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# Number System

In our daily life we use "decimal number system". Now don't give me that look, decimal number system is just a numbering system which we use to count things, measure quantities, maintain our bills, bank maintains their accounts etc..etc. Yes, we use only 10 symbols to do any kind of counting, these 10 symbols are '0', '1', '2', '3', '4', '5', '6', '7', '8' and '9'. Since there are only 10 symbols this numbering system it is called deci-mal(deci means 10).

There are also other numbering systems namely..

Octa Decimal : Here we use only eight symbols (octa means 8), these are '0', '1', '2', '3', '4', '5', '6' and '7'

Hexa Decimal : This numbering system uses total 16 symbols: 0 to 9, 'A', 'B' , 'C', 'D', 'E' and 'F'

Binary : Here we use only two symbols '0' and '1'

Buy why on the earth will any body will require these weired numbering system ? Yes, you are correct..all these weird numbering systems are computer/digital system friendly. These number systems are widely used in digital systems like microprocessor, logic circuits, computers etc. All System designers prefer to use these numbering systems, as these are more continent from digital systems point of view. For example any digital system understands only two things "no voltage" and "voltage" i.e '0' and '1' at input/output. Hence always use Hexa-decimal and binary numbering system while designing. It is good idea not to combine decimal and hexa-decimal while putting specifications.

To understand how other numbering systems can be used, lets re-analyze how we use decimal numbering system..

In decimal system we first use all the symbols while counting and when we run out of symbols we re-use these symbols on the ten's position in the same sequence. But symbols at ten's position changes only when we run out of symbols at one's position. For example, lets say we are counting bottles. First we will use 0 to 9 to count 9 bottles now the next counted bottle will be counted as 10, observe this carefully, since we ran out of symbol we started using ten's position, again symbol at ten's position will change when we run out of symbol at one's position i.e When our counting moves from 19 to 20. This rule applies to ones, tens, hundred, thousand ... to all decimal places.

The same rule is applied when we count using any other numbering system. Lets say you have 12 bottles (decimal), but you want to count it using octa-decimal numbering system.

```Bottle count in :

Decimal  Octa-Decimal  Hexa-Decimal  Binary
0          0            0            0
1          1            1            1
2          2            2           10
3          3            3           11
4          4            4          100
5          5            5          101
6          6            6          110
7          7            7          111
8         10            8         1000
9         11            9         1001
10         12            A         1010
11         13            B         1011

```

Observe that, while counting in octa-decimal when we run out of symbol after 7, we started using ten's position. In our daily life we start from 1 instead of 0, but for simplicity in above example we started counting from 0 even in decimal. Remember that in hexa decimal and binary we always count from 0. we will see other arithmetic operation on binary in next topic.