Hexdecimal format

[Articron 738]

Just a quicky on the basics on how to form and/or read a hexadecimal format. I'll also include code implementations so the people that learn by reading code will also have an easy time understanding the concept.
 
Take a look at this little table:
 
DEC              HEX
0                      0
1                      1
2                      2
3                      3
4                      4
5                      5
6                      6
7                      7
8                      8
9                      9
A                     10
B                     11
C                     12
D                     13
E                     14
F                     15 
 
 
1. Converting decimal to hexadecimal formats
 
Assume we want to convert 250 into a hexadecimal format.
 
Step 1: We need to grab the 16-modulus of 250
Note: If you are unfamiliar with modulus, a quick google will get you up to speed with that quite quick.
 
250 mod 16 = 10 
(because the highest 16-multiplied value below 250 is 240... 250 - 240 = 10)
 
Step 2: Use that modulus to know your hexadecimal value from the table
 
For the value 10, our hex character is 'A' according to the table.
 
Step 3: Divide our total value(=250) by 16
 
250 / 16 = 15,625 = 15

Note: Always round down
 
Step 4: repeat step 1 - step 3 untill our value of 250 is zero
 
If we repeat step 1 to 3 for the value 15, our endpoint would be the character 'F'.
 
Important: we append new characters to our hexadecimal format on the left.
 
 
Conclusion: 250 = FA
 
If you were to implement this in code:

 final char[] HEX_TABLE = {
   '0','1','2','3',
   '4','5','6','7',
   '8','9','a','b',
   'c','d','e','f'
 };

String toHexadecimal(int num) {
        int val = num;
        String result = "";
        while (val > 0) {
            int tableId = val % 16;
            result = HEX_TABLE[tableId] + result;
            val /= 16;
        }
        return result;
}

2. Converting hexadecimal to decimal formats

 

Assume the following hex format: #1DC

 

To convert these characters back to the format we like, we'll have to do the opposite of what we did in the previous chapter.

 

We'll have to multiply the decimal value with 16 to the power of X

X is determined by the position of our character.

 

In this case, 1DC has 3 characters.

1 will be multiplied by 16^2,

D will be multiplied by 16^1

C will keep its own value, as it will be multplied with 16^0, which equates to 1

 

Convert these characters back by the use of the decimal/hex table I gave you:

1 = 1

D = 13

C = 12

 

Our equation becomes the following:

 

(1 x 16^2) + (13 x 16^1) + (12 x 16^0) 

256 + 208 + 12 = 476

 

Conclusion: 1DC = 476

 

 

In a code implementation, it would look like this:

final char[] HEX_TABLE = {
 '0','1','2','3',
 '4','5','6','7',
 '8','9','a','b',
 'c','d','e','f'
};

int hexToDec(String string) {
        int result = 0;
        char[] hex = string.toCharArray();
        int hexPow = hex.length - 1;
        for (int i = 0; i < hex.length; i++) {
            for (int x = 0; x < HEX_TABLE.length; x++) {
                if (hex[i] == HEX_TABLE[x]) {
                    result += x * Math.pow(16,hexPow--);
                }
            }
        }
        return result;
 }