What is a Number System?

Last Updated : 25 Apr, 2025

A number system is a way of writing numbers using specific symbols or digits. It helps us represent numbers mathematically. There are different types of number systems, such as the decimal system, binary system, octal system, and hexadecimal system.

Here, we will discuss the types of number systems in detail, along with solved examples.

Types of Number Systems

Based on the base value and the number of allowed digits, number systems are of many types. The four common types of Number Systems are:

Decimal Number System

Number system with a base value of 10 is termed a Decimal number system. It uses 10 digits i.e. 0-9 for the creation of numbers. Here, each digit in the number is at a specific place with a place value of a product of different powers of 10. Here, the place value is termed from right to left as first place value called units, second to the left as Tens, so on Hundreds, Thousands, etc.

For example, 10264 has place values as,
(1 × 10⁴) + (0 × 10³) + (2 × 10²) + (6 × 10¹) + (4 × 10⁰)
= 1 × 10000 + 0 × 1000 + 2 × 100 + 6 × 10 + 4 × 1
= 10000 + 0 + 200 + 60 + 4
= 10264

Binary Number System

Number System with base value 2 is termed as Binary number system. It uses 2 digits i.e. 0 and 1 for the creation of numbers. The numbers formed using these two digits are termed Binary Numbers. The binary number system is very useful in electronic devices and computer systems because it can be easily performed using just two states ON and OFF i.e. 0 and 1.

Decimal Numbers 0-9 are represented in binary as: 0, 1, 10, 11, 100, 101, 110, 111, 1000, and 1001
For example, 14 can be written as (1110)₂, 19 can be written as (10011)₂and 50 can be written as (110010)₂.

Octal Number System

Octal Number System is one in which the base value is 8. It uses 8 digits i.e. 0-7 for the creation of Octal Numbers. Octal Numbers can be converted to Decimal values by multiplying each digit with the place value and then adding the result.

Octal Numbers are useful for the representation of UTF-8 numbers.
Example,
(135)₁₀ can be written as (207)₈
(215)₁₀ can be written as (327)₈

Hexadecimal Number System

The Number System with base value 16 is termed as Hexadecimal Number System. It uses 16 digits for the creation of its numbers. Digits from 0-9 are taken like the digits in the decimal number system but the digits from 10-15 are represented as A-F i.e. 10 is represented as A, 11 as B, 12 as C, 13 as D, 14 as E, and 15 as F.

Hexadecimal Numbers are useful for handling memory address locations.The hexadecimal number system provides a condensed way of representing large binary numbers stored and processed.