Conversion hex-> dec - we are looking for beautiful solutions

After discussing the algorithms for finding numbers in the line , the idea arose to consider some other tasks in the same vein. The task of converting an integer from a hexadecimal system into a decimal system seemed appropriate: not very cumbersome, with at least one obvious algorithm and, perhaps, many not obvious, and understandable.



Given a string containing a nonnegative integer in a hexadecimal system. The number is written in numbers 0..9A..F (letters - only big), it is guaranteed that there are no non-digit characters in the string. It is required to receive the line containing decimal record of such number. The length of the input string does not exceed 100,000 bytes.
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Write solutions in any languages ​​- the most beautiful, the shortest, the most effective ... For solutions on a Turing machine, I suggest using only the characters "space, 0, 1" (do not enter new ones), and write the input and output numbers in quadruple bits (separated by spaces or not - at your discretion). On Brainfuck, the input string must be entered, and the output string must be printed.

UPD. Using built-in or library BigNum, of course, is good, but somehow not very interesting. Let's do without it!

For the seed, the solution is in C # (which cannot be called either beautiful, short or effective):

         static unsafe string Hex2Dec (string x) {
             int l = x.Length;
             int ll = l + l / 4 + 3;
             sbyte [] m = new sbyte [ll];
             int i = l;
             foreach (char c in x) m [- i] = (sbyte) (c <'A'? c-'0 ': c-' A '+ 10);
             int lk = ll;
             while (l> 0) {
                 int k = 0, l1 = 0;
                 while (l> 0) {
                     k = (k << 4) + m [- l];
                     m [l] = (sbyte) (k / 10);
                     if (l1 == 0 && k> = 10) l1 = l + 1;
                     k% = 10;
                 }
                 m [- lk] = (sbyte) (k + 48);
                 l = l1;
             }
             string res;
             fixed (sbyte * c = m) {res = new string (c, lk, ll-lk);  }
             return res;
         }