11. What is a universal gate? Please justify your reasoning and give an example. 12. Implement the following Product-of-Sums function using logic gates. F = (X+Y)(Y+Z) 13. For the given function in question 12, implement F as a Sum-of-Products using logic gates. 14. Implement a 4-bit parallel adder using full adders. Clearly label the bits ofthe inputs. 15. Consider the question 14. If the carry propagation delay for a full adder is 2ns, how fast can the inputs to the 4-bit parallel adder be updated? 16. You are given a task of designing a circuit to produce a repetitive sequence of 1,2,3,1,2,3,... Represent this problem in a state diagram. 17. Consider the question 16. Derive the state table. 18. Consider the question 16 and 17. Draw the circuit diagram for the circuit. 19. Assume that you have access to a clock signal at a frequency of f. Propose a circuit that generates another clock signal with a frequency of f/4. 20. What is the difference between combinational and sequential logic circuits.

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