**Sequential Circuit Design for Detecting Sequence 11****Problem Statement:**Implement a sequential circuit that processes a single input value $ X $ and produces a single output value $ Z $. The input data arrives serially in a bitstream. The output will remain 0 until the sequence "11" is detected. Upon detecting this sequence, the output will be 1, and the detection process will restart. Note that overlapping sequences of "11" are not considered (i.e., a string of three consecutive 1s will not count as overlapping pairs of 1s).**Input and Output Example:**- **Input (X):** 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0- **Output (Z):** 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0**Tasks:**a. Draw a state diagram and provide a corresponding state table for this circuit.b. Provide the flip-flop input equations for each flip-flop used. D flip-flops are to be used. There is no need to draw the circuit.**State Diagram and State Table:**- Construct a state diagram with states that represent the progression towards detecting "11". States may include "Start", "Detected 1", and "Detected 11".- Create a state table showing current states, input values, next states, and outputs.**Flip-Flop Input Equations:**- Derive the input equations for D flip-flops based on state transitions. Use the state table to identify how the current state and input $ X $ affect the next state and output $ Z $.This problem is a classical example of designing a finite state machine (FSM) for pattern detection in digital systems and requires understanding state transitions and flip-flop operations.

The given problem is from digital electronics. Here the sequence to be detected is 11 so we require only 1 Flip Flop with 2 states 0 or 1. The detailed solution is given in the next step

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Electrical Engineering

2. Implement a sequential circuit that has a single input value X and a single output value Z. Input data arrives serially (also referred to as "in a bitstream"). Output will be Os until the sequence 11 has been detected. Upon detecting this sequence a 1 will be output and then the process will start all over again (hence a string of three consecutive Is will not count as overlapping pairs of 1s) X: 0 1 0 0 0 1 1 0 1 1 1 0 1 1 1 1 0 Z: 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 0 a. Draw a state diagram and give a corresponding state table for this circuit. b. Give the flip-flop input equations for each flip-flop you use. Use D flip-flops. You do not have to draw the circuit.

2. Implement a sequential circuit that has a single input value X and a single output value Z. Input data arrives serially (also referred to as "in a bitstream"). Output will be Os until the sequence 11 has been detected. Upon detecting this sequence a 1 will be output and then the process will start all over again (hence a string of three consecutive Is will not count as overlapping pairs of 1s) X: 0 1 0 0 0 1 1 0 1 1 1 0 1 1 1 1 0 Z: 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 0 a. Draw a state diagram and give a corresponding state table for this circuit. b. Give the flip-flop input equations for each flip-flop you use. Use D flip-flops. You do not have to draw the circuit.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Concept explainers

Latches and Flip Flop

Just like logic gates, the latches and flip-flops are the important elements of an electronic circuit. The logic gates form the important part of combinatorial circuits, while the latches and flip-flops form the essential part of a sequential circuit. Sequential circuits form the important concept of automata theory in electronics and electrical engineering, these circuits are a kind of logic circuit whose output depends on both present input and past inputs, that is, the input history.

Question

**Sequential Circuit Design for Detecting Sequence 11**

**Problem Statement:**
Implement a sequential circuit that processes a single input value $ X $ and produces a single output value $ Z $. The input data arrives serially in a bitstream. The output will remain 0 until the sequence "11" is detected. Upon detecting this sequence, the output will be 1, and the detection process will restart. Note that overlapping sequences of "11" are not considered (i.e., a string of three consecutive 1s will not count as overlapping pairs of 1s).

**Input and Output Example:**
- **Input (X):** 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0
- **Output (Z):** 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0

**Tasks:**
a. Draw a state diagram and provide a corresponding state table for this circuit.

b. Provide the flip-flop input equations for each flip-flop used. D flip-flops are to be used. There is no need to draw the circuit.

**State Diagram and State Table:**
- Construct a state diagram with states that represent the progression towards detecting "11". States may include "Start", "Detected 1", and "Detected 11".
- Create a state table showing current states, input values, next states, and outputs.

**Flip-Flop Input Equations:**
- Derive the input equations for D flip-flops based on state transitions. Use the state table to identify how the current state and input $ X $ affect the next state and output $ Z $.

This problem is a classical example of designing a finite state machine (FSM) for pattern detection in digital systems and requires understanding state transitions and flip-flop operations.

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