Octal Number System Understanding

The octal number system is a base-8 number system, meaning it uses eight distinct symbols, typically 0, 1, 2, 3, 4, 5, 6, and 7. Each position in an octal number represents a power of 8. Converting a number from the decimal (base-10) system to the octal (base-8) system involves repeatedly dividing the decimal number by 8 and noting the remainders.

Converting Decimal 149 to Octal

To convert a decimal number like 149 into its octal equivalent, we use the method of successive division by the base, which is 8 for the octal system. We divide the number by 8, note the remainder, and then divide the quotient by 8 again, repeating the process until the quotient becomes 0. The octal number is then formed by reading the remainders from bottom to top (from the last remainder to the first).

Step-by-Step Decimal to Octal Conversion of 149

Let's convert the decimal number \(149\)_{10} to its octal equivalent step by step:

Following these divisions:

• First, divide 149 by 8. The quotient is 18, and the remainder is 5.
• Next, divide the quotient 18 by 8. The quotient is 2, and the remainder is 2.
• Finally, divide the quotient 2 by 8. The quotient is 0, and the remainder is 2.

Final Octal Representation of 149

To obtain the octal number, we collect the remainders in reverse order (from bottom to top). The remainders are 2, 2, and 5. Therefore, reading them from the last remainder to the first, we get 225.

So, the decimal number \(149\)_{10} is equivalent to \(225\)_{8} in the octal number system.