Question

How to convert binary number 110111 to octal?

Answer 1

To convert the binary number \( 110111 \) to octal, follow these steps:

1. **Group the binary digits** into sets of three, starting from the right. If necessary, add leading zeros to the leftmost group to make it three digits:
   - \( 110111 \) becomes \( 110 \, 111 \).

2. **Convert each group to octal**:
   - \( 110_2 \) (binary) = \( 6_8 \) (octal)
   - \( 111_2 \) (binary) = \( 7_8 \) (octal)

3. **Combine the octal digits**:
   - So, \( 110111_2 \) converts to \( 67_8 \).

Therefore, the binary number \( 110111 \) is equal to \( 67 \) in octal.

Answer 2

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

1. **Group the Binary Digits**: Start by grouping the binary digits into sets of three, starting from the right (least significant digit). If the number of binary digits isn’t a multiple of three, you can add leading zeros to make it fit.

2. **Convert Each Group to Octal**: Convert each 3-digit binary group to its equivalent octal digit.

3. **Combine the Octal Digits**: Put the octal digits together to form the final octal number.

Let’s apply these steps to the binary number `110111`:

### Step 1: Group the Binary Digits

Group the digits from the right into sets of three:

- Original binary number: `110111`
- Grouped: `110 111`

### Step 2: Convert Each Group to Octal

Convert each 3-bit binary group to its octal equivalent:

- **110** in binary:
  - \( 1 \times 2^2 + 1 \times 2^1 + 0 \times 2^0 \)
  - \( 4 + 2 + 0 = 6 \)
  - So, `110` in binary is `6` in octal.

- **111** in binary:
  - \( 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 \)
  - \( 4 + 2 + 1 = 7 \)
  - So, `111` in binary is `7` in octal.

### Step 3: Combine the Octal Digits

Combine the octal digits from the previous step:

- The binary number `110111` is `67` in octal.

So, the binary number `110111` converts to the octal number `67`.