Problem 3: (25 points) Using D flip-flops and NAND gates, design a Moore finite state machine with one input x and one output z. When x = 0, the state of the circuit remains unchanged. When x = 1, the circuit goes through the state transitions from QAQB = 00 to 10,to 11, to 01, back to 00, and repeats. When in states 00, 01 and 10 the circuit output is 1, otherwise it is zero.

1. (5 points) Sketch the state diagram.

2. (5 points) Complete the state table in Table 1. In columns three and four, the notation x and x indicates that the input is in a logic high-state and low-state, respectively.

3. (3 points) Use a two-variable Karnaugh map to obtain a logic equations in terms of QA and QB for the output z.

4. (6 points) Using the three-variable Karnaugh map in Figure 15, obtain logic equations in terms of x, QA, and QB for the flip-flop inputs DA and DB.

5. (6 points) Neatly sketch a logic circuit that realizes the finite state machine using only NAND gates.

PLEASE HELP ONLY NEED 4 AND 5 ANSWERED!!!

Present State Next StateOutput Table 1: State table for a Moore finite state machine QAQB Q4 00 01 1 0 713 nz 324 QB Figure 15: Three-variable Karnaugh map