Decimal to Binary converter with a flaw
Change your code for binary_converter() to return the empty string ('') instead of '0', when you pass it the input zero.

Then, write a new function binary_converter_for_realz(), which checks whether the input is zero; if passed zero, it just returns '0', otherwise it invokes binary_converter() and returns whatever it returns.

This basically treats 0 as a special case, which it is: we don't want a leading zero, except when the integer is zero, in which case we do.