Binary to Octal Converter

Convert binary numbers to octal format. This tool groups bits into triplets and translates them to octal digits. A compact representation sometimes used in computing and permissions.

Binary Input

Octal Output

Binary to Octal Reference Table

Octal

Binary

Octal

Binary

000

100

001

101

010

110

011

111

How Binary to Octal Conversion Works

Group binary digits into sets of 3 (triplets), starting from the right. Each triplet directly maps to one octal digit (0-7). For example: 101 110 = 5 6 = 56 in octal.

Octal is commonly used in Unix file permissions (e.g., 755, 644).

How It Works

This binary to octal converter transforms binary numbers (base-2) into octal format (base-8). It groups binary digits into sets of three and converts each group to its octal equivalent.

The conversion process:

Group into threes: Starting from the right, group binary digits into sets of 3 bits.
Pad if needed: Add leading zeros to the leftmost group if it has fewer than 3 bits.
Convert each group: Each 3-bit group converts to one octal digit (000=0, 111=7).
Concatenate result: Join all octal digits to form the final octal number.

For example: 111101101 becomes 755 (111=7, 101=5, 101=5). This grouping works because 8 = 2^3, so exactly 3 binary bits map to each octal digit.

When You'd Actually Use This

Unix File Permissions

Convert binary permission bits to octal chmod values (rwx bits to 755, 644, etc.).

Digital Circuit Design

Convert binary outputs to octal for documentation and analysis of digital systems.

Learning Number Systems

Understand the relationship between binary and octal for computer science education.

Legacy Code Maintenance

Interpret octal literals in older code and understand their binary representation.

Data Compression Studies

Explore how different bases represent the same data with varying efficiency.

Aviation Applications

Convert binary data to octal for aircraft transponder code analysis.

What to Know Before Using

Group from right to left

Always start grouping from the right (least significant bit). This ensures correct place values.

Leading zeros don't change value

001101 = 1101 = 15 (octal). Leading zeros can be added to complete the leftmost group.

Each 3 bits = 1 octal digit

This is the key relationship. N binary bits produce N/3 (rounded up) octal digits.

Octal only uses digits 0-7

If your conversion produces 8 or 9, something went wrong. 3 bits max value is 7 (111).

Unix permissions use special meaning

Each octal digit represents read(4)+write(2)+execute(1) for user/group/others.

Common Questions

What's the binary to octal conversion table?

000=0, 001=1, 010=2, 011=3, 100=4, 101=5, 110=6, 111=7. Just 8 conversions to memorize.

How do I convert octal back to binary?

Expand each octal digit to 3 bits. 755 becomes 111 101 101. Simple reverse operation.

Why group by 3s specifically?

Because 8 = 2^3. Three binary bits exactly represent values 0-7, which is one octal digit. Perfect mapping.

What if binary length isn't divisible by 3?

Add leading zeros. 1011010 (7 bits) becomes 001 011 010 = 132 (octal). Leading zeros don't change value.

Why was octal popular in computing?

Early computers had 12, 24, or 36-bit words (divisible by 3). Octal was more compact than binary. Hex replaced it for 8-bit systems.

What does chmod 755 mean in binary?

7=111 (rwx), 5=101 (r-x), 5=101 (r-x). Full permissions for owner, read+execute for group and others.

Is octal still relevant today?

Less than hex, but still used in Unix file permissions, some legacy systems, and aviation. Good to understand for these cases.

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