string to int conversion not using atoi()

I'm trying to figure out how to convert a string to an int without using atoi(). I'm doing a programming excersise from a book I'm reading, and it says
"Use the character classification functions to prepare an implementation of atoi()." So that means using the ctype.h functions...
But short of creating an entire algorithm to find the number of digits of the int, then multiplying the 1st digit by 10^n, then add the second digit times 10^n-1 and so on. Is that what I need to do? Or is there a way simpler process to do this? Maybe someone could just explain how the atoi() function does its thing, I couldn't find the source code anywhere through google and just opening up stdlib.h didn't make much sense to me...

Basically it works like this:

Code:

---

string: 150
sum: 0
pointer to the character 1
begin loop
  sum = sum * 10
  sum = sum + the number pointer is pointing to
  move pointer to next character
  if we aren't pointing to the end of the string, repeat the loop
end loop

sum now holds the value

---

broken down by example (loop unrolled)

Code:

---

string = 125
sum = 0

sum = sum * 10 // 0 * 10 is still 0
sum = sum + 1  // Now sum is 1

sum = sum * 10 // Now sum is 10
sum = sum + 2  // Now sum is 12

sum = sum * 10 // Now sum is 120
sum = sum + 5  //  Now sum is 125

---

Thanks Thantos, I understand it and that's definitely a much better way than what I was about to do. That way I don't have to check the number of digits and use that as an exponent to 10 to multiply each digit, if you catch my drift. Now all I gotta do is make the function read in the string and create another string that is only an int, and go from there.