## Binary number - Wikipedia

The word binary comes from "Bi-" meaning two. We see "bi-" in words such as "bicycle" (two wheels) or "binocular" (two eyes).

It is customary to prefix hexadecimal numbers with 0x and octals with 0. The converter will accept this common notation which is, however, not necessary.

(Note: Both the National Council of Teachers of Mathematics content standards and Common Core State Mathematics Standards emphasize counting and number systems, but not binary number operations explicitly.)

The binary system works under the exact same principles as the decimal system, only it operates in base 2 rather than base 10. In other words, instead of columns being

Anything composed of two parts. In modern computers, information is stored in banks of components that act like switches. Since switches can be either on or off, they have a binary character, and we say that the computer uses “binary arithmetic” to do its work.

The oldest systems of counting used base one. Making marks on a wall, using one mark for each item counted is an example of unary counting. Some old systems of measurement use the duodecimal radix (base twelve). This is shown in English , as there are words such as dozen (12) and gross (144 = 12x12), and lengths such as feet (12 inches ).

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These extremes correspond to a balanced tree (each node except the tree leaves has a left and right child , and all tree leaves are at the same level) and a degenerate tree (each node has only one outgoing branch ), respectively.

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A binary relation is the special case * n* = 2 of an * n* -ary relation * R* ⊆ * A* 1 × … × * A* * n* , that is, a set of * n* -tuples where the * j* th component of each * n* -tuple is taken from the * j* th domain * A* * j* of the relation. An example for a ternary relation on Z × Z × Z is " ... lies between ... and ...", containing . the triples (5,2,8) , (5,8,2) , and (−4,9,−7) .

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mathematics math·e·mat·ics (măth′ə-măt′ĭks) n. (used with a sing. verb) The study of the measurement, properties, and relationships of ...