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Encyclopedia > Positional system

Positional notation is a system in which each position has a value represented by a unique symbol or character. For each position, the resultant value of each position is the value of that character multiplied by a power of the base number for that numeral system. The position of each character or symbol (usually called a digit) counting from the right determines the power of the base that is to be multiplied by that digit.

For example, in the decimal or base 10 number system, each position starting from the right is a successive power of 10. The first position represents 100, the second position 101, the third 102, the fourth 103, and so on.

Fractional values are indicated by a separator, which varies by locale. Usually this separator is a period or full stop, or a comma. Digits to the right of it are multiplied by the base (10 in this example) raised to a negative power or exponent. The first position to the right of the separator indicates 10-1, the second position 10-2, and so on for each successive position.

The total value of a number in a positional system is the total of each individual multiplication of a digit and its associated base multiplied by itself the number times represented by its position less 1.

As an example, the number 2674 in a base 10 number system is :

( 2 103 ) + ( 6 102 ) + ( 7 101 ) + ( 4 100 )


( 2 1000 ) + ( 6 100 ) + ( 7 10 ) + ( 4 1 )

External Links

  • Base Converter (http://www.cut-the-knot.org/binary.shtml)
  • Implementation of Base Conversion (http://www.cut-the-knot.org/recurrence/conversion.shtml)
  • Conversion of Fractions in Various Bases (http://www.cut-the-knot.org/blue/frac_conv.shtml)
  • Addition and Multiplication Tables in Various Bases (http://www.cut-the-knot.org/blue/SysTable.shtml)

See also Algorism.

  Results from FactBites:
Numeral system - Wikipedia, the free encyclopedia (3590 words)
Numeral systems are sometimes called number systems, but that name is misleading: different systems of numbers, such as the system of real numbers, the system of complex numbers, the system of p-adic numbers, etc., are not the topic of this article.
The sign-value system does not need arithmetic numerals because they are made by repetition (except for Ionic system), and the positional system does not need geometric numerals because they are made by position.
Sexagesimal numerals were a Mixed radix system that retained the alternating base 10 and base 6 in a sequence of cuneiform vertical wedges and chevrons and was by 1950 BC a positional notation system.
Positional notation - Wikipedia, the free encyclopedia (1124 words)
Positional notation or place-value notation is a numeral system in which each position is related to the next by a constant multiplier, a common ratio, called the base (or radix) of that numeral system.
The idea of indicating magnitude by means of position was embodied long ago by the use of the abacus in all its various forms.
The sexagesimal or base sixty system was used for the integral and fractional portions of Babylonian numerals, by Hellenistic astronomers using Greek numerals for the fractional portion only, and is still used for modern time and angles, but only for minutes and seconds.
  More results at FactBites »



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