(a) Reduce the following state table to a minimum number of states. Present Next State Output Z X=0 X = 1 State X=0 X = 1 A D G 1 0 B C 0 1 C D 0 0 D A 1 0 E G 0 1 F D 0 G Ε 0 1 H A с 0 0 (b) You are given two identical sequential circuits which realize this state table. One circuit is initially in state R and the other circuit is initially in state E EHGEBEC Ε Η F
(a) Reduce the following state table to a minimum number of states. Present Next State Output Z X=0 X = 1 State X=0 X = 1 A D G 1 0 B C 0 1 C D 0 0 D A 1 0 E G 0 1 F D 0 G Ε 0 1 H A с 0 0 (b) You are given two identical sequential circuits which realize this state table. One circuit is initially in state R and the other circuit is initially in state E EHGEBEC Ε Η F
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Transcribed Image Text:### State Reduction and Distinguishing Sequential Circuits
**Problem Statement:**
(a) Reduce the following state table to a minimum number of states.
| Present State | Next State | Output Z |
|---------------|------------|-----------|
| | X = 0 | X = 1 | X = 0 | X = 1 |
| A | D | G | 1 | 0 |
| B | C | E | 0 | 1 |
| C | D | H | 0 | 0 |
| D | A | G | 1 | 0 |
| E | G | F | 0 | 1 |
| F | D | B | 1 | 0 |
| G | C | E | 0 | 1 |
| H | A | C | 0 | 0 |
(b) You are given two identical sequential circuits which realize this state table. One circuit is initially in state **B** and the other circuit is initially in state **E**. Specify an input sequence of length two that could be used to distinguish between the two circuits and provide the corresponding output sequence from each circuit.
### Explanation of Steps for Part (a):
1. **Step 1: Identify Equivalent States**:
- Check states with identical outputs and transitions for all inputs.
- Use methods such as state implication charts or partitioning to identify and merge equivalent states.
2. **Step 2: Form Reduced State Table**:
- Create a revised state table with only unique, non-equivalent states.
### Explanation of Steps for Part (b):
1. **Step 1: Define Input Sequence**:
- Choose an input sequence of length two to test the behavior of both circuits starting from their initial states.
2. **Step 2: Trace State Transitions**:
- Follow the state transitions and outputs for the given input sequence starting from state **B** for the first circuit and from state **E** for the second circuit.
3. **Step 3: Compare Outputs**:
- Compare the output sequences to find distinguishing patterns.
#### Example:
- Input Sequence: X1 = 0, X2 = 1
- Circuit starting from state **B**:
- State Update with X1 = 0: **B** -> **C**
- Output with X1 = 0: Z = 0
- State Update with X2
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