INTRODUCTION OF NUMBER SYSTEM

The number system or the numeral system is the system of naming or representing numbers. We know that a number is a mathematical value that helps to count or measure objects and it helps in performing various mathematical calculations. There are different types of number systems in Maths like ,

•    Decimal Number System
•    Binary Number System
•    Octal Number System
•    Hexadecimal Number System

 

DECIMAL NUMBER SYSTEM (Base- 10)

The decimal number system has a base of 10 because it uses ten digits from 0 to 9. In the decimal number system, the positions successive to the left of the decimal point represent units, tens, hundreds, thousands and so on. This system is expressed in Decimal Numbers. Every position shows a particular power of the base (10).

Example of Decimal Number System:

The decimal number 2547 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:

(2×10³) + (5×10²) + (4×10¹) + (7×10⁰)

(2×1000) + (5×100) + (4×10) + (7×1)

2000 + 500 + 40 + 7

2547

 

BINARY NUMBER SYSTEM(Base- 2)

The base 2 number system is also known as the 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, 1101011 is a binary number.

We can convert any system into binary and vice versa.

Example :-

Write (28)₁₀ as a binary number.

Solution:

 

Base 2 Number System Example

∴ (28)₁₀ = 11100₂ 

OCTAL NUMBER SYSTEM(Base- 8)

In the Octal Number System, the base is 8 and it uses numbers from 0 to 7 to represent numbers. Octal numbers are commonly used in computer applications. Converting an octal number to decimal is the same as decimal conversion and is explained below using an example.

Example: Convert 239₁₀ into decimal.

Solution = 354₈

Hexadecimal Number System(Base- 16)

In the hexadecimal system, numbers are written or represented with base 16. In the hex system, the numbers are first represented just like in the decimal system, i.e. from 0 to 9. Then, the numbers are represented using the alphabet from A to F. The below-given table shows the representation of numbers in the Hexadecimal Number System.