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

1. Divide the decimal number 108 by 8:

   $108 \div 8 = 13 \text{ remainder } 4$

2. Divide the quotient (13) by 8:

   $13 \div 8 = 1 \text{ remainder } 5$

3. 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: $154_8 = (1 \times 8^2) + (5 \times 8^1) + (4 \times 8^0) = (1 \times 64) + (5 \times 8) + (4 \times 1) = 64 + 40 + 4 = 108_{10}$.