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

Octal Number System

Category : 10th Class

*   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

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

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