# Most Computers are Digital

- Recognize only two discrete states: on or off. On means 1 and off means 0.
- Computers are electronic devices powered by electricity, which has only two states, on or off

Data in computer is represent in binary form. To understand data representation one has to know four number system.

- Decimal number system: In this system we use ten different symbol to represent any number. Therefore itâ€™s base is ten. Following are the symbol use in this system. 0, 1, 2 ,3, 4, 5, 6, 7 ,8, 9. (0-9)
- Binary number system: In this system we use only two symbols are used. i.e 0, 1. There itâ€™s base is two.
- Octal: In this system eight symbol is used i.e 0, 1, 2, 3, 4, 5, 6, 7. Therefore itâ€™s base is eight. (0-7)
- Hexadecimal: In this system sixteen symbol is used i.e 0 1 2 3 4 5 6 7 8 9 A B C D E F. Therefore itâ€™s base is sixteen. (0-F)

**Conversion From one number system to another**

**DECIMAL CONVERSION:****Decimal to binary:**Divide the given decimal number by 2 till possible and write the remainder in reverse order.**I**. (225)_{10}= (11100001)_{2}_{}**Decimal to octal:**Divide the given decimal number by 8 till possible and write the remainder in reverse order.

e.g (225)_{10}= (341)_{8}_{}**Decimal to hexa:**Divide the given decimal number by 16 till possible and write the remainder in reverse order.

e.g (225)_{10}= (E1)_{16}_{}

**BINARY CONVERSION****Binary to Decimal**

**(11011101)**_{2}= (221)_{10}_{}**Binary to Octal:**to find the octal value from the binary number,**e.g**(11100001)_{2}**=**( 341 )_{8}**011 100 001 -------- 1**^{st}group 001, second group 100 and 3^{rd}group 011.

**Individual value 001 = 1 , 100 = 4, 011 = 3**_{8}**Binary to Hexadecimal****(11011101)**_{2}= (DD)_{16}_{}_{16}= (DD)_{16}

**OCTAL CONVERSION****Octal to Decimal****(76)**_{8}= (62)_{10}_{}**Octal to Binary**

**(76)**_{8}= (111110)_{2}_{}

**HEXA DECIMAL CONVERSION****Hexadecimal to Decimal****(2AD)**_{16}= (685)_{10}_{}**Hexadecimal to Binary****(2AD)**_{16}= (001010101101)_{2}_{}