Octal numbers use a base-8 system (digits 0 to 7), while binary numbers use a base-2 system (digits 0 and 1). The key to converting binary to octal lies in grouping binary digits into sets of three. Let’s go through this process in detail, with plenty of examples to make it crystal clear.

## Why Convert Binary to Octal?

Before diving into the steps, it’s helpful to know why you might need to convert binary to octal:

**Shorter Representation:**Octal numbers provide a more compact way to represent binary numbers. A long binary number can be shortened significantly in octal, making it easier to read and use.**Computing Convenience:**In computer systems, octal is often used to represent binary values in a more manageable format, especially in programming and digital electronics.

## How to Convert Binary to Octal: Step-by-Step

### 1. Group Binary Digits into Sets of Three

- Starting from the rightmost digit, break the binary number into groups of three. If the number of binary digits isn’t a multiple of three, add extra zeros to the left of the binary number to make it complete.
- Example: Let’s convert
`1101011`

to octal.- Grouping into sets of three:
`1 101 011`

- Add extra zeros to make three digits in each group:
`001 101 011`

- Grouping into sets of three:

### 2. Convert Each Group to Its Decimal Equivalent (Octal Digit)

- Each 3-bit group can be treated as a small binary number. Convert each group into its decimal equivalent (ranging between 0 and 7), which will become an octal digit.
- Example: For
`001 101 011`

:`001`

= 1×2² + 0×2¹ + 0×2⁰ =**1**`101`

= 1×2² + 0×2¹ + 1×2⁰ = 4 + 0 + 1 =**5**`011`

= 0×2² + 1×2¹ + 1×2⁰ = 2 + 1 =**3**

### 3. Combine the Octal Digits to Form the Final Octal Number

- Put together the digits you calculated from each group to get the octal number.
- Example: The binary number
`1101011`

converts to octal as**153**.

## Examples to Practice

### Example 1: Binary `101110`

**Step 1:** Group into sets of three: `101 110`

**Step 2:** Convert to decimal:

`101`

= 1×2² + 0×2¹ + 1×2⁰ = 4 + 0 + 1 =**5**`110`

= 1×2² + 1×2¹ + 0×2⁰ = 4 + 2 + 0 =**6**

**Step 3:** Combine digits: The octal number is **56**.

### Example 2: Binary `111001`

**Step 1:** Group into sets of three: `111 001`

**Step 2:** Convert to decimal:

`111`

= 1×2² + 1×2¹ + 1×2⁰ = 4 + 2 + 1 =**7**`001`

= 0×2² + 0×2¹ + 1×2⁰ =**1**

**Step 3:** Combine digits: The octal number is **71**.

### Tips for Quick Conversion

When dealing with binary to octal conversion, always split the binary number into groups of three. Add leading zeros if the leftmost group has fewer than three digits. For example, `110`

becomes `110`

, and `10101`

becomes `010 101`

.

You can speed up the conversion by memorizing the decimal equivalents of 3-bit binary groups:

`000`

= 0`001`

= 1`010`

= 2`011`

= 3`100`

= 4`101`

= 5`110`

= 6`111`

= 7

After converting, check that the octal digits range between 0 and 7. If any digit is outside this range, there might be a mistake in the grouping or conversion process.

## Practice Exercise

Try converting this binary number to octal on your own: `1001101`

.

- Group the digits into sets of three:
**__** - Convert each group to its decimal equivalent:
**__** - Write down the final octal number:
**__**

By following these simple steps, you’ll master binary to octal conversion in no time! Practice with various binary numbers to get more comfortable with the process.