Category : 10th Class
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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