Binary to Octal Converter
Enter any binary number and get its octal equivalent immediately. The converter shows every 3-bit grouping step so you can follow the math, displays the decimal value for cross-checking, and includes a reverse mode so you can convert octal back to binary just as quickly.
How binary to octal conversion works
Binary (base 2) and octal (base 8) share a special relationship: 8 is exactly 2 cubed, so one octal digit represents exactly three binary digits. To convert, group the binary digits into chunks of three starting from the right (padding with leading zeros if the total is not a multiple of three), then replace each group with its octal equivalent using the lookup table. For example, 11001 becomes 011 001, and 011 maps to 3 while 001 maps to 1, giving the octal result 31. No arithmetic is needed, just pattern matching, which is why this conversion can be done quickly by hand.
How to use this converter
Select "Binary to Octal" from the direction menu and type or paste your binary number (digits 0 and 1 only) into the binary field. The octal result, decimal equivalent, and number of 3-bit groups all appear instantly. The "Show your work" panel below the result walks through every grouping and lookup step with the actual digits you entered. To go the other way, switch the direction to "Octal to Binary", enter any octal number (digits 0 through 7), and the converter will expand each digit into its 3-bit binary representation.
Why octal matters in computing
Octal was a common shorthand in early computing because many systems used 6-bit, 12-bit, 24-bit, or 36-bit word sizes, all multiples of three. Engineers and programmers found it far easier to read three-digit octal values than long binary strings. File permissions on Unix and Linux systems still use octal today: the permission string rwxr-xr-- is written as 754 in octal, where 7 = 111 (read, write, execute), 5 = 101 (read, execute), and 4 = 100 (read only). Although hexadecimal (base 16) is now more common for representing 8-bit bytes, octal remains valuable for understanding permissions, legacy systems, and number theory.
Converting octal back to binary
The reverse process is equally straightforward. Every octal digit (0 through 7) expands to exactly three binary digits using the same lookup table. Octal 6 becomes 110, octal 3 becomes 011, so octal 63 becomes binary 110 011, or 110011 after removing the space. This makes the binary-to-octal and octal-to-binary conversions the simplest inter-base conversions in computing, because each step is a direct substitution with no carries or remainders.
3-bit binary to octal lookup table
| 3-bit binary | Octal digit | Decimal value |
|---|---|---|
| 000 | 0 | 0 |
| 001 | 1 | 1 |
| 010 | 2 | 2 |
| 011 | 3 | 3 |
| 100 | 4 | 4 |
| 101 | 5 | 5 |
| 110 | 6 | 6 |
| 111 | 7 | 7 |
Every possible 3-bit binary group and its corresponding octal digit. Use this as a quick reference when converting by hand.
Frequently asked questions
How do I convert binary to octal by hand?
Group the binary digits from right to left into sets of three, adding leading zeros to the leftmost group if it has fewer than three digits. Then replace each group with its octal digit using the 3-bit lookup table (000=0, 001=1, 010=2, 011=3, 100=4, 101=5, 110=6, 111=7). Concatenate the octal digits to get your result. For example, 1101100 becomes (1)(101)(100), which maps to 1, 5, 4, giving 154 in octal.
What is 11001 in binary as an octal number?
Group 11001 from the right: (11)(001). Pad the first group to three digits: (011)(001). Then 011 = 3 and 001 = 1, so 11001 in binary equals 31 in octal. The decimal value is 25.
Why do binary and octal convert so cleanly?
Because 8 = 2^3. Any number that is a power of 2 will have a clean mapping to and from binary, where each digit of the higher-base number corresponds to a fixed-width group of binary digits. For base 8, that group is always 3 bits. For base 16 (hexadecimal), it is always 4 bits. For base 4, it is 2 bits.
How is octal used in Linux file permissions?
Unix and Linux represent file permissions for owner, group, and others as three octal digits. Each digit encodes read (4), write (2), and execute (1) permissions summed together. So 7 (= 4+2+1 = 111 in binary) means all three permissions, 5 (= 4+1 = 101) means read and execute, and 4 (= 100) means read only. A permission of 754 means the owner has full access, the group can read and execute, and others can only read.
What is the largest octal number that fits in 8 binary digits?
8 binary digits (a byte) can hold values from 0 to 255 in decimal. In octal, 8 bits split as (11)(111111), padded to (00)(11)(111111). Wait - for 8 bits, the groups are (00)(111)(111), so the maximum is 377 in octal (11111111 in binary, 255 in decimal). Three octal digits are always enough to represent any 8-bit value.