Loading...
Loading...
Enter octal values and get their binary equivalents instantly. Each digit expands to 3 bits - no intermediate arithmetic needed.
Octal value (digits 0-7)
Binary (base-2)
Octal is base-8, and 8 = 2³. This means every octal digit (0 through 7) has a direct, fixed-length binary representation using exactly 3 bits. The digit 0 is 000, 1 is 001, 2 is 010, 3 is 011, 4 is 100, 5 is 101, 6 is 110, and 7 is 111.
Converting octal to binary requires only a symbol substitution. For each octal digit, write its 3-bit equivalent in sequence. The octal number 755 becomes 111 101 101. The octal number 644 becomes 110 100 100. There is no carrying, no division, and no lookup table longer than 8 entries.
This clean mapping is why octal was historically used as shorthand for binary on systems with 12-bit, 24-bit, or 36-bit architectures. It is also why Unix file permissions use octal - each permission group is exactly 3 bits, and 3 bits = 1 octal digit.
When a Unix system stores file permissions internally, it keeps them as a 9-bit integer (plus additional bits for the file type and special flags like setuid). The nine permission bits break into three groups of three: owner bits, group bits, and others bits.
Converting a chmod value to binary makes the individual bits explicit. The value 755 in octal becomes 111 101 101 in binary. You can then read off each bit: the owner has read, write, and execute set; group has read and execute but not write; others have read and execute but not write. This is the standard permission for executable files and directories.
When writing code that checks permission bits with bitwise operations, having the binary representation helps you verify that your mask values are correct. Paste the octal chmod value here to see which exact bits it sets.
A 9-bit binary number is awkward to read and write. The octal equivalent is at most 3 digits. For legacy systems with 18-bit or 36-bit words, octal gave engineers 6 or 12 digits - far more manageable than 18 or 36 bits. Even today, when hex is more common, octal survives wherever the underlying data naturally divides into 3-bit groups.
This tool lets you go in the reverse direction - start from a compact octal value and expand it to the full binary representation for direct inspection of individual bits.
Does the output include leading zeros for each 3-bit group?
Yes. Each octal digit always expands to exactly 3 bits, with leading zeros padded as needed. The digit 1 becomes 001, not just 1. This preserves the full bit width so the bit positions are correct when you read the output against a register map or permission table.
What is the binary for chmod 777?
Each 7 expands to 111, giving 111 111 111 in binary. All 9 permission bits are set. This grants read, write, and execute to the owner, group, and others.
Can I enter octal numbers with a leading zero prefix?
Yes. The leading zero used in C-style octal literals (such as 0755) is stripped automatically before conversion. The converter treats 0755 and 755 identically.