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Expert-verified Found in: Page 863 ### Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095 # Draw the state diagrams for the finite-state machines with these state tables.   (a): State diagram of the finite-state machine is shown below. (b): State diagram of the finite-state machine is shown below. (c): State diagram of the finite-state machine is shown below. See the step by step solution

## Step 1: General form

Finite-State Machines with Outputs (Definition):

A finite-state machine$${\bf{M = }}\left( {{\bf{S,}}\,\,{\bf{I,}}\,\,{\bf{O,}}\,\,{\bf{f,}}\,\,{\bf{g,}}\,\,{{\bf{s}}_0}} \right)$$ consists of a finite set S of states, a finite input alphabet I, a finite output alphabet O, a transition function f that assigns to each state and input pair a new state, an output function g that assigns to each state and input pair output and an initial state$${{\bf{s}}_0}$$.

## Step 2: Draw the state diagram for the given state table

Given that, a state table is shown below: Using the state table draw a state diagram for the finite-state machines.

Construction:

Now, we make a node for each state as$${{\bf{s}}_{\bf{0}}}{\bf{,}}{{\bf{s}}_{\bf{1}}}{\bf{,}}{{\bf{s}}_{\bf{2}}}$$.

Then, $${{\bf{s}}_0}$$ is assigned as the start.

And the labelled arrow is added for every transition, where the label is $$\left( {{\bf{x,y}}} \right)$$ with x the input and y the output of the transition.

Not: the output is given under g in the table.

The state diagram is shown below. Therefore, the result shows the diagram of a finite-state machine.

## Step 3: Draw the state diagram for the given state table

Given that, a state table is shown below. Using the state table draw a state diagram for the finite-state machines.

Construction:

Now, we make a node for each state as$${{\bf{s}}_{\bf{0}}}{\bf{,}}{{\bf{s}}_{\bf{1}}}{\bf{,}}{{\bf{s}}_{\bf{2}}}{\bf{,}}{{\bf{s}}_{\bf{3}}}$$.

Then, $${{\bf{s}}_0}$$ is assigned as the start.

And the labelled arrow is added for every transition, where the label is $$\left( {{\bf{x,y}}} \right)$$ with x the input and y the output of the transition.

Not: the output is given under g in the table.

The state diagram is shown below Hence, the result shows the diagram of a finite-state machine.

## Step 4: Draw the state diagram for the given state table

Given that, a state table is shown below. Using the state table draw a state diagram for the finite-state machines.

Construction:

Now, we make a node for each state as$${{\bf{s}}_{\bf{0}}}{\bf{,}}{{\bf{s}}_{\bf{1}}}{\bf{,}}{{\bf{s}}_{\bf{2}}}{\bf{,}}{{\bf{s}}_{\bf{3}}}{\bf{,}}{{\bf{s}}_{\bf{4}}}$$.

Then, $${{\bf{s}}_0}$$ is assigned as the start.

And the labelled arrow is added for every transition, where the label is $$\left( {{\bf{x,y}}} \right)$$ with x the input and y the output of the transition.

Not: the output is given under g in the table.

The state diagram is shown below. Therefore, the result shows the diagram of a finite-state machine. ### Want to see more solutions like these? 