This homework is due 9 April, 4:30 PM.
For the FSM (Finite State Machine) specified by the state table below, derive the minimized next-state (Q1* Q2*) and output (z) equations. (Show your K-maps.) Use the following state assignment for Q1 Q2: A = 00, B = 10, C = 11, and D = 01.
| state | x | |
|---|---|---|
| 0 | 1 | |
| A | B/1 | C/0 |
| B | D/1 | C/1 |
| C | B/1 | A/0 |
| D | B/0 | C/1 |
For each of the following state tables, construct the state diagram.
Use state table from Problem 1.
| state | x1 x2 | z1 z2 | ||||||
|---|---|---|---|---|---|---|---|---|
| 00 | 01 | 10 | 11 | |||||
| A | A | C | A | B | 0 | 1 | ||
| B | A | C | B | C | 0 | 0 | ||
| C | D | D | C | D | 1 | 0 | ||
| D | A | B | A | B | 1 | 0 | ||
For the FSM in Problem 2B above, derive the minimized next-state (Q1* Q2*) and output (z1 z2) equations. Use the following state assignment for Q1 Q2: A = 00, B = 10, C = 11, and D = 01.
Using the state table from Problem 1, construct a state sequence chart for the input sequence x = 0 1 1 0 1 1 0 0 0 1. Initial state is A. Note: A state sequence chart shows input, current state, next state, and output each cycle. For example, here is the first cycle done for you:
| cycle | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| x | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 |
| current state | A | B | ||||||||
| next state | B | |||||||||
| z | 1 |
Design a Mealy state machine that will detect each of the following sequences. When the sequence is detected, a single output z is set to 1. Your design should include a state diagram and a state table for each machine.