The table presented is a state transition table used in digital design to represent the behavior of a sequential circuit. Here's a detailed breakdown:### Columns1. **Present State \( y_2y_1 \):** - Represents the current state of the system, given by two binary variables \( y_2 \) and \( y_1 \).2. **Next State:** - Divided into two sub-columns based on the condition \( w \). - **\( w = 0 \):** - Next state of the system when the input \( w \) is 0, denoted by binary variables \( Y_2Y_1 \). - **\( w = 1 \):** - Next state when the input \( w \) is 1, also represented by \( Y_2Y_1 \).3. **Output \( z \):** - The output of the system for the given present state.### Rows- **\( 00 \):** - **Present State:** \( 00 \) - **Next State when \( w = 0 \):** \( 10 \) - **Next State when \( w = 1 \):** \( 11 \) - **Output:** 0- **\( 01 \):** - **Present State:** \( 01 \) - **Next State when \( w = 0 \):** \( 01 \) - **Next State when \( w = 1 \):** \( 00 \) - **Output:** 0- **\( 10 \):** - **Present State:** \( 10 \) - **Next State when \( w = 0 \):** \( 11 \) - **Next State when \( w = 1 \):** \( 00 \) - **Output:** 0- **\( 11 \):** - **Present State:** \( 11 \) - **Next State when \( w = 0 \):** \( 10 \) - **Next State when \( w = 1 \):** \( 01 \) - **Output:** 1### ExplanationThis table is used to determine the behavior of a sequential system based on its current state and the input parameter \( w \). The transition to a new state is determined **Title: Designing Finite State Machines Using D Flip-Flops****Introduction**A Finite State Machine (FSM) is defined by the state-assigned table in Figure P6.1. The task is to derive a circuit that realizes this FSM using D flip-flops. **Instructions**1. Analyze the state-assigned table provided in Figure P6.1.2. Use the table to understand the transition and output states of the FSM.3. Design the circuit using D flip-flops that accurately reflects the state transitions and outputs specified in the table.**Steps for Circuit Derivation:**- **Understand State Transitions:** - Identify the current and next state values. - Note any inputs that affect the transitions.- **Determine Output Logic:** - Understand the output associated with each state or transition.- **Design Logic Circuits:** - Create logic expressions for each D flip-flop input based on state transitions. - Use logic gates to implement these expressions.- **Configure D Flip-Flops:** - Connect the outputs of the logic circuits to the D inputs of the flip-flops. - Ensure the flip-flops are clocked properly to enable state changes.**Conclusion**Designing FSMs using D flip-flops involves transcribing state transitions into logic expressions and using these to drive the flip-flop inputs. Properly developed, this ensures the FSM behaves as defined by the state-assigned table.

State - Assigned table with flip flop input columns

Answered: SM is defined by the state-assigned…

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SM is defined by the state-assigned table in Figure P6.1. Derive a circuit that realizes FSM using D flip-flops.

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Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

The table presented is a state transition table used in digital design to represent the behavior of a sequential circuit. Here's a detailed breakdown:

### Columns

1. **Present State \( y_2y_1 \):**
- Represents the current state of the system, given by two binary variables \( y_2 \) and \( y_1 \).

2. **Next State:**
- Divided into two sub-columns based on the condition \( w \).

- **\( w = 0 \):**
- Next state of the system when the input \( w \) is 0, denoted by binary variables \( Y_2Y_1 \).

- **\( w = 1 \):**
- Next state when the input \( w \) is 1, also represented by \( Y_2Y_1 \).

3. **Output \( z \):**
- The output of the system for the given present state.

### Rows

- **\( 00 \):**
- **Present State:** \( 00 \)
- **Next State when \( w = 0 \):** \( 10 \)
- **Next State when \( w = 1 \):** \( 11 \)
- **Output:** 0

- **\( 01 \):**
- **Present State:** \( 01 \)
- **Next State when \( w = 0 \):** \( 01 \)
- **Next State when \( w = 1 \):** \( 00 \)
- **Output:** 0

- **\( 10 \):**
- **Present State:** \( 10 \)
- **Next State when \( w = 0 \):** \( 11 \)
- **Next State when \( w = 1 \):** \( 00 \)
- **Output:** 0

- **\( 11 \):**
- **Present State:** \( 11 \)
- **Next State when \( w = 0 \):** \( 10 \)
- **Next State when \( w = 1 \):** \( 01 \)
- **Output:** 1

### Explanation

This table is used to determine the behavior of a sequential system based on its current state and the input parameter \( w \). The transition to a new state is determined

**Title: Designing Finite State Machines Using D Flip-Flops**

**Introduction**
A Finite State Machine (FSM) is defined by the state-assigned table in Figure P6.1. The task is to derive a circuit that realizes this FSM using D flip-flops.

**Instructions**
1. Analyze the state-assigned table provided in Figure P6.1.
2. Use the table to understand the transition and output states of the FSM.
3. Design the circuit using D flip-flops that accurately reflects the state transitions and outputs specified in the table.

**Steps for Circuit Derivation:**

- **Understand State Transitions:**
- Identify the current and next state values.
- Note any inputs that affect the transitions.

- **Determine Output Logic:**
- Understand the output associated with each state or transition.

- **Design Logic Circuits:**
- Create logic expressions for each D flip-flop input based on state transitions.
- Use logic gates to implement these expressions.

- **Configure D Flip-Flops:**
- Connect the outputs of the logic circuits to the D inputs of the flip-flops.
- Ensure the flip-flops are clocked properly to enable state changes.

**Conclusion**
Designing FSMs using D flip-flops involves transcribing state transitions into logic expressions and using these to drive the flip-flop inputs. Properly developed, this ensures the FSM behaves as defined by the state-assigned table.

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