## What is decimal number system?

Decimal numbers system is the general number system used in our real life for calculating the quantities. This number systems uses 0 to 9 numbers called digits. It consists of total 10 numbers so that it’s base is also 10.These 10 numbers are used to represent in carry forward method to represent any number.

Decimal representation = (Number)_{10}.

Normally the base 10 will not represented, by default any number is considered as decimal number.

## What is binary number system?

Binary number system is an important number system which is used by the computer to do the logic and arthemtic operations. It consists of two bits ‘1’ and ‘0’. So that the base of binary number system is ‘2’. Base is nothing but number of digits in number system.

Binary representation = (Binary Number)_{2}

Positional notation of binary number system

2^{2}+2^{1}+2^{0}. 2^{-1}+2^{-2}+2^{-3}

In computer all the numbers and characteristics are converted in to binary number systems 0 and 1. Active high is called ‘1’ and active low is called ‘0’.

## What is octal number system?

The octal means ‘8’ in the octal number system which consists of 8 digits 0 to 7. So the base of the system is 8.

Octal number system = (octal number)_{8}

i.e. The number 27 in octal number system = 27_{8}

Positional notation of binary number system

8^{2}+8^{1}+8^{0}. 8^{-1}+8^{-2}+8^{-3}

## What is hexa decimal number system?

The hexa decimal number system is widely used number system which consists of 16 symbols to represent any quantity. The symbols or digits are 0 to 9 and A to F. The base of the hexa decimal number system is 16.

Hexa Decimal number system = (Hexa number)_{16}

Example of hexa decimal number system = 67AB_{16}

## How to convert decimal to binary number system?

Decimal to binary number system:

The decimal number system can be converted by dividing a decimal number system with the base of binary system and using bottom top approach. The final remainder will be the MSB and consecutive quotients will be the next bits. Because the base is 2, definitely the quotients may be 1 or 0.

Example: Convert decimal number 25_{10} in to binary number.

Therefore 25_{10} = 11001_{2}

Binary to decimal number system:

The binary number can be converted to decimal number system by using position weight-age system. I.e. multiplying bits of the number with their position weights.

Example: Convert binary number 1010.10 in to decimal number

In the above example the binary number contains two parts one is left of the decimal and second one is right of the decimal.

1010.10_{2} = 1 * 2^{3} + 0 * 2^{2} + 1 * 2^{1} + 0 * 2^{0} . 1 * 2^{-1} + 0 * 2^{-2}

= 8+2.1/2

= 10.5.

## How to convert to decimal to octal number system?

decimal number to octal number system:

The decimal number can be converted to octal number system by using bottom to top division approach which is same as decimal to binary conversion.

Example : Convert decimal number 746 in to octal number system

Result: 746_{10} = 1352_{8}

octal number to decimal number system:

Using position weight-age method the octal number can be converted in to decimal number system.

Example : Convert octal number 1352_{8} in to decimal number system

1352_{8} = 1 * 8^{3} + 3 * 8^{2} + 5 * 8^{1} + 2 * 8^{0}

= 512 + 192 + 40 +2

= 746

#### How to convert binary number to octal number system?

Binary to octal number:

The binary number should be divided in to in such a way that each division consists of three bits. Append the zeros for the MSB division if it does not contain three digits because appending ‘0’ to MSB doesn’t disturb anything. convert each division in to the corresponding decimal number. The total number gives the octal number of the given binary number. Here three digits per division is considered because octal base ‘8’ is equal to cube of binary base ( 2^{3} = 8).

Example : Convert binary number 1010110 to octal number system

i.e. 1010110_{2} = 126_{8}

Octal to binary number system

It is the reverse process to the above said method. The combined binary number corresponds to each digit in octal system gives the required output.

Example : convert 126_{8} in to binary number system.

126_{8} = 1 2 6

= 001 010 110

= 1010110_{2}