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Units of information

Unit of measure for digital data

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Through Unit of measurement, Computing and Information

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.

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