# Digital Electronics: State machine

• 6021023
In summary, this conversation discusses the states and configuration of a system, consisting of two flip flops, and the corresponding state transition table and state diagram. The circuit is a Mealy machine, with the inputs and outputs being the same. The state transition table has 8 rows, with the columns A, B, and Y representing the inputs, and Next X and Next Y representing the outputs of the flip flops. The logic equation AB'Y + A'BY' is used to calculate the Next X and Next Y outputs for each row.
6021023

## Homework Statement

(a) How many states does this system have?
(b) How many rows will there be in a state transition table?
(c) Provide the state transition table.
(d) Draw a state diagram of the system.
(e) Describe what the circuit does in words.

## The Attempt at a Solution

a) I think there are two flip flops (or are they switches?), so that means that there are four states: 00, 01, 10, and 11.

b) I think the state transition table will have 8 rows. These numbers will be at the beginning of each row:

000
001
010
011
100
101
110
111

6021023 said:

## Homework Statement

(a) How many states does this system have?
(b) How many rows will there be in a state transition table?
(c) Provide the state transition table.
(d) Draw a state diagram of the system.
(e) Describe what the circuit does in words.

## The Attempt at a Solution

a) I think there are two flip flops (or are they switches?), so that means that there are four states: 00, 01, 10, and 11.

b) I think the state transition table will have 8 rows. These numbers will be at the beginning of each row:

000
001
010
011
100
101
110
111

Good. Correct so far. Now make label those three columns as A, B and Y (the inputs to the logic), and make 2 more columns for the "Next X, Next Y" outputs of the FFs. Use the logic terms shown for the J&K inputs for the 2 FFs to calculate what the Next X and Next Y outputs will be for each row. That is your transition table. Then use that to answer the rest of the questions.

Show us what you end up with!

A B Y Next X Next Y
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

I'm a little bit confused as to what to do after this. I see the equation AB'Y + A'BY' going into J and K. So that means that J and K will always be the same. Is that right?

6021023 said:
A B Y Next X Next Y
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

I'm a little bit confused as to what to do after this. I see the equation AB'Y + A'BY' going into J and K. So that means that J and K will always be the same. Is that right?

Yes, from the diagram, it does appear that J and K for each FF are the same. What does a JK FF do when both inputs are the same?

When both J and K are 0, then there is no change in outputs.
When they are both 1, then the outputs are toggled.

A B Y Next X Next Y
0 0 0

I still get stuck at this part. I can tell that next Y is going to be 0, but I can't say what next X is, because the table doesn't tell me what X currently is.

Another question. Is the circuit a Mealy machine, since the output is going back into the input?

## 1. What is a state machine in digital electronics?

A state machine is a mathematical model used to describe the behavior of a system that can be in one of several possible states at any given time. In digital electronics, a state machine is typically implemented using logic gates and flip-flops to control the flow of data and signals within a digital system.

## 2. How does a state machine work?

A state machine works by transitioning between different states based on certain inputs and conditions. Each state represents a specific behavior or operation of the system. The transitions between states are controlled by a clock signal and logic gates, which determine when and how the system should change states.

## 3. What are the types of state machines in digital electronics?

There are two main types of state machines in digital electronics: Mealy machines and Moore machines. Mealy machines use both inputs and current state to determine the next state and output, while Moore machines only use the current state to determine the next state and output.

## 4. What are the applications of state machines in digital electronics?

State machines are widely used in digital electronics for a variety of applications, including circuit design, data processing, and control systems. They are particularly useful in sequential logic circuits, where the behavior of the system depends on the sequence of inputs.

## 5. What are the advantages of using state machines in digital electronics?

State machines offer several advantages in digital electronics, including simplicity, modularity, and scalability. They are also highly reliable and can be easily tested and debugged. Additionally, state machines can be designed to handle complex operations and decision-making processes, making them a versatile tool in digital system design.

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