# Decimal to hex conversion

Decimal to hex conversion is needed in different occasions, but most frequently when you need to represent a number for a specific computer program. Here you will learn how to do the calculations and also how to create a converter in C language. Of course, you can use the online converter, as well.

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## Online decimal to hex converter

Input the decimal value The hex number is
 Input the decimal value 0 The hex number is 0

## How it works

The hexadecimal number system uses 16 characters to represent the numbers. These characters(digits) include the decimal digits (0..9) and the first six letters (A..F). It doesn't matter if you use uppercase or lowercase letters. Hex values are often preceded by the 0x (zero x) prefix. It indicates that the value that follows is a hexadecimal number.

To convert from decimal to hex, we use the following algorithm:

1. Divide the decimal number by 16 (the base of the target notation). Save the result and the remainder.
2. Repeat step 1, but this time divide the result from the previous operation. Continue to divide until the result is equal to 0.
3. Go through all remainders. Change (10 to A), (11 to B), (12 to C), (13 to D), (14 to E), (15 to F). Take the remainders in reversed order – this is the final result.

Example: 1610 = ? (hex)

Part 1: 16 / 16 = 1 and remainder 0. Remember the result(1) and the remainder (0).
Repeat Part 1, using the result: 1 / 16 = 0 and remainder 1. We reached result 0, so we continue with 3:
Part 3: The remainders that we have are 0 and 1. No substitution is needed. Their reversed order is 10. This is the final result:

1610 = 1016

Example: 17310 = ?(hex)
173 / 16 = 10 result, 13 rem
10 / 16 = 0 result, 10 rem
Substitute: 13 = D, 10 = A. Reverse them for the final result: AD

Try to convert several numbers in the range of 20-300 and then test your result with the tool above.

## C program to convert decimal to hex

Just like the other converters that we have done, we will create a program that converts up to 64 bit numbers. For that reason we use unsigned long for the input type.

Note that long is not guaranteed to be a 64 bit number. If your compiler supports C99, you can use the uint64_t type, which is defined in stdint.h

To save the hex result we use a string, in the case of C language that is a char pointer. The biggest 64 bit number can be saved in 16-digit hexadecimal number. That's why we use allocate space for 17 characters(16 value digits + the null terminator).

Keep in mind that we want to take the remainder from the division in reversed order. We could write them in normal order and then loop through all of them to reverse their order. This will take one additional loop. Instead we write them in reversed order and from there on we just read them normally. No additional loops needed.

For that reason we move the pointer to the last position: hex += 16;

We put the terminating null at the end and start the loop. Inside it we do the following:

• Move the pointer of the result one position to the left
• Divide the decimal and save the result and the remainder.
• The remainder of the division is a decimal number, but we need a hex char. We do the conversion in the remainderToHex function.

Once the loop is over, we have our result.

You can download the source of the complete example from here: dec-to-hex.zip

int main(void)
{
unsigned long decimal;
char *hex;
scanf(
"%lu", &decimal);

hex = decimalToHex(decimal);

printf("%lu in decimal equals %s in hexadecimal\n", decimal, hex);
return
0;

}

char* decimalToHex(unsigned long decimal)
{
char *hex = (char*)malloc(17);
if(hex == NULL)
exit(1);
hex += 16;
*hex = '\0';
char remainder;
while(decimal > 0)
{
--hex;
remainder = remainderToHex(decimal % 16);
*hex = remainder;
decimal = decimal / 16;
}
return hex;
}

I also prepared a tutorial for the reversed conversion: Hex to decimal, as well as others like Decimal to binary.

#### Do you learn better from video?

Learn faster with deeper understanding!
The "Computer programming for beginners" course is the perfect place to begin with programming.

› Decimal to hex
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