[8 marks] The truth table below defines the truth value off for each combination of truth values of a, b, c and d. b d f F F F F F F F FT F F F TF T F F T T F F TFF F F T F T F F TTF T FT TT F TF F F T TF F T F T F T F F T T F T T F T T F F T T T F T F T T T F F F (a) Find a logic forinula for f that uses each variable at most once. Then verify the correctness of your formula by drawing a truth table corresponding to this formula, including the truth values of all relevant sub-formulas. Enter your response in the table on the next page. We have provided at least as many columns as you'll need. Be sure to replace the words column heading X by your sub-formulas! C d column heading 1 column heading 2 column heading 3 F F F T F F T F F FTT F T F F F T F T E T TF F T TT T F F F T F FT IFTF T T F F F (b) Now draw a circuit with inputs a, b, c, d, whose output is the value / described by the truth table. Design your circuit only using AND, OR, XOR or NOT gates. Your mark will depend on using as few AND, OR, and XOR gates as possible