Binary to Octal

A Binary to Octal Converter is a tool that converts numbers from the binary number system (base-2) into the octal number system (base-8). This conversion is widely used in computer science and digital electronics to simplify long binary numbers by grouping bits.

Binary only uses two digits: 0 and 1, while octal uses eight digits: 0–7.

Conversion Principle:

To convert binary to octal, group the binary digits in sets of three (starting from the right) and convert each triplet into its octal equivalent.

Example:

Binary 110101 → Grouped as 000 110 101 →

= (000 → 0), (110 → 6), (101 → 5)

→ Octal = 065

Common Uses for Binary to Octal Conversion:

• Computer Programming: Shortens binary representation for readability in source code.
• Digital Circuit Design: Eases visualization of binary states.
• Operating Systems: Octal permissions are used in UNIX/Linux file systems.
• Data Representation: Used in machine code, assembly language, and debugging.
• Education: Helps students understand relationships between number systems.

Key Features of Binary to Octal Converter:

• Accurate Grouping: Precisely splits binary digits into groups of three.
• Real-Time Output: Instant display of octal value from binary input.
• Handles Leading Zeros: Auto-fills with zeros for proper grouping.
• Fractional Support: Also converts binary fractions into octal.
• Simple UI: Easy for beginners, programmers, and engineers.
• Reliable: Supports large binary numbers without error.

The Binary to Octal Converter helps transform complex binary strings into compact octal representations.

Enter a Binary Number:

Example: 10110111

Auto Grouping:

Binary digits are grouped into sets of 3 from the right (e.g., 010 110 111).

Conversion:

Each group is translated into a single octal digit.

View Octal Result:

Displayed as 267 in this case.

Use Across Applications:

Ideal for coding, circuit design, file permissions, and learning.

Formula:

Group binary digits in triplets (from right to left), then convert.

Example 1: Binary: 1010

→ Pad with zeros: 001 010

→ 001 = 1, 010 = 2 → Octal = 12

Example 2: Binary: 11001101

→ Group: 000 110 011 101

→ Octal: 0 6 3 5 → 0635

Example 3 (with fraction): Binary: 1011.101

→ Integer part: 1011 → 001 011 → 1 3

→ Fraction part: 101 → 101 000 → 5

→ Octal = 13.5

Binary

Octal

000

0

001

1

010

2

011

3

100

4

101

5

110

6

111

7

Steps to Convert Binary to Octal:

1. Start with the binary number.
2. Add leading/trailing zeros to make full 3-bit groups.
3. Group bits in sets of three from right (for integers) or left (for fractions).
4. Convert each group to an octal digit.

Formula:



Binary (base-2) → Octal (base-8) = Group of 3 bits → 1 octal digit