# Number Systems

Number Systems:number is a mathematical object used to count, measure, and label. The original examples are the natural numbers1, 2, 3, 4, and so forth. For being manipulated, individual numbers need to be represented by symbols, called numerals; for example, “5” is a numeral that represents the number five. As only a small number of symbols can be memorized, basic numerals are commonly organized in a numeral system, which is an organized way to represent any number.

## What is Number System?

A number system is a system of writing for expressing numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner. It provides a unique representation to every number and represents the arithmetic and algebraic structure of the figures. It also allows us to operate arithmetic operations like addition, subtraction, and division. Different number systems are mentioned below.

1. Decimal number system (Base- 10)
2. Binary number system (Base- 2)
3. Octal number system (Base-8)
4. Hexadecimal number system (Base- 16)

Computer numeral system When we type any letter or word, the computer translates them into numbers since computers can understand only numbers. A computer can understand only a few symbols called digits, and these symbols describe different values depending on the position they hold in the number. The value of any digit in a number can be determined by -The digit -Its position in the number -The base of the number system

## Decimal Number System

Decimal number system has base 10 because it uses ten digits from 0 to 9. In decimal number system, the positions successive to the left of the decimal point represent units, tens, hundreds, thousands and so on. Every position shows a particular power of the base (10). For example, the decimal number 1457 consists of the digit 7 in the units position, 5 in the tens place, 4 in the hundreds position, and 1 in the thousands place whose value can be written as (1×1000) + (4×100) + (5×10) + (7×1) (1×103) + (4×102) + (5×101) + (7×1) 1000 + 400 + 50 + 7 1457