10th Class Computers Science Classification of Computer and Number System Octal Number System

   Octal Number System

The whole octal number system is based on 8. It means whole octal number system depends on 0, 1, 2, 3, 4, 5, 6 and 7 digits. All the numbers in an octal number system are written by using these eight digits. The place value of a digit in a number increases in the power of 8 from right to left. The following example shows the place value of each digit in the number 1546 from right to left:

Place value of 7 'is: \[6*{{8}^{0}}=6\]

Place value of 6 is: \[4*{{8}^{1}}=32\]

Place value of 2 is: \[5*{{8}^{2}}=320\]

Place value of 1 is: \[1*{{8}^{3}}=512\]

 Converting Decimal Number into Octal

While converting a decimal number into octal you need to do the successive division of decimal number by 8 until the quotient becomes less than 8. Then write the remainders in reverse order to get the desired results. The following example shows how to convert decimal number into octal:

8) 100

8) 124

8) 14

Remainders in reverse order = 144

144 is the conversion of 100 into octal.  

 Converting Octal to Binary

To convert octal to binary you need to convert each octal digit to its 3-bit binary equivalent. The following example shows how to convert octal number into binary:

\[{{\left( 455 \right)}_{8}}\] to binary

4-100

5-101

5-101

\[{{\left( 455 \right)}_{8}}\text{ }=\text{ }{{\left( 100101101 \right)}_{2}}\]