Number System in Digital Electronics |01|

Number System

⇒ Each number is represented by its base(Radix) in the Number System.

⇒ Here, we learn the four-number system

• Decimal Number System
• Binary Number System
• Octal Number System
• Hexa-Decimal Number System

1. Decimal Number System

⇒ A number system that uses 0 to 9 numbers as symbols to represent any data.

⇒ Symbols of the Decimal Number System: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

⇒ No. of Symbols in the Decimal Number system is 10.

⇒ The Base(Radix) of the decimal Number System is 10.

⇨For Example 2359

    The decimal number system takes it as a (2 x 10^3) + (3 x 10^2) + (5 x 10^1) + (9 x 10^0) 

    

⇨ (2 x 10^3) + (3 x 10^2) + (5 x 10^1) + (9 x 10^0)

 = (2 x 1000) + (3 x 100) + (5 x 10) + (9 x 1)

 = (2000) + (300) + (50) + (9)

 = 2359 in Decimal

2. Binary Number System

⇒ A number system that uses 0 & 1 numbers as symbols to represent any data.

⇒ 1 represents ON(High voltage) and 0 represents OFF(Low voltage) in circuit.

⇒ Symbols of the Decimal Number System: 0, 1

⇒ No. of Symbols in the Decimal Number system is 2.

⇒ The Base(Radix) of the decimal Number System is 2.

⇨For Example 10011

    The decimal number system takes it as a (1 x 2^4) + (0 x 2^3) + (0 x 2^2) + (1 x 2^1) + (1 x 2^0)

    

⇨ (1 x 2^4) + (0 x 2^3) + (0 x 2^2) + (1 x 2^1) + (1 x 2^0)

 = (1 x 16) + (0 x 8) + (0 x 4) + (1 x 2) + (1 x 1)

 = (16) + (0) + (0) + (2) + (1)

 = 19 in decimal

3. Octal Number System

⇒ A number system that uses 0 to 7 numbers as symbols to represent any data.

⇒ Symbols of the Decimal Number System: 0, 1, 2, 3, 4, 5, 6, 7

⇒ No. of Symbols in the Decimal Number system is 8.

⇒ The Base(Radix) of the decimal Number System is 8.

⇨For Example 1234

    The decimal number system takes it as a (1 x 8^3) + (2 x 8^2) + (3 x 8^1) + (4 x 8^0) 

    

⇨ (1 x 8^3) + (2 x 8^2) + (3 x 8^1) + (4 x 8^0)

 = (1 x 512) + (2 x 64) + (3 x 8) + (4 x 1)

 = (512) + (128) + (24) + (4)

 = 668 in Decimal

4. Hexa-Decimal Number System (Positional number system)

⇒ A number system that uses 0 to 9 and A to F numbers as symbols to represent any data.

⇒ Symbols of the Decimal Number System: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

⇒ Where, 

     A=10, B=11, C=12, D=13, E=14, F=15 

⇒ No. of Symbols in the Decimal Number system is 16.

⇒ The Base(Radix) of the decimal Number System is 16.

⇨For Example 23AE

    The decimal number system takes it as a (2 x 16^3) + (3 x 16^2) + (A x 16^1) + (E x 16^0) 

    

⇨ (2 x 16^3) + (3 x 16^2) + (A x 16^1) + (E x 16^0) 

 = (2 x 16^3) + (3 x 16^2) + (10 x 16^1) + (14 x 16^0) )

 = (2 x 4096) + (3 x 256) + (10 x 16) + (14 x 1)

 = 9134 in Decimal