Binary to Octal Converter

Convert Binary to Octal

Enter a binary number below to convert it to octal. Our converter handles binary numbers of any length.

Please enter a valid binary number (0s and 1s only).

How to Convert Binary to Octal

Converting binary numbers to octal is a common operation in computer science and digital systems. Here's a comprehensive guide on how to perform this conversion:

Conversion Formula

The process of converting binary to octal involves grouping binary digits and mapping them to their octal equivalents. There isn't a direct formula, but we follow these steps:

  1. Group binary digits from right to left in sets of three.
  2. Convert each group of three binary digits to its octal equivalent (0-7).
  3. Combine the octal digits to form the final octal number.

Conversion Steps

  1. Start from the rightmost digit of the binary number.
  2. Group the digits into sets of three, moving from right to left.
  3. If the leftmost group has fewer than three digits, pad it with zeros on the left.
  4. Convert each group of three binary digits to its octal equivalent (0-7).
  5. Write down the octal digits from left to right to get the final octal number.

Example Conversion

Let's convert the binary number 1010111 to octal.

Step 1: Group Binary Digits

1 010 111

Step 2: Convert Each Group

001 = 1

010 = 2

111 = 7

Step 3: Combine Results

Therefore, 1010111 in binary = 127 in octal

Visual Representation

1010111 Binary Input Grouping Process: 001 010 111 ↓ ↓ ↓ 1 2 7 Group by 3 127 Octal Result Conversion Details: 001 (binary) = 1 (octal) 010 (binary) = 2 (octal) 111 (binary) = 7 (octal)

This diagram illustrates the process of converting the binary number 1010111 to its octal equivalent 127.

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