Binary to Octal Converter

Conversion Direction

Binary Number

BIN

1010₂ = 12₈

77₈ = 111111₂

Enter a value and click Convert

The Binary to Octal Converter is a free online tool that performs binary to octal conversion and also works as an octal to binary converter. Whether you need a bin to oct online tool for quick homework checks or a reliable binary to octal conversion calculator for programming tasks, this utility handles both directions instantly. By understanding the relationship between the two number systems, you can also perform the conversions manually.

Binary and Octal Number Systems

Binary (base‑2) uses only two digits, 0 and 1, making it the fundamental language of digital circuits. Octal (base‑8) uses eight digits, 0 through 7, and is often employed as a compact way to represent binary data. Because $2^3=8$ , every octal digit can be expressed as a three‑digit binary sequence. The mapping is summarized in the table below.

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

Converting Binary to Octal

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

Starting from the rightmost bit (least significant), split the binary string into groups of three bits. If the leftmost group has fewer than three bits, add leading zeros.
Replace each three‑bit group with the matching octal digit from the table above.

Example: Convert binary $\text{11001}_2$ to octal.
Group the bits from the right: $\text{011}\; \text{001}$ (an extra zero is added at the front).
$\text{011}_2 = 3_8$ and $\text{001}_2 = 1_8$ , so the octal equivalent is $\text{31}_8$ .

Converting Octal to Binary

The reverse operation is even more straightforward:

Write each octal digit as its three‑bit binary equivalent (using the table).
Concatenate the groups to form the complete binary number.

Example: Convert octal $\text{715}_8$ to binary.
$7_8 \rightarrow 111_2$ , $1_8 \rightarrow 001_2$ , $5_8 \rightarrow 101_2$ . Combining them gives $\text{111001101}_2$ .

Using the Online Converter

This binary to octal converter simplifies the process even further. For binary‑to‑octal conversion, select the appropriate mode and enter your binary digits—the tool instantly displays the octal result. For octal‑to‑binary, just switch the mode and input an octal number to obtain its binary representation. No manual grouping or table references are needed.

Whether you are learning number systems or performing quick conversions, this free binary to octal converter serves as a handy bin to oct online tool for both students and professionals.

FAQ

1. How do I manually convert a binary number to octal?

Start from the rightmost bit and split the binary digits into groups of three. Add leading zeros to the leftmost group if necessary. Then replace each three‑bit group with its octal equivalent using the standard mapping table (e.g., 000→0, 001→1, …, 111→7).

2. What is the octal equivalent of binary 11001?

Following the grouping method: 011 001. 011 corresponds to 3 and 001 to 1, so the octal result is 31.

3. How do I convert octal 715 to binary?

Replace each octal digit with its three‑bit binary equivalent: 7→111, 1→001, 5→101. Concatenating them gives 111001101.

4. Can this converter handle both binary-to-octal and octal-to-binary conversions?

Yes. Simply select the desired conversion direction before entering your number. The tool will output the result instantly for either operation.

How to Use

Select the conversion direction: Binary to Octal or Octal to Binary.
Enter a valid binary number (0s and 1s) or octal number (0-7) in the input field.
Click the Convert button to instantly see the converted value in the target number system.