Python Convert Decimal Numbers to Octal and vice versa

Working with different number systems is a common task in programming, especially in computer science, digital electronics, and networking. Python makes it easy to convert between Decimal (Base-10) and Octal (Base-8).

In this article, you’ll learn how to:

• Convert a Decimal number to Octal
• Convert an Octal number to Decimal
• Do both using built-in functions and manual methods

Decimal and Octal Numbers

Decimal Number (Base-10)

• The decimal system is the standard number system we use every day.
• It uses 10 digits: 0 to 9.
• Each digit’s place value is a power of 10.
• Example: 347 = ( 3 × 10² ) + ( 4 × 10¹ ) + ( 7 × 10⁰ ) = 300 + 40 + 7

Octal Number (Base-8)

• The Octal Number System is a base-8 number system.
• Uses 8 digits only: 0 to 7
• Each place value is a power of 8
• Example: 157 (octal) = ( 1 × 8² ) + ( 5 × 8¹ ) + ( 7 × 8⁰ ) = 64 + 40 + 7 = 111 (in decimal)

Convert Decimal to Octal In Python

1. Using Built-in oct() Function

In this approach, we will be using the built-in function oct() that converts a decimal to an octal string.

Syntax: oct(x)

• x must be an integer.
• Returns a string starting with '0o', indicating octal.
• For Example, oct(26) = '0o32'

Use the below syntax if you want to remove the ‘0x’ prefix:

octal = oct(26)[2:] # Output: '32'

Note: [2:] slices a string from index 2 to the end, skipping the first two characters.

Code Example

decimal = 26
octal = oct(decimal)
print(f"Octal value: {octal[2:]}")Code language: Python (python)

Output:

Octal value: 32

2. Using format() Function

The format() function in Python converts an integer decimal to its octal representation as a string, without the '0o' prefix.

Syntax: format(number, 'X')

• number must be an integer (can be positive or negative).
• 'X': Format code for octal. ‘o’ for octal.
• Returns a string of octal representation of the integer.
• For Example, format(255, 'o') = '377'

Note: No '0o' like with oct().

Code Example

decimal = 255
octal = format(decimal, 'o')
print(f"Octal value: {octal}")

# Output:
# Octal value: 377Code language: Python (python)

3. Using F-String Formatting

An F-string (formatted string literal) lets you embed variables, expressions, or formatting instructions directly into a string using {}.

Just prefix the string with f or F and place variables or expressions inside {}.

For Example,

name = "Alice"
age = 25
f"My name is {name} and I am {age} years old."    # Output: My name is Alice and I am 25 years old.

Numbers can be formatted like this:

f"{3.14159:.2f}" # Output: '3.14' → 2 decimal places
f"{{5:b}}" # Output: '101' → binary of 5

f"{255:x}" # Output: 'ff' → hexadecimal of 255
:x inside the f-string formats the decimal as hexadecimal

f"{65:o}" # Output: '101' → Octal of 65

Code Example

decimal = 65
print(f"Octal value: {decimal:o}")  # Lowercase 'o' for octal

# Output:
# Octal value: 101Code language: Python (python)

4. Using a While Loop

In this approach, we manually convert the decimal number into an octal number using while loop.

Algorithm to convert Decimal to Octal in Python:

1. If the decimal number n is 0, return "0" as the octal result.
2. Initialize an empty string octal = "" to store the octal result.
3. Repeat the following steps while n > 0:
   • Find the remainder when n is divided by 8:
     remainder = n % 8
   • Convert the remainder to a string and prepend it to octal:
     octal = str(remainder) + octal
   • Update n by integer division by 8:
     n = n // 8
4. After the loop ends, return the string octal.

For Example: Convert Decimal 65 to Octal: n = 65

Step 1: n = 65
remainder: 65 % 8 = 1 
→ octal = "1"
n = 65 ÷ 8 = 8

Step 2: n = 8
remainder: 65 % 8 = 0 
→ octal = "01"
n = 8 ÷ 8 = 1

Step 3: n = 1
remainder: 1 % 8 = 1 
→ octal = "101"
n = 1 ÷ 8 = 0

Step 4: n = 0 : stop
The loop ends when the decimal becomes 0.

The octal representation of 65 is: 101

Code Example

def decimal_to_octal(n):
    if n == 0:
        return "0"
    octal = ""
    while n > 0:
        octal = str(n % 8) + octal
        n = n // 8
    return octal

decimal = 65
print("Octal value:", decimal_to_octal(decimal))

# Output:
# Octal value: 101Code language: Python (python)

Octal to Decimal Conversion in Python

1. Using Built-in int() with Base 8

In this approach, we will be using the built-in function int() which converts a octal string to a decimal integer.

Syntax: int(x, base)

• x: A string or number (in our case, a octal string, like "101")
• base: The base of the number system (8 for octal)
• For Example, int("101", 8) # Output: 65

Code Example

oct = "101"
decimal = int(oct, 8)
print(f"Decimal value of {oct} is {decimal}")

# Output:
# Decimal value of 101 is 65Code language: Python (python)

2. Manual Conversion Using Loop

This approach does not use the built-in function but manually converts the Octal number into a Decimal Number using a for loop in Python.

For example, the octal number "127" means:
= ( 1 × 8² ) + ( 2 × 8¹ ) + ( 7 × 8⁰ ) 
= ( 1 × 64 ) + ( 2 × 8 ) + ( 7 × 1 )  
= 64 + 16 + 7  
= 87 (in decimal)

Code Example

# function to convert octal to decimal
def octal_to_decimal(octal_str):
    decimal = 0
    power = 0

    # Start from the rightmost digit
    for digit in reversed(octal_str):
        decimal += int(digit) * (8 ** power)
        power += 1

    return decimal

# Example
octal = "127"
print("Decimal value:", octal_to_decimal(octal))

# Output:
# Decimal value: 87Code language: Python (python)

Explanation

1. Initialize a variable decimal = 0
   • This will hold the final converted value.
2. Initialize power = 0
   • This represents the position of the digit (starting from the rightmost digit, which is 8⁰).
3. Reverse the octal string
   • So we can process from the least significant digit to the most significant one.
4. Loop through each digit in the reversed octal string:
   • Convert the digit (character) to an integer: int(digit)
   • Multiply it by 8^power (i.e., 8 ** power)
   • Add the result to decimal
   • Increment power by 1
5. After the loop, return or print the final value of decimal.

Summary

Python provides simple and powerful tools for converting between decimal and octal numbers:

• Use built-in functions like oct() and int(..., 8) for quick results.
• Try manual methods to understand how number systems work internally.