You need to take each element of the string (which is why a char array would be easier to use) starting with the right-most or least significant one. Then you need to convert the character to its number equivalent. Then you need to process that number to build up the full value.
To convert the character '0' to the number zero just subtract the Ascii value for the character '0' which is 48.
To convert the character 'A' to the number 10 subtract 55 because 'A' has the Ascii value 65.
...R