Searching Through a String for Position of 1st Non-Zero digit

I have a text string in a cell, something like:

000024AC1011.

I need to find a way to find the first nonzero character in the string, and what position it is in. For instance, in the above example, 2 is the first non-zero character, so the function would return 5, since the 2 is the fifth character into the string.

I'm stumped on this one! Please help!
Thanks so much!