For example, the decimal number 12 ( = $1 \times 10^1 + 2 \times 10^0$ ) is expressed as 14( = $1 \times 8^1 + 4 \times 8^0$) in the octal number system.
The decimal number 108 in the octal number system is
Decimal to Octal Conversion Explained
The question asks to convert the decimal number 108 (base-10) into its octal equivalent (base-8). The octal system uses digits 0 through 7.
Conversion Method: Division by Base
To convert a decimal number to octal, we repeatedly divide the decimal number by the target base (which is 8 for octal) and keep track of the remainders. The octal number is formed by the remainders read in reverse order (from bottom to top).
Step-by-Step Conversion of 108
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Divide the decimal number 108 by 8:
$108 \div 8 = 13 \text{ remainder } 4$
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Divide the quotient (13) by 8:
$13 \div 8 = 1 \text{ remainder } 5$
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Divide the quotient (1) by 8:
$1 \div 8 = 0 \text{ remainder } 1$
Final Octal Representation
Reading the remainders from bottom to top (1, 5, 4), we get the octal representation of the decimal number 108.
Therefore, decimal 108 is equivalent to octal 154.
Check: $154_8 = (1 \times 8^2) + (5 \times 8^1) + (4 \times 8^0) = (1 \times 64) + (5 \times 8) + (4 \times 1) = 64 + 40 + 4 = 108_{10}$.
Important Questions from Number System and Binary Codes
A byte is
Binary addition of 16 and -83 using 2’s compliment results in:
If (211) x= (152) 8, then the value of base x is
What is the decimal value for HEX 2A
The binary equivalent of decimal 22 is:
