Consider adding two unsigned fixed$-$point numbers, one with n$1-$bits total and a f$1-$bits fractional part, and the other with n$2-$bits total and a f$2-$bits fractional part. What is the minimum number of total bits needed so that in the worst case the output can be represented exactly How many of those need to be assigned to the fractional part? Provide you answer and reasoning in the provided box below.