Numeral system

Numerals or numeral systems is the collection of notations or symbols to represent numbers. Like letters in a language which represent our speech graphically, numerals also represent number graphically. So A numeral is a symbol or name that stands for a number. For example 6, 70 and fourteen etc. All are numerals. 

 

Numeral systems are sometimes called number systems but they are not as same. A number is an abstract concept and a numeral is a way to express a number. A number two can be written in different numerals such as 2, II, or 10 (in binary system). What we write is a numeral, but most often we call them as numbers. That's why a confusion always remains over numeral and number.

There are different kinds of numeral system. It can be classified as positional or by base. Suppose Roman numerals, Indian numerals etc. are positional numeral system and binary, decimal are by base. Binary numeral has base 2 and decimal have base 10.

In real world, Decimal Numeral System is widely used. In every calculations at home, office, and in business, this numeral system is used. It has base 10(ten). Decimal numeral system includes a zero (0) and use symbols (1, 2, 3, 4, 5, 6, 7, 8, and 9)  to represent any number, no matter how large or how small. 

Binary numeral system has base 2 (two). It use 0 and 1 to represent any number. It is used in digital device (in computer and other electronic devices).

Below is example of Decimal and Binary numerals :

Decimal 0 -> Binary  0

Decimal 1 -> Binary  1

Decimal 2 -> Binary  10

Decimal 3 -> Binary  11

Decimal 4 -> Binary  100

Decimal 7 -> Binary  111

Decimal 20 -> Binary  10100

Hexadecimal numeral system has base 16. It uses sixteen distinct symbols. 0–9 to represent values zero to nine, and A, B, C, D, E, F  to represent values ten to fifteen. Hexadecimal numerals are widely used in computer system design.

Below is example of Decimal and Hexadecimal numerals :

Decimal 0  -> Hexadecimal  0

Decimal 1  -> Hexadecimal  1

Decimal 30 -> Hexadecimal  1E

Decimal 41 -> Hexadecimal  29