a) [4 marks] Use Boolean algebra to minimize the following function into sum-of-products (SOP) form: f = (x + y + z)(x + y + z). Show your work for full marks.
b) [1 mark] Report the cost of the minimum SOP form, where cost is defined as the number of gates plus the number of gate inputs. You may assume that variables are freely available in true/complemented form (i.e. inversion incurs no cost).