as soon as possible ### 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

(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

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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as soon as possible

### 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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