Question 1: (a) Simplify the Boolean function F together with the don't care conditions d in sum of products form. Indicate all essential prime implicants, and state which remaining prime implicant you selected F(wx.yz) - 2m(0,1,3,7,8,10,13), d(wxy,z)- 2m(2,4,9,15) You may use the template "K-map-4.xls" provided on urcourses. You do not have to draw the circuit (b) Simplify the above Boolean function using product of sums, with Maxterms, instead of sum of products with minterms. (c) Convert the product of sums from part (b) into sum of products form using Boolean simplification. Is this equivalent to what you found in part (a)? Should it be? Why or why not? Question 2: Design a combinational circuit with 4 inputs, Ay A2 A1, Ao and three outputs, X, Y, z. The inputs resnt a binary number in the range [0..15], and the outputs represent characteristics of the numbers. Specifically, X should be true if the number is divisible by 3; Y should be true if the number is divisible by 4; and Z should be true if the number is divisible by 7. As an example, if the input is A3A2A,A1100, this represents the number 12, which is divisible by 3 and4 but not 7, so the output should be XYZ-110. Recall that 0 is divisible by any integer (a) Implement the circuit with AND gates, OR gates, and NOT gates. You may use the k-map template provided for your design work. (b) Implement the circuit using only NAND gate:s (c) Implement the circuit using AND, OR, NOT, and XOR gates. How much simpler is this design than the design in part (a)? Question 3 Show that a Full Adder is a Universal Device