Question

How do you convert to octal?

Answer 1

To convert a number to octal (base-8), follow these steps:

1. **Divide the Decimal Number by 8:** Take the decimal number and divide it by 8. Record the quotient and the remainder.

2. **Record the Remainder:** The remainder from this division is the least significant digit (rightmost digit) of the octal number.

3. **Repeat with the Quotient:** Use the quotient from the previous division as the new number to divide by 8. Repeat the division and record the new remainder.

4. **Continue Until the Quotient is Zero:** Keep dividing and recording remainders until the quotient is zero.

5. **Write the Octal Number:** The octal number is written by arranging the remainders in reverse order (from last to first).

### Example Conversion

Let's convert the decimal number 156 to octal:

1. **Divide 156 by 8:**
   - Quotient: 19
   - Remainder: 4

2. **Divide 19 by 8:**
   - Quotient: 2
   - Remainder: 3

3. **Divide 2 by 8:**
   - Quotient: 0
   - Remainder: 2

4. **Write the octal number:** Arrange the remainders from last to first: 234.

So, 156 in decimal is 234 in octal.

Answer 2

To convert a number from decimal (base 10) to octal (base 8), you can use the following steps:

### Method 1: Repeated Division

1. **Divide the Decimal Number by 8:**
   - Write down the decimal number you want to convert.
   - Divide it by 8, noting both the quotient and the remainder.

2. **Record the Remainder:**
   - The remainder will be a digit in the octal system (it will be between 0 and 7).

3. **Repeat the Division:**
   - Use the quotient from the previous division as the new number to divide by 8.
   - Record the remainder.

4. **Continue Until the Quotient is Zero:**
   - Keep dividing by 8 and recording the remainders until the quotient is zero.

5. **Write Down the Octal Number:**
   - The octal number is obtained by reading the remainders in reverse order (from last remainder to the first).

### Example: Convert Decimal 156 to Octal

1. **Divide 156 by 8:**
   - Quotient = 19, Remainder = 4

2. **Divide 19 by 8:**
   - Quotient = 2, Remainder = 3

3. **Divide 2 by 8:**
   - Quotient = 0, Remainder = 2

4. **Read the remainders in reverse order:**
   - Octal Number = 234

So, the decimal number 156 is equivalent to octal 234.

### Method 2: Using Built-in Functions

In many programming languages, you can convert decimal to octal directly using built-in functions or methods. For example:

- **Python:** `oct(decimal_number)`
- **JavaScript:** `decimal_number.toString(8)`
- **Java:** `Integer.toOctalString(decimal_number)`

Using these methods can simplify the conversion process, especially for larger numbers.

Let me know if you have any more questions or need further clarification!