Units of information

Comparison of units of information: bit, trit, nat, ban. Quantity of information is the height of bars. Dark green level is the "nat" unit.

Capacity of some standard data storage system or communication channel, used to measure the capacities of other systems and channels.

- Units of information

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Information

Processed, organized and structured data.

Partial map of the Internet, with nodes representing IP addresses
Galactic (including dark) matter distribution in a cubic section of the Universe
Information embedded in an abstract mathematical object with symmetry breaking nucleus
Visual representation of a strange attractor, with converted data of its fractal structure

The bit is a typical unit of information.

Entropy (information theory)

Average level of "information", "surprise", or "uncertainty" inherent to the variable's possible outcomes.

Two bits of entropy: In the case of two fair coin tosses, the information entropy in bits is the base-2 logarithm of the number of possible outcomes; with two coins there are four possible outcomes, and two bits of entropy. Generally, information entropy is the average amount of information conveyed by an event, when considering all possible outcomes.

The different units of information (bits for the binary logarithm

Bit

Comparison of units of information: bit, trit, nat, ban. Quantity of information is the height of bars. Dark green level is the "nat" unit.

The bit is the most basic unit of information in computing and digital communications.

Byte

Percentage difference between decimal and binary interpretations of the unit prefixes grows with increasing storage size

The byte is a unit of digital information that most commonly consists of eight bits.

Ternary numeral system

A ternary numeral system (also called base 3 or trinary) has three as its base.

Use of ternary numbers to balance an unknown integer weight from 1 to 40 kg with weights of 1, 3, 9 and 27 kg (4 ternary digits actually gives 34 = 81 possible combinations: −40 to +40, but only the positive values are useful)

One trit is equivalent to log2 3 (about 1.58496) bits of information.

Octet (computing)

Comparison of units of information: bit, trit, nat, ban. Quantity of information is the height of bars. Dark green level is the "nat" unit.

The octet is a unit of digital information in computing and telecommunications that consists of eight bits.

Logarithmic scale

Way of displaying numerical data over a very wide range of values in a compact way—typically the largest numbers in the data are hundreds or even thousands of times larger than the smallest numbers.

A logarithmic scale from 0.1 to 100
Semi-log plot of the Internet host count over time shown on a logarithmic scale
The two logarithmic scales of a slide rule
Map of the solar system and distance to Alpha Centauri using a logarithmic scale.
Various scales: lin–lin, lin–log, log–lin, and log–log. Plotted graphs are: y = 10x ( red ), y = x ( green ), y = loge(x) ( blue ).
Plot on log–log scale of equation of a line

Examples of logarithmic units include units of data storage capacity (bit, byte), of information and information entropy (nat, shannon, ban), and of signal level (decibel, bel, neper).

Orders of magnitude (data)

Usually a factor of ten.

Plots of logarithm for bases 0.5, 2, and e

This article presents a list of multiples, sorted by orders of magnitude, for units of information measured in bits and bytes.

Binary logarithm

[[File:Binary logarithm plot with ticks.svg|thumbnail|right|upright=1.35|Graph of

Leonhard Euler was the first to apply binary logarithms to music theory, in 1739.
A 16-player single elimination tournament bracket with the structure of a complete binary tree. The height of the tree (number of rounds of the tournament) is the binary logarithm of the number of players, rounded up to an integer.
Binary search in a sorted array, an algorithm whose time complexity involves binary logarithms
A microarray for approximately 8700 genes. The expression rates of these genes are compared using binary logarithms.
HP-35 scientific calculator (1972). The log and ln keys are in the top row; there is no log2key.

In information theory, the definition of the amount of self-information and information entropy is often expressed with the binary logarithm, corresponding to making the bit the fundamental unit of information.

Chen–Ho encoding

Memory-efficient alternate system of binary encoding for decimal digits.

Arithmetic values thought to have been represented by parts of the Eye of Horus

Chen–Ho encoding is limited to encoding sets of three decimal digits into groups of 10 bits (so called declets).