Texts: Please use the Red ID 826193856.
3.2 Now we will design your own Red ID counter using a Finite State Machine (FSM). We aim to design a Moore FSM. The number of states in this FSM will be the total Red ID number represented by four binary variables A, B, G, D. We use one external input in this counter, namely X (X = 1 denotes upward counting and X = 0 denotes downward counting).
Here is an example of the sequential Red ID counter: Suppose that your Red ID number is 876543210. Since there are 9 numbers in your Red ID sequence, there should be 9 states in your FSM. Using X as an input, a typical state graph of the sequential Red ID counter for the sequence 876543210 is shown in Figure 3.
0000
10
0100
301
Figure 3. Example of a sequential Red ID counter
- Indicate your Red ID number in decimal below. (5 points)
- Fill up the next state table of your Red ID counter. Please use Q1, Q2, Q3, Q4 as your binary state variables, A, B, C, D as your binary outputs, and X as your binary input. (15 points)
3.3 Express each of the next state variables Q1, Q2, Q3, Q4 as a minterm expansion (no need to simplify the logic expressions), as a function of Q1, Q2, Q3, Q4, X. (20 points)
3.4 Using Karnaugh maps or any logic simplification methods of your choice, obtain the simplified expression for each of the four output variables A, B, C, D, as a function of Q1, Q2, Q3, Q4. (20 points)
