On modern computers, both unsigned/signed ints are just bit patterns and it's only some operations that differ. add/sub/mul/left-shift are the same, but cmp/div/right-shift differ. Look up twos-complement representation for more information.
Left shift also differs. Raw shifting left can have the affect of turning a negative number positive by setting the sign bit to 0, so there's a sign maintaining left shift as well. Also, Left/Right shift of negative numbers have the opposite effect as they do with positive, with left shifting a negative number dividing and right shifting multiplying.
You are mistaken, left shift is the same for both signed and unsigned and any instance of a left shift turning a signed int into a positive number is just normal underflow.
