Computer || Number System

The technique to represent and work with numbers is called number system. 

popular number systems include 

• Decimal number system
• Binary number system
• Octal number system
• Hexadecimal number system, etc.

NOTE : Decimal number system is the most common number system. 

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Decimal Number System ( Base 10 )

Decimal number system is a base 10 number system having 10 digits from 0 to 9. This means that any numerical quantity can be represented using these 10 digits. 

• Decimal number system is also a positional value system. This means that the value of digits will depend on its position. 

Example :

Let three numbers  734, 971 and 207. 

The value of 7 in all three numbers is different

• In 734, value of 7 is 7 hundreds or 700 or 7 × 100 or 7 × 102
• In 971, value of 7 is 7 tens or 70 or 7 × 10 or 7 × 101
• In 207, value 0f 7 is 7 units or 7 or 7 × 1 or 7 × 100

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Binary Number System ( Base 2 )

The number system having just these two digits  0 & 1 is called binary number system.

• Each binary digit is also called a bit. 
• Binary number system is also positional value system, where each digit has a value expressed in powers of 2.

In any binary number, the rightmost digit is called least significant bit (LSB) and leftmost digit is called most significant bit (MSB).

Computer memory is measured in terms of how many bits it can store.

• 1 byte (B) = 8 bits
• 1 Kilobytes (KB) = 1024 bytes
• 1 Megabyte (MB) = 1024 KB
• 1 Gigabyte (GB) = 1024 MB
• 1 Terabyte (TB) = 1024 GB
• 1 Exabyte (EB) = 1024 PB
• 1 Zettabyte = 1024 EB
• 1 Yottabyte (YB) = 1024 ZB

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Octal Number System ( Base 8 )

Octal number system has eight digits – 0, 1, 2, 3, 4, 5, 6 and 7. Octal number system is also a positional value system with where each digit has its value expressed in powers of 8.

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Hexadecimal Number System ( Base 16 )

Hexadecimal number system has 16 symbols – 0 to 9 and A to F where A is equal to 10, B is equal to 11 and so on till F. Hexadecimal number system is also a positional value system with where each digit has its value expressed in powers of 16.

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Number System Relationship

BINARY	OCTAL	DECIMAL	HEXADECIMAL
0000	0	0	0
0001	1	1	1
0010	2	2	2
0011	3	3	3
0100	4	4	4
0101	5	5	5
0110	6	6	6
0111	7	7	7
1000	10	8	8
1001	11	9	9
1010	12	10	A
1011	13	11	B
1100	14	12	C
1101	15	13	D
1110	16	14	E
1111	17	15	F

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