# Understanding Residue 3 Automata to Moore Machines | Zulfi

• Comp Sci
• zak100
In summary, To create a residue 3 automata using Moore, we must first determine the initial state, which is q0. When the input is 0, the state machine stays in state q0. When the input is 1, the state transitions from q0 to q1. This pattern continues for subsequent inputs, where the state transitions to the next state (i.e. from q1 to q2) based on the input's mod 3 value.
zak100
Homework Statement
Create a residue Moore Machine using FA
Relevant Equations
No equations
Hi,
I am trying to create residue 3 automata using Moore. I can't understand why we go to state q1 when we have input 0 in q0 and similalry why we go to q2 when we have input zero in q1.

I have attached an image of FA.

Some body please guide me.

Zulfi.

To analyze this, make sure to start simple.

By definition, the initial state of the state machine is q0. Let's start there.

So what if your input string is the simplest possible input string, "0". One can't get much simpler than that. So now ask yourself, what is 0 mod 3? That should tell you something about how q0 must transition when the input is 0.

Now let's change the input to the next most simple string, "1". What is 1 mod 3? This should tell you something about the transition from q0 when the input is a 1.

Continuing on, what if the input string was "10 (binary; i.e., '2' decimal.)" Ask yourself, "well, what is 2 mod 3?" Do you see now why the state must transition from q1 to q2 when the input is a 0?

Continue with the following strings:
11 (binary): What is 3 mod 3?
100 (binary): What is 4 mod 3?
101 (binary): What is 5 mod 3?

zak100 said:
I can't understand why we go to state q1 when we have input 0 in q0

And for clarity, that's not right. When in state q0, with input 0, the state machine stays in state q0.

## 1. What is a Moore Machine?

A Moore Machine is a type of finite state machine that consists of a set of states, inputs, outputs, and a transition function. It is used to model sequential logic circuits and is widely used in digital electronics and computer science.

## 2. How does a Moore Machine work?

A Moore Machine works by transitioning between states based on the current state and input. Each state has a corresponding output, which is determined by the current state and input. The machine follows a predefined set of rules to determine the next state and output, which allows it to perform specific tasks or functions.

## 3. What is the difference between a Moore Machine and a Mealy Machine?

The main difference between a Moore Machine and a Mealy Machine is in the way they handle outputs. In a Moore Machine, the outputs are only dependent on the current state, while in a Mealy Machine, the outputs are dependent on both the current state and input. This means that Moore Machines have a slight delay in their outputs compared to Mealy Machines.

## 4. What are the benefits of using Moore Machines?

Moore Machines offer several benefits, including simplicity, modularity, and determinism. They are easier to design and understand compared to other types of finite state machines, and can be easily modified or expanded upon. Additionally, since the outputs are only dependent on the current state, Moore Machines have a predictable behavior, making them useful for safety-critical systems.

## 5. How can I use Moore Machines in my research or project?

Moore Machines can be used in a variety of applications, such as control systems, digital circuits, and software design. They are particularly useful in tasks that involve sequential logic, such as pattern recognition, data processing, and decision-making. With a good understanding of Moore Machines, you can apply them to your research or project to improve efficiency and accuracy.

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