# Binary to Octal Converter

## Converting a Binary Number to Octal

Binary and octal numeral systems are commonly used in computing. The binary system (base-2) uses only two digits: 0 and 1, while the octal system (base-8) uses eight distinct digits: 0 to 7. Octal numbers provide a more compact way to represent binary values, which is particularly useful in digital electronics and programming.

To convert a binary number to its octal equivalent, the binary number is first grouped into sets of three bits, starting from the right. Each group of three bits is then converted to its corresponding octal digit. If the number of bits is not a multiple of three, you can add leading zeros to the leftmost group to make it three bits long.

For example, the binary number 1101101 can be converted to octal by following these steps:

001 101 101

The first group, 001, is equivalent to 1 in octal, the second group, 101, is equivalent to 5 in octal, and the third group, 101, is also equivalent to 5 in octal. Therefore, the octal equivalent of 1101101 is 155.

## Examples

Let’s explore some examples to understand how to convert binary numbers to their octal equivalents.

### 1. Convert the binary number 1101101 to octal.

#### Answer

First, we identify the given number:

**Given:**

- Binary: 1101101

Next, we group the binary digits into sets of three, starting from the right. Since the number of digits is not a multiple of three, we add leading zeros to the left:

**Steps:**

- 001 101 101

We then convert each group to its corresponding octal digit:

- 001 = 1
- 101 = 5
- 101 = 5

The final octal value is formed by concatenating these digits:

**Octal Equivalent:**

155

**Result:**

∴ The octal equivalent of the binary number 1101101 is 155.

### 2. Convert the binary number 10110 to octal.

#### Answer

We start by identifying the number:

**Given:**

- Binary: 10110

Next, we group the binary digits into sets of three, starting from the right. Since the number of digits is not a multiple of three, we add a leading zero to the left:

**Steps:**

- 010 110

We then convert each group to its corresponding octal digit:

- 010 = 2
- 110 = 6

The final octal value is formed by concatenating these digits:

**Octal Equivalent:**

26

**Result:**

∴ The octal equivalent of the binary number 10110 is 26.

### 3. Determine the octal equivalent of the binary number 111111.

#### Answer

First, we identify the given number:

**Given:**

- Binary: 111111

Next, we group the binary digits into sets of three, starting from the right:

**Steps:**

- 111 111

We then convert each group to its corresponding octal digit:

- 111 = 7
- 111 = 7

The final octal value is formed by concatenating these digits:

**Octal Equivalent:**

77

**Result:**

∴ The octal equivalent of the binary number 111111 is 77.

### 4. Convert the binary number 100011 to octal.

#### Answer

We start by identifying the number:

**Given:**

- Binary: 100011

Next, we group the binary digits into sets of three, starting from the right:

**Steps:**

- 100 011

We then convert each group to its corresponding octal digit:

- 100 = 4
- 011 = 3

The final octal value is formed by concatenating these digits:

**Octal Equivalent:**

43

**Result:**

∴ The octal equivalent of the binary number 100011 is 43.