Binary Number System . Premium Decimal Number System.

 

Binary Number System. Premium Decimal Number System.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, 110101 is a binary number.

Do you know Number system ?

Click the link https://smword007.blogspot.com/2022/01/What-is-Numbe-System--premium-Definition-of-Number-Systems..html

What is Binary Number System?

What is Decimal Number System?

What is Octal Number System?

What is Hexadecimal Number System?

Binary Number System (Base 2 Number System):

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, 110101 is a binary number.

We can convert any system into binary and vice versa.

Example

Write (14)₁₀ as a binary number.

Solution:

Base 2 Number System Example

∴ (14)₁₀ = (1110)₂

Decimal Number System (Base 10 Number System):

The decimal number system has a base 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: Convert (1011)₂ into decimal.

Solution:

1011   =   1 x 2³+ 0 x 2² + 1 x 2¹ + 1 x 2⁰

           =   1 x 8 + 0 +1 x 2 + 1 x 1                                       

           =   8 + 0 + 2 + 1

           =   11

v  (1011)₂ = (11)₁₀

Octal Number System (Base 8 Number System):

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 (215)₈ into decimal.

Solution:

(215)₈ = 2 × 8² + 1 × 8¹ + 5 × 8⁰

= 2 × 64 + 1 × 8 + 5 × 1

= 128 + 8 + 5

= (141)₁₀

Hexadecimal Number System (Base 16 Number System):

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