Python Program to Convert Octal to Decimal Number

You can convert an octal number to decimal in Python using decimal_number = int(octal_string, 8), where octal_string is the octal input as a string.

Examples

Input7

Output7

Input10

Output8

Input377

Output255

How to Think About It

To convert octal to decimal, think of each digit in the octal number as a place value multiplied by powers of 8. Starting from the rightmost digit, multiply it by 8 raised to the position index (starting at 0) and add all these values together to get the decimal number.

Algorithm

1

Get the octal number as a string input.

2

Initialize a decimal result to zero.

3

For each digit in the octal string from right to left, convert it to an integer.

4

Multiply the digit by 8 raised to the power of its position index.

5

Add the result to the decimal total.

6

Return or print the decimal total.

Code

python

octal_str = input("Enter an octal number: ")
decimal_num = int(octal_str, 8)
print(f"Decimal number: {decimal_num}")

Output

Enter an octal number: 377
Decimal number: 255

Dry Run

Let's trace the input '377' through the code

1

Input octal string

octal_str = '377'

2

Convert octal to decimal

decimal_num = int('377', 8) which equals 3*8^2 + 7*8^1 + 7*8^0 = 192 + 56 + 7 = 255

3

Print result

Output: Decimal number: 255

Digit	Position (right to left)	Calculation	Running Total
7	0	7 * 8^0 = 7	7
7	1	7 * 8^1 = 56	63
3	2	3 * 8^2 = 192	255

Why This Works

Step 1: Using int() with base 8

The int() function can convert a string in any base to decimal by specifying the base as 8 for octal.

Step 2: Octal place values

Each digit in octal represents a power of 8, starting from the rightmost digit at power 0.

Step 3: Summing values

Multiplying each digit by its place value and adding all results gives the decimal equivalent.

Alternative Approaches

Manual calculation using loop

python

octal_str = input("Enter octal number: ")
decimal_num = 0
power = 0
for digit in reversed(octal_str):
    decimal_num += int(digit) * (8 ** power)
    power += 1
print(f"Decimal number: {decimal_num}")

This method shows the step-by-step calculation but is longer than using int() with base 8.

Using recursion

python

def octal_to_decimal(octal_str):
    if len(octal_str) == 0:
        return 0
    return octal_to_decimal(octal_str[:-1]) * 8 + int(octal_str[-1])

num = input("Enter octal number: ")
print(f"Decimal number: {octal_to_decimal(num)}")

This recursive approach is elegant but less efficient for very long numbers.

Complexity: O(n) time, O(1) space

Time Complexity

The conversion scans each digit once, so time grows linearly with the number of digits.

Space Complexity

Only a few variables are used, so space is constant regardless of input size.

Which Approach is Fastest?

Using Python's built-in int() with base 8 is fastest and simplest compared to manual or recursive methods.

Approach	Time	Space	Best For
int() with base 8	O(n)	O(1)	Simple and fast conversion
Manual loop calculation	O(n)	O(1)	Learning and understanding conversion
Recursive method	O(n)	O(n)	Elegant code but uses more stack space