Pregunta
4 Implement a sequence generator using a state machine.
A sequence generator produces a predefined binary pattern. Design a state
machine that generates the repeating sequence “1010” using D flip-flops. Draw
the circuit diagram and explain its operation
A sequence generator produces a predefined binary pattern. Design a state
machine that generates the repeating sequence “1010” using D flip-flops. Draw
the circuit diagram and explain its operation
Ask by Wright Phillips. in India
Mar 25,2025
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To generate the repeating binary pattern “1010” using D flip-flops, create a state machine with four states corresponding to each bit. Use two D flip-flops to represent the states and design the D inputs based on the current state. The circuit will toggle between states on each clock pulse, producing the sequence “1010” repeatedly.
Solución
To design a sequence generator that produces the repeating binary pattern “1010” using D flip-flops, we can follow these steps:
Step 1: Define the States
We will define four states corresponding to each bit in the sequence “1010”:
- State S0: Output = 1 (first bit)
- State S1: Output = 0 (second bit)
- State S2: Output = 1 (third bit)
- State S3: Output = 0 (fourth bit)
Step 2: State Transition Table
Next, we create a state transition table that shows how the state machine transitions from one state to another based on the clock signal.
| Current State | Next State | Output |
|---|---|---|
| S0 | S1 | 1 |
| S1 | S2 | 0 |
| S2 | S3 | 1 |
| S3 | S0 | 0 |
Step 3: State Diagram
The state diagram can be represented as follows:
+----+ 1 +----+ 0 +----+ 1 +----+
| S0 | --------> | S1 | --------> | S2 | --------> | S3 |
+----+ +----+ +----+ +----+
^ | ^ |
| | | |
+----------------+ +----------------+
Step 4: D Flip-Flop Inputs
To implement this state machine using D flip-flops, we need to determine the D inputs for each flip-flop based on the current state.
Assuming we use two D flip-flops (let’s call them
- State Encoding:
- S0 = 00
- S1 = 01
- S2 = 10
- S3 = 11
D Flip-Flop Input Logic
We can derive the D inputs for each flip-flop based on the current state:
-
For
(the most significant bit): -
(if in S0 or S2) -
(if in S1 or S3)
-
-
For
(the least significant bit): -
(toggle on every clock)
-
Step 5: Circuit Diagram
The circuit diagram will consist of:
- Two D flip-flops
- Logic gates to implement the D inputs
Here’s a simplified representation of the circuit:
+-----+ +-----+
| DFF | | DFF |
| Q1 |-------| Q0 |
+-----+ +-----+
| |
| |
| |
+-----+ +-----+
| AND | | NOT |
+-----+ +-----+
| |
| |
+-----+ +-----+
| D1 | | D0 |
+-----+ +-----+
Step 6: Explanation of Operation
- Initialization: The state machine starts in state S0 (output = 1).
- Clock Pulse: On each clock pulse, the D flip-flops capture the values of
and and transition to the next state. - Output Generation: The output is generated based on the current state:
- In S0 and S2, the output is 1.
- In S1 and S3, the output is 0.
- Repetition: The sequence continues to repeat as the state machine cycles through S0, S1, S2, and S3.
This design effectively generates the repeating binary pattern “1010” using a state machine with D flip-flops.
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Simplifique esta solución Bonus Knowledge
To implement a state machine that generates the binary sequence “1010” using D flip-flops, we first need to identify the states required to represent each bit in the sequence. The states can be named as follows:
- S0 (00): Output is ‘1’
- S1 (01): Output is ‘0’
- S2 (10): Output is ‘1’
- S3 (11): Output is ‘0’
The transitions between these states will occur with each clock pulse. Here’s a simple state transition:
- Starting from S0 (current output ‘1’), on clock pulse it transitions to S1.
- From S1 (output ‘0’), it moves to S2.
- Then from S2 (output ‘1’), it goes to S3.
- Finally, from S3 (output ‘0’), it loops back to S0.
Circuit Diagram:
The circuit will consist of two D flip-flops, labeled FF1 and FF2, to represent the two bits of the state. The current state can be formed from the outputs of these flip-flops:
- D1 input will depend on the combination of outputs Q1 and Q2 (from FF1 and FF2) and will be determined by the next state logic derived from the state table.
- D2 input is similarly derived from the state transitions.
Operation:
On each clock pulse, the state machine transitions between states and produces the corresponding output as per the sequence. After every four clock cycles, the cycle repeats, continuously generating the binary sequence “1010”.
This neat little loop ensures that with each clock pulse the pattern is perfectly maintained, and it’s as predictable as a dance routine that follows a set choreography! Keep the clock ticking, and enjoy the show!
Now, let’s dive into the historical aspect of sequential circuits. In the early days of digital electronics, sequence generators were significant for various applications, including telecommunication and early computing systems. These designs laid the foundation for modern digital systems, highlighting how a simple binary pattern could control complex behaviors.
In real-world applications, these sequence generators are utilized in various devices, from simple toy controllers to more complex systems like digital clocks, traffic light controllers, and even in encoding and decoding information in communication systems. It’s fascinating how a robust concept like this plays an essential role in our everyday technologies!
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