Units of information

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In digital 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 information contained in messages and the entropy of random variables.

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 b 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 log2 8 = 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. [3]
Base b = 10
the unit is called decimal digit , hartley , ban, decit, or dit, and is equal to log2 10 (≈ 3.322) bits. [1] [4] [5] [6]
Base b = e, the base of natural logarithms
the unit is called a nat , nit, or nepit (from Neperian), and is worth log2e (≈ 1.443) bits. [1]

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. An 8-bit 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). 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 number of possible values as one hexadecimal digit has. [7]

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 32 bits, but other past and current architectures use words with 4, 8, 9, 12, 13, 16, 18, 20, 21, 22, 24, 25, 29, 30, 31, 32, 33, 35, 36, 38, 39, 40, 42, 44, 48, 50, 52, 54, 56, 60, 64, 72 [8] 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.

SymbolPrefix SI meaning Binary useSize 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%
Rronna1027 = 10009290 = 1024923.79%
Qquetta1030 = 1000102100 = 10241026.77%

In the past, uppercase K has been used instead of lowercase k to indicate 1024 instead of 1000. However, this usage was not consistently applied.

On the other hand, for external storage systems (such as optical discs), the SI prefixes are commonly used with their decimal values (powers of 10). Many attempts have sought to resolve the confusion by providing alternative notations for power-of-two multiples. The International Electrotechnical Commission (IEC) issued a standard for this purpose by defining a series of binary prefixes that use 1024 instead of 1000 as the main radix: [9]

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
Zizebi, binary zetta1 zebibyte (ZiB)270 bytes1024 EiB
Yiyobi, binary yotta1 yobibyte (YiB)280 bytes1024 ZiB

The JEDEC memory standard JESD88F notes that the definitions of kilo (K), giga (G), and mega (M) based on powers of two are included only to reflect common usage, but are otherwise deprecated. [10]

Size examples

Obsolete and unusual units

Several other units of information storage have been named:

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

See also

Notes

  1. ↑ However, if the SI guideline to include a space before the unit is ignored, 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 the most basic unit of information in computing and digital communication. 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, on/off, or +/− are also widely used.

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 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 bit endianness.

<span class="mw-page-title-main">Binary-coded decimal</span> System of digitally encoding numbers

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 that indicates a multiple of a unit of measurement by an integer power of two. The most commonly used binary prefixes are kibi (symbol Ki, meaning 210 = 1024), mebi (Mi, 220 = 1048576), and gibi (Gi, 230 = 1073741824). They are most often used in information technology as multipliers of bit and byte, when expressing the capacity of storage devices or the size of computer files.

<span class="mw-page-title-main">Gigabyte</span> Unit of digital information

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.

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 provides 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 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.

<span class="mw-page-title-main">Nibble</span> Four-bit unit of digital storage

In computing, a nibble (occasionally nybble, nyble, or nybl 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 telecommunications 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 (0–F) and called a hex digit.

In computer architecture, 8-bit integers or other data units are those that are 8 bits wide. Also, 8-bit central processing unit (CPU) and arithmetic logic unit (ALU) architectures are those that are based on registers or data buses of that size. Memory addresses for 8-bit CPUs are generally larger than 8-bit, usually 16-bit. 8-bit microcomputers are microcomputers that use 8-bit microprocessors.

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

In computing, a word is the natural unit of data used by a particular processor design. A word is a fixed-sized datum handled as a unit by the instruction set or the hardware of the processor. The number of bits or digits in a word is an important characteristic of any specific processor design or computer architecture.

File size is a measure of how much data a computer file contains or, alternately, how much storage it consumes. Typically, file size is expressed in units of measurement based on the byte. By convention, file size units use either a metric prefix or a binary prefix.

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. IEEE 1541-2021 revises and supersedes IEEE 1541–2002, which is 'inactive'.

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/IEC 80000, Quantities and units, is an international standard describing 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). It serves as a style guide for using physical quantities and units of measurement, formulas involving them, and their corresponding units, in scientific and educational documents for worldwide use. The ISO/IEC 80000 family of standards was completed with the publication of the first edition of Part 1 in November 2009.

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.

In telecommunications, data transfer rate is the average number of bits (bitrate), characters or symbols (baudrate), or data blocks per unit time passing through a communication link in a data-transmission system. Common data rate units are multiples of bits per second (bit/s) and bytes per second (B/s). For example, the data rates of modern residential high-speed Internet connections are commonly expressed in megabits per second (Mbit/s).

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

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.

References

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  9. ↑ ISO/IEC standard is ISO/IEC 80000-13:2008. 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
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