Question

How to convert to octal from binary?

Answer 1

Converting a binary number to octal (base-8) is a straightforward process that involves grouping the binary digits into sets of three. Here’s a detailed step-by-step guide to help you understand the conversion process:

### Step-by-Step Conversion from Binary to Octal

1. **Write Down the Binary Number:**
   Start with the binary number you want to convert. For example, let’s use `110110101`.

2. **Group Binary Digits in Sets of Three:**
   Starting from the right (least significant bit), group the binary digits into sets of three. If there are not enough digits to form a complete group on the left (most significant bit), add leading zeros to make a full group.

   For the binary number `110110101`:
   - Group it from right to left: `110`, `110`, `101`
   - If necessary, pad with zeros on the left: `011`, `011`, `010`, `1` (Pad `1` to `001`)

   So, the binary number `110110101` groups as `011`, `101`, `110`, `110`.

3. **Convert Each Group to an Octal Digit:**
   Convert each 3-bit binary group to its equivalent octal digit. Here’s the conversion table for 3-bit binary groups to octal digits:

   | Binary | Octal |
   |--------|-------|
   | 000    | 0     |
   | 001    | 1     |
   | 010    | 2     |
   | 011    | 3     |
   | 100    | 4     |
   | 101    | 5     |
   | 110    | 6     |
   | 111    | 7     |

   Convert each binary group:
   - `011` = `3`
   - `101` = `5`
   - `110` = `6`
   - `110` = `6`

4. **Combine the Octal Digits:**
   Combine the octal digits obtained from each binary group to form the final octal number.

   For the binary number `110110101`, grouping from right to left gives us:
   - `011` (3)
   - `101` (5)
   - `110` (6)
   - `110` (6)

   So, `110110101` in binary converts to `3566` in octal.

### Example Walkthrough

Let’s go through an example with a different binary number: `101011011`.

1. **Binary Number:** `101011011`
2. **Group Binary Digits:**
   - Start grouping from the right: `101`, `011`, `011`, `010`
   - Pad on the left if needed: `010`, `011`, `011`, `101`
3. **Convert Each Group:**
   - `010` = `2`
   - `011` = `3`
   - `011` = `3`
   - `101` = `5`
4. **Combine the Octal Digits:** `2335`

So, the binary number `101011011` converts to `2335` in octal.

### Summary

To convert from binary to octal:
- Group the binary digits into sets of three.
- Convert each 3-bit group to its octal equivalent using the binary-to-octal conversion table.
- Combine these octal digits to get the final octal number.

This method works because each octal digit corresponds to exactly three binary digits, making the conversion direct and simple.

Answer 2

To convert a binary number to octal, follow these steps:

### 1. **Group the Binary Digits:**
   - Starting from the right (least significant bit), group the binary digits into sets of three.
   - If the number of digits is not a multiple of three, pad the leftmost group with zeros.

   **Example:** Convert `1101010` to octal.
   - Grouping: `001 101 010` (added one zero to the left).

### 2. **Convert Each Group to Octal:**
   - Convert each group of three binary digits to its equivalent octal digit using the table below:

   | Binary | Octal |
   |--------|-------|
   | 000    | 0     |
   | 001    | 1     |
   | 010    | 2     |
   | 011    | 3     |
   | 100    | 4     |
   | 101    | 5     |
   | 110    | 6     |
   | 111    | 7     |

   **Example:** Using the groups from above:
   - `001` → `1`
   - `101` → `5`
   - `010` → `2`

### 3. **Write the Octal Number:**
   - Combine the octal digits obtained from each group.

   **Example:** The binary number `1101010` is `152` in octal.

### **Summary Example:**
- **Binary:** `1101010`
- **Grouped:** `001 101 010`
- **Octal Conversion:** `152`

So, `1101010` in binary equals `152` in octal.