**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.

**Decimal**number system (Base- 10)- Binary number system (Base- 2)
- Octal number system (Base-8)
- 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)

(1×10^{3}) + (4×10^{2}) + (5×10^{1}) + (7×1)

1000 + 400 + 50 + 7

1457

**Base 2 Number System**

Base 2 number systems are also known as Binary number system wherein, only two binary digits exist, i.e., 0 and 1. Specifically, the usual base-2 is a radix of 2. The figures described under this system are known as binary numbers which are the combination of 0 and 1. For example, 110101 is a binary number.

We can convert any system into binary and vice versa.

For example, to write (14)_{10} as binary number

Solution:

(14)_{10} = 1110_{2}

**Base 10 Number System**

This system is expressed in decimal numbers. The base to the decimal is 10. This shows that there are ten symbols, 0 to 9. Similarly, the system using the symbols 0, 1, two will be of base 3, four symbols will be of base 4 and so on.

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