What is Number System ? Base & Types

What is Number System ?

    A  number system defines a set of values to represent quantity. A number system define how a number can be represented using distinct symbols. 

A number can be represented differently in different systems.

For Example: –

• There are several systems for representing, counting numbers.
• These include the usual base “10” or decimal system : 1,2,3 ,…..10,11,12,..99,100,…

The BASE of a number system

Base of number system is also called as Radix

    The number of values from that a digit can assume is equal to the base of a system .

Different Types Of Number System

1. Decimal Number System.
2. Binary Number system
3. Octal Number System.
4. Hexadecimal Number system.

1) Decimal Number System

    The decimal number system has a base of 10 i.e. it has 10 distinct symbols from 0 to 9 (0,1,2,3,4,5,6,7,8,9). It is a positional value system in which the value of the digit depends on its position.

• Base of decimal number system 10
• It has 10 distinct symbols from 0 to 9 (0,1,2,3,4,5,6,7,8,9)
• Used by humans ? Yes
• Not use in computer

For example: consider the decimal number 321,

where the digit 3 represents hundreds, 2 represents the tens and 1 represents the ones. 321=300+20+1

Here 3 carries the highest weight of the three digits, hence it is the most significant bit (MSB) and 1 carries the least weight of the three digits, hence it is the least significant bit(LSB).

2) Binary Number System

• The Binary number system has a base of 2.  
• It has 2 distinct symbols from 0 to 1.
• The 0 and 1 is called as a Bit.
• Any binary number can be represented by a string of 1’s and 0’s.
• Not use by humans
• Use in computer
• A group of four binary bits is known as NIBBLE.
• A group of 8 binary bits known as a byte.

The various digit positions in this system have weights as follows:

For example: 1) consider the Binary  number  (1011)₂

        1            0            1             1

= (1x2³)+(0x2²)+(1x2¹)+(1x2⁰)

=    8   +    0  +   2   +   1

=    (11)₁₀

For example: 2) consider the Binary number (1101.101)₂

1            1         0          1     .     1          0 

= (1x2³)+(1x2²)+(0x2¹)+(1x2⁰)+(1x2^-1)+(0x2^-2)

= 8 + 4 + 0 + 1 + 0.5 + 0.25

= (13.75)₁₀

3) Octal Number System

• The Octal number system has a base of 8 i.e. it has 8 distinct symbols from 0 to 7 (0,1,2,3,4,5,6,7).
• Not use by humans
• The various digit positions in this system have weights as follows:

For example: 1) consider the Octal number  (35.7)₈

      3            5     .       7

=(3x8¹) + (5x8⁰) + (7x8^-1)

=  24  +   5  + 0.875

= (29.875)₁₀                   

4) Hexadecimal Number System

• The Hexadecimal number system has a base of 16.
• It has 16 distinct symbols from 0 to 9, A to F 
• Symbols are (0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F).

The various digit positions in this system have weights as follows:

For example: 1) consider the Hexadecimal number  (11A.62)₁₆

       1              1               A       .       6              2

= (1x16²) + (1x16¹) + (Ax16⁰) + (6x16^-1) + (2x16^-2)

= (1x256) + (1x16) + (10x1) + (6/16) + (2/256)

= 256 + 16 + 10 + 0.375 + 0.0078

= (282.382)₁₀

Counting By using different number system

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