# numeration

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## numeration,

in mathematics, process of designating numbers**number,**

entity describing the magnitude or position of a mathematical object or extensions of these concepts.

**The Natural Numbers**

Cardinal numbers describe the size of a collection of objects; two such collections have the same (cardinal) number of objects if their

**.....**Click the link for more information. according to any particular system; the number designations are in turn called numerals. In any place value system of numeration, a base number must be specified, and groupings are then made by powers of the base number. The position of a numeral in a grouping indicates which power of the base it is to be multiplied by. The most widely used system of numeration is the decimal system

**decimal system**

[Lat.,=of tenths], numeration system based on powers of 10. A number is written as a row of digits, with each position in the row corresponding to a certain power of 10.

**.....**Click the link for more information. , which uses base 10. Thus, in the decimal system, the numeral 342 means (3×10

^{2})+(4×10

^{1})+(2×10

^{0}), or 300+40+2. The binary system

**binary system,**

numeration system based on powers of 2, in contrast to the familiar decimal system, which is based on powers of 10. In the binary system, only the digits 0 and 1 are used.

**.....**Click the link for more information. uses base 2 and is important because of its application to modern computers. Whereas the decimal system uses the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, the binary system uses only the two digits 0 and 1. In the binary system, the numeral 111, for example, means (1×2

^{2})+(1×2

^{1})+(1×2

^{0}), i.e., 4+2+1, or 7, in the decimal system. The decimal numeral 7 and the binary numeral 111 are thus designations for the same number. The duodecimal system uses 12 as a base and has some advantages arising from the fact that 12 is divisible by four different numbers—2, 3, 4, 6—other than 1 and 12 itself. The base 12 requires the use of 12 different digits. Thus, in addition to the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, the symbols X (called "dek") and E (called "el") to represent the numbers 10 and 11 have been suggested by the Duodecimal Society of America. The duodecimal numeral 24E, for example, means (2×12

^{2})+(4×12

^{1})+(11×12

^{0}), i.e., (2×144)+(4×12)+(11×1), or 347, in the decimal system. The hexadecimal system, or base 16, uses the digits 0 through 9 and the letters A through F (or a through f) to represent 16 different digits. Hexadecimal numeration is often used in computing because it more readily translates the binary system used by computers than decimal numeration does. A computer byte, which is composed of 8 bits (binary digits), must be represented by the numbers 0 through 255 in the decimal system, but in the hexadecimal system it is represented by 00 through FF. The decimal, binary, duodecimal, and hexadecimal systems of numeration constitute only four examples. The ancient Babylonians used a system of base 60, which still survives in our smaller divisions both of time and of angle, i.e., minutes and seconds. In general, any integer

*n*greater than one can be used as the base of a numeration system, and the system will employ

*n*different digits.

The Columbia Electronic Encyclopedia™ Copyright © 2013, Columbia University Press. Licensed from Columbia University Press. All rights reserved. www.cc.columbia.edu/cu/cup/

## numeration

[‚nü·mə′rā·shən] (mathematics)

The listing of numbers in their natural order.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## numeration

**1.**the act or process of writing, reading, or naming numbers

**2.**a system of numbering or counting

Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005

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