] 54, [9] 56, [9] 60, [9] 64, [9] 72, [9] 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
1000103kbit kilobit
10002106Mbit megabit
10003109Gbit gigabit
100041012Tbit terabit
100051015Pbit petabit
100061018Ebit exabit
100071021Zbit zettabit
100081024Ybit yottabit
Binary
Value IEC JEDEC
1024210Kibit kibibit Kbitkilobit
10242220Mibit mebibit Mbitmegabit
10243230Gibit gibibit Gbitgigabit
10244240Tibit tebibit -
10245250Pibit pebibit -
10246260Eibit exbibit -
10247270Zibit zebibit -
10248280Yibit yobibit -
SymbolPrefix SI Meaning Binary meaningSize difference
kkilo103  = 10001210 = 102412.40%
Mmega106  = 10002220 = 102424.86%
Ggiga109  = 10003230 = 102437.37%
Ttera1012 = 10004240 = 102449.95%
Ppeta1015 = 10005250 = 1024512.59%
Eexa1018 = 10006260 = 1024615.29%
Zzetta1021 = 10007270 = 1024718.06%
Yyotta1024 = 10008280 = 1024820.89%

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: [10]

Multiple-byte units
Decimal
Value Metric
1000kB kilobyte
10002MB megabyte
10003GB gigabyte
10004TB terabyte
10005PB petabyte
10006EB exabyte
10007ZB zettabyte
10008YB yottabyte
Binary
Value IEC JEDEC
1024KiBkibibyteKBkilobyte
10242MiBmebibyteMBmegabyte
10243GiBgibibyteGBgigabyte
10244TiBtebibyte
10245PiBpebibyte
10246EiBexbibyte
10247ZiBzebibyte
10248YiByobibyte
SymbolPrefix
Kikibi, binary kilo1 kibibyte (KiB)210 bytes1024 B
Mimebi, binary mega1 mebibyte (MiB)220 bytes1024 KiB
Gigibi, binary giga1 gibibyte (GiB)230 bytes1024 MiB
Titebi, binary tera1 tebibyte (TiB)240 bytes1024 GiB
Pipebi, binary peta1 pebibyte (PiB)250 bytes1024 TiB
Eiexbi, binary exa1 exbibyte (EiB)260 bytes1024 PiB

The JEDEC memory standards however define uppercase K, M, and G for the binary powers 210, 220 and 230 to reflect common usage. [11]

Size examples

Obsolete and unusual units

Several other units of information storage have been named: [7]

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

See also

Notes

  1. However, the IEC 80000-13 abbreviation "o" for octets can be confused with the postfix "o" to indicate octal numbers in Intel convention .

Related Research Articles

The bit is a basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represented as either "1"or"0", but other representations such as true/false, yes/no, +/, or on/off are common.

The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable unit of memory in many computer architectures. To disambiguate arbitrarily sized bytes from the common 8-bit definition, network protocol documents such as The Internet Protocol (1981) refer to an 8-bit byte as an octet. Those bits in an octet are usually counted with numbering from 0 to 7 or 7 to 0 depending on the endianness. The first bit is number 0, making the eighth bit number 7.

Binary-coded decimal

In computing and electronic systems, binary-coded decimal (BCD) is a class of binary encodings of decimal numbers where each digit is represented by a fixed number of bits, usually four or eight. Sometimes, special bit patterns are used for a sign or other indications.

A binary prefix is a unit prefix for multiples of units in data processing, data transmission, and digital information, notably the bit and the byte, to indicate multiplication by a power of 2.

The gigabyte is a multiple of the unit byte for digital information. The prefix giga- means 109 in the International System of Units (SI). Therefore, one gigabyte is one billion bytes. The unit symbol for the gigabyte is GB.

Giga ( or ) is a unit prefix in the metric system denoting a factor of a short-scale billion or long-scale milliard (109 or 1000000000). It has the symbol G.

In computer science, an integer is a datum of integral data type, a data type that represents some range of mathematical integers. Integral data types may be of different sizes and may or may not be allowed to contain negative values. Integers are commonly represented in a computer as a group of binary digits (bits). The size of the grouping varies so the set of integer sizes available varies between different types of computers. Computer hardware nearly always provide a way to represent a processor register or memory address as an integer.

The kilobyte is a multiple of the unit byte for digital information.

The kilobit is a multiple of the unit bit for digital information or computer storage. The prefix kilo- (symbol k) is defined in the International System of Units (SI) as a multiplier of 103 (1 thousand), and therefore,

The megabyte is a multiple of the unit byte for digital information. Its recommended unit symbol is MB. The unit prefix mega is a multiplier of 1000000 (106) in the International System of Units (SI). Therefore, one megabyte is one million bytes of information. This definition has been incorporated into the International System of Quantities.

Nibble group of four bits (half a "byte"); unit of information

In computing, a nibble (occasionally nybble or nyble to match the spelling of byte) is a four-bit aggregation, or half an octet. It is also known as half-byte or tetrade. In a networking or telecommunication context, the nibble is often called a semi-octet, quadbit, or quartet. A nibble has sixteen (24) possible values. A nibble can be represented by a single hexadecimal digit and called a hex digit.

In computer and machine-based telecommunications terminology, a character is a unit of information that roughly corresponds to a grapheme, grapheme-like unit, or symbol, such as in an alphabet or syllabary in the written form of a natural language.

An order of magnitude is a factor of ten. Thus, four orders of magnitude are a factor of 10,000 or 104.

A unit prefix is a specifier or mnemonic that is prepended to units of measurement to indicate multiples or fractions of the units. Units of various sizes are commonly formed by the use of such prefixes. The prefixes of the metric system, such as kilo and milli, represent multiplication by powers of ten. In information technology it is common to use binary prefixes, which are based on powers of two. Historically, many prefixes have been used or proposed by various sources, but only a narrow set has been recognised by standards organisations.

IEEE 1541-2002 is a standard issued in 2002 by the Institute of Electrical and Electronics Engineers (IEEE) concerning the use of prefixes for binary multiples of units of measurement related to digital electronics and computing.

The octet is a unit of digital information in computing and telecommunications that consists of eight bits. The term is often used when the term byte might be ambiguous, as the byte has historically been used for storage units of a variety of sizes.

ISO 80000 or IEC 80000 is an international standard introducing the International System of Quantities (ISQ). It was developed and promulgated jointly by the International Organization for Standardization (ISO) and the International Electrotechnical Commission (IEC).

The JEDEC memory standards are the specifications for semiconductor memory circuits and similar storage devices promulgated by the Joint Electron Device Engineering Council (JEDEC) Solid State Technology Association, a semiconductor trade and engineering standardization organization.

This timeline of binary prefixes lists events in the history of the evolution, development, and use of units of measure for information, the bit and the byte, which are germane to the definition of the binary prefixes by the International Electrotechnical Commission (IEC) in 1998.

In computing, a syllable is a name for a platform-dependent unit of information storage. Depending on the target hardware, various bit widths are associated with it. Commonly used in the 1960s and 1970s, the term has mostly fallen into disuse in favour of terms like byte or word.

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