Converting from hexadecimal to decimal java

Question

Converting from hexadecimal to decimal java

I don't understand how the number is translated in this example. I mean, I don't understand the last step... We take a character from a string, then calculate its index, change the letters from the 16-system to numbers, and then... How then ? Everything works correctly, I checked (compiled), but if I sit on a piece of paper and count, I don't get it at all, how does the program come to the right decision... Can someone slightly step-by-step decompose how the post. string works correctly when calculating val a variable.

    public static int hex2decimal(String s) {
    String digits = "0123456789ABCDEF";
    s = s.toUpperCase();
    int val = 0;
    for (int i = 0; i < s.length(); i++) {
        char c = s.charAt(i);
        int d = digits.indexOf(c);
        val = 16*val + d;
    }
    return val;
}

0

English java

Author: Oleksandr, 2016-07-09

Source

1 answers

score 4 · Accepted Answer

A number in hexadecimal, such as A1B, is converted to decimal by the formula A*16^2 + 1*16 + B, where A=10, and B=11. Result 2587. However, instead of raising the base of the number system 16 to a power at each step, you can use a method akin to the Gorner scheme to calculate the values of the polynomials at a point. That is, (A*16 + 1)*16 + B. Thus, at the zero iteration of the loop, val=0*16+A=10 will be calculated, then val=10*16+1=161, then 161*16+11=2587.

Actually, on the fingers of the idea is this: adding the next digit at the end of the line, this is equivalent to multiplying by 16 and adding this digit to the sum. Similarly, in the decimal system, adding a digit means multiplying by 10 and adding a digit: 123 = 12*10 + 3