Java Hexadecimal to Decimal conversion: Custom Logic

Question

I am trying to figure out how to convert hex into a string and integer so I can manipulate an RGB light on my arduino micro-controller through it's serialport. I found a good example on the java website, but I'm having a difficult time understanding some of the methods and I am getting hung up. I could easily just copy-paste this code and have it work but I want to fully understand it. I will add comments to my understandings and hopefully someone can provide some feedback.

public class HexToDecimalExample3{    
public static int getDecimal(String hex){    //this is the function which we will call later and they are declaring string hex here. Can we declare string hex inside the scope..?
    String digits = "0123456789ABCDEF";      //declaring string "digits" with all possible inputs in linear order for later indexing
             hex = hex.toUpperCase();        //converting string to uppercase, just "in case"
             int val = 0;                    //declaring int val. I don't get this part.
             for (int i = 0; i < hex.length(); i++)  //hex.length is how long the string is I think, so we don't finish the loop until all letters in string is done. pls validate this
             {  
                 char c = hex.charAt(i);     //char is completely new to me. Are we taking the characters from the string 'hex' and making an indexed array of a sort? It seems similar to indexOf but non-linear? help me understand this..
                 int d = digits.indexOf(c);  //indexing linearly where 0=1 and A=11 and storing to an integer variable
                 val = 16*val + d;           //How do we multiply 16(bits) by val=0 to get a converted value? I do not get this..
             }  
             return val;  
}  
public static void main(String args[]){    
System.out.println("Decimal of a is: "+getDecimal("a"));  //printing the conversions out.
System.out.println("Decimal of f is: "+getDecimal("f"));  
System.out.println("Decimal of 121 is: "+getDecimal("121"));  
}}    

To summerize the comments, it's primarily the char c = hex.charAt(i); AND the val = 16*val + d; parts I don't understand.

Answer 1

Ok, let's go line for line

public static int getDecimal(String hex)

hex is the parameter, it needs to be declared there, so you can pass a String when you call the function.

String digits = "0123456789ABCDEF";

Yes, this declares a string with all characters which can occur in a hexadecimal number.

hex = hex.toUpperCase();

It converts the letters in the hex-String to upper case, so that it is consistent, i.e. you always have F and never f, no matter which is being input.

int val = 0;  

This is the variable where the corresponding decimal value will later be in. We will do our calculations with this variable.

for (int i = 0; i < hex.length(); i++)

hex.length() is the number of characters in the hex-String provided. We execute the code inside this for loop once per character.

char c = hex.charAt(i);

Yes, char represents a single character. We retrieve the character from the hex-String at index i, so in the first iteration it is the first character, in the second iteration the second character and so on.

int d = digits.indexOf(c);

We look which index the character has in the digit-String. In that way we determine the decimal representation of this specific digit. Like 0-9 stay 0-9 and F becomes a 15.

val = 16*val + d;

Let's think about what we have to do. We have the decimal value of the digit. But in hexadecimal we have this digit at a specific position with which it gets multiplied. Like the '1' in '100' is actually not a 1, but 100 * 1 because it is at this position. 10 in hexadecimal is 16 in decimal, because we have 1 * 16. Now the approach here is a little bit complicated. val is not uninitialized. val is 0 at the beginning and then contains the cumulated values from the previous iterations. Since the first character in the String is the highest position we don't know directly with what we have to multiply, because we don't know how many digits the number has (actually we do, but this approach doesn't use this). So we just add the digit value to it. In the consecutive iterations it will get multiplied by 16 to scale it up to the corresponding digit base value. Let me show you an example:

---

Take 25F as hex number. Now the first iteration takes the 2 and converts it to a 2 and adds it to val. The 16 * val resolves to 0 so is not effective in the first time.

The next iteration multiplies the 2 with 16 and takes the 5 (converted to 5) and adds it to val. So now we have (I split it mathematically so you understand it): 2 * 16 + 5

Next we get the F which is decimal 15. We multiply val by 16 and add the 15.

We get 2 * 256 + 5 * 16 + 16 (* 1), which is actually how you calculate the decimal value of this hex value mathematically.

Another possibility to compute val is:

val += Math.pow(16, hex.length() - i - 1) * d;