How to convert a decimal number to hexadecimal in Python

A decimal is a term that describes the base- $10$ number system; for example, $(47)_{10}$

A hexadecimal is a term that describes the base- $16$ number system.

The digits used in hexadecimal are $0–9$ , followed by $A–F$ , where $A$ represents the decimal number $10$ , $B$ represents $11$ , and so on up to $F$ representing $15$ .

There are two ways in which we can convert decimal to hexadecimal numbers:

Using manual steps to convert
Using the hex() function

Using manual steps

Step 1: Start by entering the decimal number provided.

Step 2: Divide the decimal value by $16$ .

Step 3: Convert the remainder obtained in Step 2 to the equivalent hexadecimal digit. If the remaining is less than $10$ , the remainder should be used as the hexadecimal digit. Use the matching letter $A-F$ instead, where $A$ represents $10$ , $B$ represents $11$ , and so on.

Step 4: Add the hexadecimal digit received to the front of the result.

Step 5: Steps 2–4 must be repeated until the decimal number reaches zero.

Step 6: The hexadecimal representation of the original decimal number is obtained as a result.

Example: Convert the decimal number $1000_{10}$ into hexadecimal.

Using the `hex()` function

We can convert a decimal number to hexadecimal in Python using the built-in hex() function. It takes a parameter decimal number and returns its hexadecimal number.

Syntax

Here is the syntax for using the hex() function:

hex(decimal_number)

Code example

The following code shows the conversion from decimal to hexadecimal using both methods:

# Method 1 (Using the manual steps)
def decimal_to_hexadecimal(decimal_num):
    hex_characters = "0123456789ABCDEF"
    if decimal_num == 0:
        return "0"
    
    hexadecimal = ""
    while decimal_num > 0:
        remainder = decimal_num % 16
        hexadecimal = hex_characters[remainder] + hexadecimal
        decimal_num //= 16
    
    return hexadecimal
decimal_number = 1000
hexadecimal_value = decimal_to_hexadecimal(decimal_number)
print("Manual steps output: ", hexadecimal_value)
# Method 2 (Using the hex function)
decimal_number = 1000
hexadecimal_value = hex(decimal_number)
print("Hex function output: ", hexadecimal_value)

Explanation

Line 2: This function takes a decimal number as input and converts it to a hexadecimal string.
Line 3: hex_characters is a string containing the hexadecimal digits. It’s used to map the remainder to the corresponding hexadecimal digit.
Line 4–5: The function starts with a special case: if the input decimal_num is 0, it directly returns “0” since the hexadecimal representation of 0 is “0”.
Line 8–13: Inside the while loop, the decimal number is continuously divided by 16, and the remainder is used to index into the hex_characters string to get the corresponding hexadecimal digit. This digit is then concatenated to the left side of the hexadecimal string. After obtaining the hexadecimal digits in reverse order, the function returns the final hexadecimal value.
Line 15: The code outside the function initializes a decimal_number variable with the value 1000.
Line 16–17: The decimal_to_hexadecimal function is called with decimal_number as an argument, and the resulting hexadecimal value is stored in the hexadecimal_value variable. The hexadecimal value is printed along with a label using the print function.
Line 21: The hex function is called with decimal_number as an argument. This function converts the decimal number to a string representing its hexadecimal value, with the 0x prefix.

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