How do I convert binary to octal?

Group binary digits in groups of 3 from right to left, padding with zeros if needed. Convert each group: 000=0, 001=1, 010=2, 011=3, 100=4, 101=5, 110=6, 111=7.

What does chmod 755 mean?

755 means owner has full access (7=rwx), group has read and execute (5=r-x), and others have read and execute (5=r-x). This is standard for web server directories and executable scripts.

Why is octal used for file permissions?

Each permission set (read, write, execute) is 3 bits, and each octal digit represents exactly 3 bits. This makes octal a natural fit: one digit per permission group (owner, group, other).

What is the difference between chmod 644 and 755?

644 (rw-r--r--) is for regular files: owner can read/write, everyone else read-only. 755 (rwxr-xr-x) adds execute permission, needed for directories (to enter them) and scripts (to run them).

Is octal used outside of Unix permissions?

Octal was more common historically in PDP-8 and other systems. Today it is used in Unix permissions, C/C++ octal literals, some assembly languages, and aviation transponder codes (squawk codes like 7700).

What happens if I set permissions to 777?

777 (rwxrwxrwx) gives everyone full read, write, and execute access — generally a security risk. It is sometimes used temporarily for debugging but should never be left on production files.

Binary to Octal Converter

Convert binary to octal and octal to binary. Step-by-step 3-bit grouping, Unix file permissions decoder, common chmod values, and complete reference table.

Direction

Octal Input

Binary (3-bit groups)

111 101 101

9 bits

Octal

0o755

3 digit(s)

Decimal

493

Hexadecimal

0x1ED

4-bit grouping

Binary (4-bit groups)

0001 1110 1101

Hex-aligned grouping

Unix Permissions

rwxr-xr-x

Owner: rwx | Group: r-x | Other: r-x

Step-by-Step Conversion

111

↕

7

101

↕

5

101

↕

5

= 111 101 101

Unix File Permissions (Octal)

Octal	Binary	Permission	Meaning
0	000	---	None
1	001	--x	Execute
2	010	-w-	Write
3	011	-wx	Write Execute
4	100	r--	Read
5	101	r-x	Read Execute
6	110	rw-	Read Write
7	111	rwx	Read Write Execute

Common Permission Sets

Octal	Symbolic	Description
777	rwxrwxrwx	Full access for everyone (dangerous)
755	rwxr-xr-x	Owner full, others read/execute (common for dirs)
750	rwxr-x---	Owner full, group read/execute, others none
700	rwx------	Owner only (private directories)
666	rw-rw-rw-	Read/write for everyone (rarely used)
644	rw-r--r--	Owner read/write, others read only (common for files)
600	rw-------	Owner read/write only (private files)
400	r--------	Owner read only (SSH keys)

Planning notes, formulas, and examples

About the Binary to Octal Converter

Octal (base 8) uses digits 0-7, with each digit mapping to exactly 3 binary bits. This makes binary-to-octal conversion as straightforward as grouping bits in threes — similar to how hexadecimal groups bits in fours. Octal's most prominent modern use is in Unix/Linux file permissions, where chmod commands like 755, 644, and 777 control read, write, and execute access.

It gives bidirectional conversion between binary and octal, along with step-by-step visualization showing how each 3-bit group maps to its octal digit. For Unix users, the built-in permissions decoder translates any 3-digit octal value into its symbolic permission string (rwxr-xr-x) and explains what each digit means for owner, group, and other users.

Whether you are a Linux system administrator setting file permissions, a CS student learning number bases, or a programmer working with legacy systems that use octal notation, this converter handles the conversion while teaching the underlying mapping. The common permissions reference table covers the most frequently used chmod values with explanations.

When This Page Helps

The octal-binary mapping (3 bits per digit) is simpler than hex, but the real value of this converter is the Unix permissions integration. Enter a chmod value like 755 and see the binary breakdown, symbolic notation, and what each permission level means — no need to memorize the permission table.

How to Use the Inputs

Select Binary → Octal or Octal → Binary.
Enter the binary or octal value.
View converted values in all bases, plus Unix permission interpretation for valid chmod values.
Follow the Step-by-Step Conversion to see 3-bit group mapping.
Check the Unix File Permissions table for the octal-to-permission mapping.
Refer to Common Permission Sets for frequently used chmod values.

Formula used

Binary to Octal: Group binary digits in groups of 3 from right, convert each group (000=0, 111=7).
Octal to Binary: Replace each octal digit with its 3-bit binary equivalent.
Unix: Each octal digit = r(4) + w(2) + x(1). E.g., 7 = rwx, 5 = r-x, 4 = r--

Example Calculation

Result: 111 101 101 (binary) = rwxr-xr-x

755 in octal: 7=111 (rwx for owner), 5=101 (r-x for group), 5=101 (r-x for others). This is the standard permission for executable files and directories in Unix/Linux.

Tips & Best Practices

Key octal-binary pairs: 0=000, 1=001, 2=010, 3=011, 4=100, 5=101, 6=110, 7=111.
For Unix permissions: r=4, w=2, x=1. Add them: rwx=7, rw-=6, r-x=5, r--=4, ---=0.
Most common permissions: 755 for directories/executables, 644 for regular files, 600 for private files.
The leading digit in 4-digit chmod (e.g., 1755) sets special bits: setuid(4), setgid(2), sticky(1).
C programming uses 0 prefix for octal literals: 0777 is octal 777. Avoid accidental octal: 010 = 8, not 10.
Python uses 0o prefix: 0o755. JavaScript also recognizes 0o prefix in strict mode.

Octal in Computing History

Octal was widely used in early computing when word sizes were multiples of 3 (6-bit, 12-bit, 36-bit). The PDP-8, one of the most popular minicomputers, used 12-bit words displayed as 4 octal digits. When 8-bit bytes and 16/32-bit words became standard, hexadecimal (which groups 4 bits) became more practical, but octal persists in Unix permissions.

Understanding Unix Permission Bits

Unix file permissions use 9 bits: 3 for owner, 3 for group, 3 for others. Each group has read (r=4), write (w=2), and execute (x=1) bits. The octal representation compresses each 3-bit group into a single digit. Special bits (setuid, setgid, sticky) use a fourth leading digit.

Security Implications of File Permissions

Incorrect permissions are a common security vulnerability. SSH private keys must be 600 or 400. Web-accessible directories should never be 777. The principle of least privilege says: grant the minimum permissions needed. Use `chmod -R` carefully — recursive permission changes can expose sensitive files.

Sources & Methodology

Last updated: March 8, 2026

Frequently Asked Questions

Group binary digits in groups of 3 from right to left, padding with zeros if needed. Convert each group: 000=0, 001=1, 010=2, 011=3, 100=4, 101=5, 110=6, 111=7.