Octal to Decimal

An Octal to Decimal Converter is a tool used to convert numbers from the octal system (base-8) into the decimal system (base-10). The octal system, using digits 0 through 7, is often used in computer science and digital electronics, especially for simplifying binary data.

The decimal system is the standard base-10 system that uses digits from 0–9, commonly used in everyday arithmetic.

Conversion Principle:

To convert octal to decimal, multiply each digit of the octal number by 8 raised to the power of its position (from right to left) and sum the results.

Example:

Octal: 157

→ (1 × 8²) + (5 × 8¹) + (7 × 8⁰)

→ (1 × 64) + (5 × 8) + (7 × 1) = 64 + 40 + 7 = 111

Common Uses for Octal to Decimal Conversion:

• Computer Systems: Used in Unix file permissions and hardware registers.
• Digital Electronics: Compact representation of binary values.
• Programming: Helpful when debugging low-level code or memory addresses.
• Networking: Some network configurations may use octal notation.
• Education: Teaching students how to convert and understand number systems.

Key Features of Octal to Decimal Converter:

• Accurate Calculation: Uses standard base-8 to base-10 conversion rules.
• Supports Fractions: Handles both integer and fractional octal numbers.
• Instant Output: Provides real-time results as you input.
• Error-Free: Eliminates manual calculation mistakes.
• Beginner Friendly: Clear and easy-to-use interface.
• Efficient: Fast conversion for long or complex octal inputs.

This converter is valuable for programmers, digital system designers, and students learning numerical base conversions.

Enter the Octal Number:

Example: 45, 173, or 12.4.

Conversion Happens Automatically:

The tool converts each digit based on its position.

View the Decimal Result:

The decimal equivalent appears instantly.

Apply as Needed:

Use the result in software, hardware, or academic applications.

Formula:

Decimal = (dₙ × 8ⁿ) + (dₙ₋₁ × 8ⁿ⁻¹) + ... + (d₀ × 8⁰)

Example 1: Octal: 46

→ (4 × 8¹) + (6 × 8⁰) = 32 + 6 = 38

Example 2: Octal: 725

→ (7 × 8²) + (2 × 8¹) + (5 × 8⁰) = 448 + 16 + 5 = 469



Example 3 (with fraction): Octal: 3.4

→ Integer part: (3 × 8⁰) = 3

→ Fractional part: (4 × 8⁻¹) = 4 × 0.125 = 0.5

→ Decimal = 3.5

Octal

Decimal

1

1

2

2

3

3

4

4

5

5

6

6

7

7

10

8

11

9

12

10

20

16

100

64

144

100

200

128

377

255

Steps to Convert Octal to Decimal:

For Integer Part:

1. Write down the octal number.
2. Multiply each digit by 8 raised to the power of its position (right to left, starting at 0).
3. Add all the results to get the decimal number.

For Fractional Part:

1. Multiply each digit after the decimal by 8 raised to a negative power.
2. Add those to the integer result.

Formula:

Decimal = Σ (digit × 8^position)