Question

Convert the decimal number 108 into its octal equivalent.

• A. 124
• B. 134
• C. 144
• D. 154

Hint:

The repeated division method works for converting decimal to any base. To convert to binary, divide by 2. To convert to hexadecimal, divide by 16. Always remember to read the remainders in reverse order (from bottom to top).

Answer 1

The Correct Option is D

To convert a decimal number to its octal (base-8) equivalent, we use the method of repeated division by 8. We record the remainder at each step.
Step 1: Divide 108 by 8.
$108 \div 8 = 13$ with a remainder of $4$.
Step 2: Divide the quotient (13) by 8.
$13 \div 8 = 1$ with a remainder of $5$.
Step 3: Divide the new quotient (1) by 8.
$1 \div 8 = 0$ with a remainder of $1$.
The process stops when the quotient becomes 0. The octal number is formed by reading the remainders from the bottom up.
Reading from bottom to top, we get 1, 5, 4.
Therefore, the octal equivalent of decimal 108 is $154_8$.