# numeration

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## numeration

numeration, in mathematics, process of designating numbers 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, which uses base 10. Thus, in the decimal system, the numeral 342 means (3×102)+(4×101)+(2×100), or 300+40+2. The binary system 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 (1×22)+(1×21)+(1×20), 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 (2×122)+(4×121)+(11×120), 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.

## 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
References in periodicals archive ?
When asked what type of mathematical knowledge, thinking, and skills students should develop in kindergarten to be successful in Grade 1, educators indicated that kindergarten students should develop mathematical knowledge, skills, and thinking associated with Number Sense and Numeration (n = 47), Problem Solving (n = 29), and Geometry and Spatial Sense (n = 20).
It would be impossible for the computation to 'know' which Case to assign to which nominal before further syntactic manipulations take place--the only way it could "know" this if there were another, entirely separate, computation that preceded the main syntactic computations from which the numeration itself could be derived.
From the above process, the numeration approximation system of solutions on finite dimensional space [H.sup.c] is given according to manifold under the proper parameter for Swift-Hohenberg equation, which can be done by computer to numerate it based on this reduced system according to above idea.
The Mayans, like the Babylonians, only used their zero for place numeration. The Mayan zero was only used for counting and never entered into arithmetic calculations such as multiplication or division.
(2) The second symmetry of the system: interchange of reactances with odd and even numeration in its positions:
He pointed out that medical services like vaccines, therapy and surgeries will be rendered to pets free of charge, adding that the department would adopt electronic numeration by sim cards which have been already activated in the new project.
Sama was the lead engineer in the design and implementation of the controls and interface for the Fan Assessment Numeration Systems (FANS) project.
In Estonia, radio frequencies, numeration resources and universal service providing is administered by the Economy and Communications Ministry.
(Possible answers: people's language and writing systems; the way they spend their free time; current military strategies; methods of counting and numeration.)
In this ALC, 20 female students will be educated to read and write their names and know the numeration.

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