Octal to Decimal Conversion is essential in programming, especially in Unix file permissions and low-level operations.
This step-by-step guide will help you understand how to convert octal to decimal easily, and the logic behind the method to apply it in real-world programming scenarios.
What is an Octal Number?
An octal number uses base-8, meaning it only includes digits from 0 to 7. Each position represents a power of 8, starting from the right.For example-- Octal
71→ Decimal57 - Octal
204→ Decimal132 - Octal
345→ Decimal229
How Octal to Decimal Conversion Works
The general formula -decimal = (digit_n * 8^n) + (digit_n-1 * 8^n-1) + ... + (digit_0 * 8^0)71 (octal) -= 7 * 8^1 + 1 * 8^0= 56 + 1 = 57Method 1: Manual Conversion Using Loop (Python)
We’ll extract each digit, multiply it by the corresponding power of 8, and add it to the result.✅ Python Code -def octal_to_decimal(octal): decimal = 0 base = 1 while octal > 0: last_digit = octal % 10 decimal += last_digit * base base *= 8 octal //= 10 return decimal# Exampleoctal_num = 204print(f"Decimal of {octal_num} is {octal_to_decimal(octal_num)}") # Output: 132- O(log N) – where N is the octal number
- Space Complexity: O(1)
Method 2: Using int() Built-in Function
Python makes life easy. The int() function can convert strings in any base.✅ Code Example -octal_str = "345"decimal = int(octal_str, 8)print(f"Decimal of {octal_str} is {decimal}") # Output: 229Method 3: Using Recursion
You can also use recursion to process digits from right to left.✅ Python Code -def recursive_octal_to_decimal(octal): if octal == 0: return 0 return (octal % 10) + 8 * recursive_octal_to_decimal(octal // 10)# Exampleoctal_num = 132print(f"Decimal of {octal_num} is {recursive_octal_to_decimal(octal_num)}") # Output: 90- Breaks down the number by digits
- Multiplies each digit by increasing powers of 8
- Recursively adds the results
Summary Table Using Python
| Method | Best Use Case | Time Complexity |
| Manual loop | Custom logic or learning purpose | O(log N) |
| Built-in int() | Fast and clean scripts | O(1) |
| Recursion | Recursive learning practice | O(log N) |
Final Thoughts
Octal to decimal conversion might sound technical at first, but with just a bit of logic or the help of Python’s built-in features, it becomes a breeze.
Whether you're handling file permissions, reading binary data, or just brushing up on number systems, these methods will serve you well.
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