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:
```Python
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.

How to convert a decimal number to hexadecimal in Python

Convert decimal to hexadecimal in Python using manual conversion (dividing by 16) or the hex() function. Detailed steps and code provided.

How to convert a decimal number to hexadecimal in Python

Using manual steps

Using the hex() function

Syntax

Code example

Explanation

Using the `hex()` function