# 
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 $15$.


# Decimal to hexadecimal conversion


**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.

# Code example

The following code shows the conversion from decimal to hexadecimal.

#include <stdio.h>

void decToHex(int decimal) 
{
    if (decimal == 0) 
    {
        printf("Hexadecimal: 0\n");
        return;
    }

    char hexadecimal[100];
    int indx = 0;

    while (decimal > 0) 
    {
        int remainder = decimal % 16;

        if (remainder < 10)
            hexadecimal[indx++] = remainder + '0';
        else
            hexadecimal[indx++] = remainder + 'A' - 10;

        decimal /= 16;
    }

    printf("Hexadecimal number is: ");

    for (int i = indx - 1; i >= 0; i--)
        printf("%c", hexadecimal[i]);

    printf("\n");
}

int main() 
{
    int decimalNum = 27;
    decToHex(decimalNum);
    return 0;
}

# Code explanation

- **Lines 5–9:** The `if` condition determines whether the input decimal is equal to zero. If it is, the hexadecimal representation is also zero, and the function outputs `"Hexadecimal: 0"` and returns.

- **Lines 18–21:** The `if-else` condition determines whether the remainder is less than $10$. If it is, the remainder is in the $0–9$ range, and the matching hexadecimal digit may be derived by adding the remainder to the ASCII value `'0'`. If the remainder is more than or equal to $10$, the hexadecimal digits are $A–F$. In this situation, the remainder is calculated by subtracting `10` and adding it to the ASCII value `'A'`.

- **Lines 28–29:** The `for` loop iterates through the hexadecimal array in reverse order, beginning at the highest index `indx - 1` and ending at `0`. The format specifier `%c` is used to print each hexadecimal digit.

- **Lines 34–39:** The `main` function assigns the value `27` to the integer variable `decimalNum`. It then runs the `decToHex` method with the input `decimalNum` to convert it into hexadecimal.


How to convert a decimal number to hexadecimal in C

Conversion of decimal to hexadecimal involves dividing by 16, converting remainders to hexadecimal, and repeating until zero. Example code provided.