How to Read an FSM Address Table

Oct 13, 2025 by wbrum.org 88 views

Introduction

A Finite State Machine (FSM) is a mathematical model that can be used to describe the behavior of a system that can be in one of a finite number of states. The FSM address table is a crucial component of a FSM, as it helps to determine the next state of the machine based on the current state and input. In this article, we will delve into the world of FSM address tables, exploring how to read and interpret them.

What is an FSM Address Table?

An FSM address table is a table that contains the next state of a machine for each possible combination of current state and input. It is a compact way to represent the transition function of a FSM, which is a function that maps each state and input to a next state.

How to Read an FSM Address Table

To read an FSM address table, you need to understand the structure of the table and how to interpret the information it contains. Here are the steps to follow:

Step 1: Identify the States and Inputs

The first step is to identify the states and inputs that are represented in the table. The states are usually listed in the first column, and the inputs are listed in the first row. For example, if the table has 3 states (S1, S2, S3) and 2 inputs (I1, I2), the table might look like this:

State	I1	I2
S1
S2
S3

Step 2: Determine the Next State

Once you have identified the states and inputs, you can determine the next state of the machine by looking at the table. The next state is the state that is listed in the cell that corresponds to the current state and input. For example, if the current state is S1 and the input is I1, the next state would be the state that is listed in the cell that is in the first row and first column.

Step 3: Interpret the Table

The FSM address table can be interpreted in several ways, depending on the specific application. Here are a few examples:

Deterministic FSM: In a deterministic FSM, the next state is uniquely determined by the current state and input. In this case, the table can be used to determine the next state of the machine.
Non-deterministic FSM: In a non-deterministic FSM, the next state is not uniquely determined by the current state and input. In this case, the table can be used to determine the possible next states of the machine.
Probabilistic FSM: In a probabilistic FSM, the next state is determined by a probability distribution over the possible next states. In this case, the table can be used to determine the probability of each possible next state.

Example FSM Address Table

Here is an example of an FSM address table:

State	I1	I2
S1	S2	S3
S2	S1	S3
S3	S1	S2

In this example, the table represents a deterministic FSM with 3 states (S1, S2, S3) and 2 inputs (I1, I2). The next state of the machine is determined by the current state and input, as shown in the table.

Determining Which Cells Correspond to the Given States

To determine which cells in the table correspond to the given states, you need to follow these steps:

Step 1: Identify the States

The first step is to identify the states that are represented in the table. In this example, the states are S1, S2, and S3.

Step 2: Determine the Next State for Each State and Input

Once you have identified the states, you can determine the next state of the machine for each state and input by looking at the table. For example, if the current state is S1 and the input is I1, the next state would be S2.

Step 3: Identify the Cells that Correspond to the Given States

The cells that correspond to the given states are the cells that contain the next state of the machine for each state and input. In this example, the cells that correspond to the given states are:

S1 -> I1 -> S2
S1 -> I2 -> S3
S2 -> I1 -> S1
S2 -> I2 -> S3
S3 -> I1 -> S1
S3 -> I2 -> S2

Conclusion

Q&A: FSM Address Table

Q1: Where should S1 be located in the table?

A1: S1 should be located in the first row of the table, as it is the initial state of the machine.

Q2: How do I determine the next state of the machine?

A2: To determine the next state of the machine, you need to look at the table and find the cell that corresponds to the current state and input. The value in that cell is the next state of the machine.

Q3: What if there are multiple next states for a given state and input?

A3: If there are multiple next states for a given state and input, it means that the machine is non-deterministic. In this case, the table can be used to determine the possible next states of the machine.

Q4: How do I know if the machine is deterministic or non-deterministic?

A4: To determine if the machine is deterministic or non-deterministic, you need to look at the table and see if there are any cells that contain multiple values. If there are, it means that the machine is non-deterministic.

Q5: Can I have a probabilistic FSM address table?

A5: Yes, you can have a probabilistic FSM address table. In this case, the table would contain the probability of each possible next state for each state and input.

Q6: How do I create a probabilistic FSM address table?

A6: To create a probabilistic FSM address table, you need to assign a probability to each possible next state for each state and input. The probabilities should add up to 1.

Q7: Can I have a FSM address table with multiple inputs?

A7: Yes, you can have a FSM address table with multiple inputs. In this case, the table would contain the next state of the machine for each possible combination of inputs.

Q8: How do I determine the next state of the machine with multiple inputs?

A8: To determine the next state of the machine with multiple inputs, you need to look at the table and find the cell that corresponds to the current state and inputs. The value in that cell is the next state of the machine.

Q9: Can I have a FSM address table with multiple outputs?

A9: Yes, you can have a FSM address table with multiple outputs. In this case, the table would contain the output of the machine for each possible combination of inputs.

Q10: How do I determine the output of the machine?

A10: To determine the output of the machine, you need to look at the table and find the cell that corresponds to the current state and inputs. The value in that cell is the output of the machine.

Conclusion

In conclusion, the FSM address table is a crucial component of a FSM, as it helps to determine the next state of the machine based on the current state and input. By following the steps outlined in this article, you can create and interpret a FSM address table, and determine the next state of the machine.