We learned how to take the 2s complement of a number by subtracting it from an appropriate power of 2. An alternative method is to write the number in binary (using the correct number of bits for the length of the representation), change each 0 bit to 1 and each 1 bit to 0 (this is called taking the 1s complement), and then adding 1 to the result (discarding any carry into an extra bit). Show that these two methods are equivalent.