PROBLEM 1 (27 PTS) a) Simplify the following using ONLY Boolean Algebra Theorems. For each resulting simplified function, sketch the logic circuit using AND, OR, XOR, and NOT gates. (14 pts) F(A, B,C) ABC(ACB b) Demonstrate the following Theorem: (5 pts) c) For the following Truth table with two outputs: (8 pts) Provide the Boolean functions using the Canonical Sum of Products (SOP), and Product of Sums o 0 0 1 0 (POS). o o 1 0 1 Express the Boolean functions using the minterms and maxterms representations. Sketch the logic circuits as Canonical Sum of Products and Product of Sums. 1 0 1 1 1 1 1 0 0 0 1 PROBLEM 2 (26 PTS) Construct the truth table describing the output of the following circuit and write the simplified Boolean equation (8 pts). Note that aebec-(aebjec = a(bec)s be(a@c) a) o 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 b) The following is the timing diagram of a logic circuit with 3 inputs. Sketch the logic circuit that generates this waveform