A unit of information is any unit of measure of digital data size. In digital computing, a unit of information is used to describe the capacity of a digital data storage device. In telecommunications, a unit of information is used to describe the throughput of a communication channel. In information theory, a unit of information is used to measure information contained in messages and the entropy of random variables. Due to the need to work with data sizes that range from small to large, units of information cover a wide range of data sizes. Units are defined as multiples of a smaller unit except for the smallest unit which is based on convention and hardware design. Multiplier prefixes are used to describe relatively large sizes. For binary hardware, the most common hardware today, the smallest unit is the bit, which represents a value that is one of two possibilities, typically shown as 0 and 1. The nibble, 4 bits, represents the value of a single hexadecimal digit. The byte (8 bits, 2 nibbles) is possibly the most commonly known and used base unit to describe data size. The word is a size that varies by and has a special importance for a particular hardware context. On modern hardware, a word is typically 2, 4 or 8 bytes, but the size varies dramatically on older hardware. Larger sizes can be expressed as multiples of a base unit via SI metric prefixes (powers of ten) or the newer and generally more accurate IEC binary prefixes (powers of two).
Information theory
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 logb 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 logc N = (logc b) logb 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 b possible states. When b is 2, the unit is the shannon, equal to the information content of one "bit". 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. 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. An 8-bit byte can represent 256 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). 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.
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 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.
Multiplicative prefixes A unit for a large amount of data can be formed using either a metric or binary prefix with a base unit. For storage, the base unit is typically a byte. For communication throughput, a base unit of bit is common. For example, using the metric kilo prefix, a kilobyte is 1000 bytes and a kilobit is 1000 bits. Use of metric prefixes is common. In the context of computing, some of these prefixes (primarily kilo, mega and giga) are used to refer to the nearest power of two. For example, 'kilobyte' often refers to 1024 bytes even though the standard meaning of kilo is 1000.
The International Electrotechnical Commission (IEC) standardized binary prefixes for binary multiples to avoid ambiguity through their similarity to the standard metric terms. These are based on powers of 1024, which is a power of 2.
The JEDEC memory standard JESD88F notes that its inclusion of the definitions of kilo (K), mega (M) and giga (G) based on powers of two are included only to reflect common usage, but that these are otherwise deprecated.
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