Conversion of Number System

Conversion of Decimal Number System into Binary Number System.

The method of conversion of decimal number system to binary number is:
• Divide the decimal number by 2 successively,
• Keep a note of the remainder in one column,
• Repeat the process until the quotient is zero,
• The answer is obtained by writing the answer in the reverse order.
For Example:

Conversion of Decimal Number System into Octal Number System.

The method of conversion of decimal number system to octal number is:
• Divide the decimal number by 8 successively,
• Keep a note of the remainder in one column,
• Repeat the process until the quotient is zero,
• The answer is obtained by writing the answer in the reverse order.
For Example:

Conversion of Decimal Number System into Hexadecimal Number System.

The method of conversion of decimal number system to hexadecimal number is:
• Divide the decimal number by 16 successively,
• Keep a note of the remainder in one column,
• Repeat the process until the quotient is zero,
• The answer is obtained by writing the answer in the reverse order.
For Example:

Conversion of Binary Number System into Decimal Number System.

The method of conversion of binary number system to deccimal number system is:
• Write the binary digits and multiply each digit with the base value i.e. 2 with the power of base value increasing from right to left starting from 0.
• Convert each power of 2 into it’s equivalent term.
• Add these terms to give the decimal number.
For Example:

Conversion of Binary Number System into Octal Number System.

There are two types of method to convert binary number to octal number, they are:
Method-I:

• Separate the given binary number into a group of 3 bits from right to left, add 0 in left most side if required.
• Replace each group by its octal equivalent.
  For Example:
  

Method-II:

• Convert given a binary number to decimal.
• Again convert this decimal number to octal number.

Conversion of Binary Number System into Hexadecimal Number System.

There are two types of method to convert binary number to hexadecimal number, they are:
Method-I:

• Separate the given binary number into a group of 4 bits from right to left, add 0 in the left most side if required.
• Replace each group by its hexadecimal equivalent.
  For Example:
  

Method-II:

• Convert binary to decimal.
• Again convert decimal to hexadecimal.

Conversion of Octal Number System into Decimal Number System.

The method of conversion of octal number system into decimal number system is:
• Write the octal digits and multiply each digit with the base value i.e. 8 with the power of base value increasing from right to left starting from 0.
• Convert each power of 8 into its equivalent term.
• Add these terms to give the decimal number.
For Example:

Conversion of Octal Number System into Binary Number System.

There are two types of method to convert octal number to binary number, they are:
Method-I:

• Take each digit individually.
• Convert it into its respective binary value of 3 bit each and combine them.
  For Example:
  

Method-II:

• Convert octal to decimal equivalent.
• Again convert the obtained decimal into binary.

Conversion of Octal Number System into Hexadecimal Number System.

The method of conversion of octal number system into hexadecimal number system is:
Method-I: Convert octal to decimal than convert decimal to hexadecimal or
Method-II: Convert the octal to binary than convert binary to hexadecimal.
For Example:

Conversion of Hexadecimal Number System into Decimal Number System.

The method of conversion of hexadecimal number system to decimal number system is:
• Write the hexadecimal digits and multiply each digit with the base value i.e. 16 with the power of base value increasing from right to left starting from 0.
• Convert each power of 16 into its decimal equivalent term.
• Add these terms to give the decimal number.
For Example:

Conversion of Hexadecimal Number System into Binary Number System.

There are two types of method to convert hexadecimal number to binary number, they are:
Method-I:

• Take each digit individually.
• Convert it into its respective binary value of 4 bit each and combine them.
  For Example:
  

Method-II:

• Convert hexadecimal to decimal equivalent.
• Again convert obtained decimal into binary.

Conversion of Hexadecimal Number System into Octal Number System.

There are two types of methods to convert hexadecimal number to octal number, they are:
Method-I: Convert hexadecimal to decimal then to octal.
Method-II: Convert hexadecimal to binary then to octal.
For Example:

Calculation in binary addition, subtraction, Multiplication and division.

a. Addition of binary numbers
The binary addition rules are shown in the table below :

Add 00011010 with 00001100

b. Subtraction of binary numbers
The binary subtraction rules are shown in the table below :

Subtract 00100101 from 00010001

c. Multiplication of binary numbers
The binary multiplication rules are shown in the table below :

Multiply 00101001 with 00000110.

d. Division of binary numbers
The binary division rules are shown in the table below :

Divide 0010101 by 110.