Number System Of Computer

 

Number Systems are very useful in the computer fundamentals section. It's an important topic and helps to convert numbers to one number system to another. After reading this post you will be able to understand about the number system of computers.

We are familiar with numbers, characters, and symbols, but this type of data is not understandable for a computer. That's why we need to use some other values or codes while working with a computer. These values or codes are known as the number system.

Some number systems are given below, which are frequently used in Computer.

a). Decimal Number System

b). Binary Number System

c). Octal Number System

d). Hexa-Decimal Number System

Decimal Number System

The Number system that we use in our day-to-day life is the decimal number system. The decimal number system has a base of 10 as it uses 10 digits from 0 to 9. In this number system, each position represents a specific power of the base 10. 

For example :

=> 8543 (A decimal number)

=> (8 x 1000) + (5 x 100) + (4 x 10) + (3 x 1)

=> (8 x 10^3) + (5 x 10^2) + (4 x 10^1) + (3 x 10^0)

Here we can see that the base of all digits of this number (8543) is 10.

Binary Number System

Some features of the binary number system are given below :

• Represents two types of digits 0's and 1's, so the base of this number system is 2.
• Uses two types of electronic pulses(circuits), where the absence of pulse shows 0 and the presence of pulse shows 1.
• Each binary digit is called a bit. a group of 4 bits is called a nibble and a group of 8 bits is called a byte.
• The leftmost bit of a number is known as Most Significant Bit (MSB) and the rightmost bit is known as Least Significant Bit (LSB). It's the same for all number systems.

For Example :

Binary to Decimal

=> 1001 (A binary number)

=> (1 x  2^3) + (0 x 2^2) + (0 x 2^1) + (1 x 2^0)

=> 8 + 0 + 0 + 1

=> 9 (A decimal number)

Here we can see that the Binary number 1001 can be written 9 in the decimal number system.

Octal Number System

Some features of the octal number system are given below :

• Represents 8 tyeps of digits from 0 to 7, so the base of number sytem is 8.
• It takes exactly three binary digits to represent an octal digit. Binary 000 is the same as octal digit 0.
• Insufficient to convert values into bytes (8 bit), so not widely used in computers.

For Example :

Octal to Decimal

=> 5463 (An octal number)

=> (5 x  8^3) + (4 x 8^2) + (6 x 8^1) + (3 x 8^0)

=> (5 x  512) + (4 x 64) + (6 x 8) + (3 x 1)

=> 2560 + 256 + 48 + 3

=> 2867 (A decimal number)

Here we can see that the Octal number 5463 can be written 2867 in the decimal number system.

Hexa-Decimal Number System

Some features of the Hexa-Decimal number system are given below :

• Represents 16 types of digits from 0 to 9 and letters of alphabets from A to F, so the base of this number system is 16. Here, digits from 10 to 15 are represented as 10-A, 11-B, 12-C, 13-D, 14-E, and 15-F.
• It is also called the Alphanumeric number system. 
• More complex number system and widely used in the computer system. It's also used in the odometer of a vehicle.

For Example :

Hexa-Decimal to Decimal

=> 12AF (An Hexa-Decimal number)

=> (1 x  16^3) + (2 x 16^2) + (A x 16^1) + (F x 16^0)

=> (1 x  4096) + (2 x 256) + (10 x 16) + (15 x 1)

=> 4096 + 512 + 160 + 15

=> 4783 (A decimal number)

Here we can see that the Octal number 5463 can be written 2867 in the decimal number system.

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