﻿ Numerical digit

# Numerical digit

A number of characters or a number ( derived from Arabic aṣ - sIFR " zero, nothing," the Sunya turn Sanskrit, " empty " translated ) is a character that is used for the representation of numbers. Such a representation consists of one or more digits (for example, a sequence of digits ), and optionally other symbols such as pre-and separators. The respective representation of a number depends on the number system used.

Often the names numerals and numeral are used interchangeably. However, the concept of number is etymologically closely connected with the place value system. Because digit means - as in the introduction we have already noted - "nothing" or " zero " and numeral for zero were for the most part in value systems - who need them - used. The term contrast, the number stands for mathematical abstractions, which are indistinguishable from digits.

## History

In different cultures, there have been different number fonts, with numbers, letters or symbols were used as numerals. The simplest numeral are strokes, the number representing the desired number.

Today, the so-called Arabic numerals ( in regionally different variations ) are predominant.

## Numeric value and importance

Each digit represents a number, the numeric value, where numbers are used with the value zero only in value systems. The same numeric value can be represented in different number systems by different digits. To symbolize both the decimal digit " 5" and the Roman numeral "V" the number five. On the other hand, the same number in different number systems represent different numbers. Example: " C " means hexadecimal Twelve, in the Roman system but hundreds.

Digits in addition systems symbolize regardless of their position the same number. In contrast, there is a digit in a place value system for the product of numerical value and importance. The significance is that power of the base, which corresponds to the position of the digit in the number sequence. Thus, for example, is the " 3 " to " 13 " for three whole, in " 0.354 ", however, for three-tenths, and in the hexadecimal " 3B " for three times 16

## Number Systems

Each number system uses only a certain amount of characters and uses them in accordance with specified rules. Strings that do not follow these rules, are not valid number symbols.

The most common value systems are the decimal base 10, the binary or dual system to the base 2 and the hexadecimal to base 16

The most common addition system is, beside the Unärsystem ( " tally " ), the Roman.

## Number representation

A number is shown in different number systems in general by various number sequences. Thus, for example, ten decimal written as "10" in binary as " 1010 " in hexadecimal as "A" and Roman as "X" the number.

Conversely symbolizes a sequence of numbers in different number systems, in which it is defined, usually different numbers. For example, the digits " 10 " in all value systems symbolizes the respective base ( decimal 10, binary 2, hexadecimal, 16, ...). In the Roman system, it is not a valid number symbol.

Within a number system, each valid number symbol accurately represents a number. Conversely, a number but are represented by different sequences of digits, such as, for example, the decimal number seven by " 7", " 007 ", " 7.0 ", " 07.0000 " or "".