Question

Give the state tables for the finite-state machines with these state diagrams.

Short answer

(a): State table of the finite-state machine is shown below.

(b): State table of the finite-state machine is shown below.

(c): State table of the finite-state machine is shown below.

Step-by-step solution

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 gthat assigns to each state and input pair output and an initial state\({{\bf{s}}_0}\).

Give the state table for the given state diagram

Given that, a state diagram is shown below.

Using the state diagram create the state table for the finite-state machines.

Construction:

Let us create the table.

The table consists of state, f input, and g input.

State the nodes as\({{\bf{s}}_{\bf{0}}}{\bf{,}}{{\bf{s}}_{\bf{1}}}{\bf{,}}{{\bf{s}}_{\bf{2}}}{\bf{,}}{{\bf{s}}_{\bf{3}}}\).

If there is an arrow from \({{\bf{s}}_{\bf{i}}}\) to \({{\bf{s}}_{\bf{j}}}\) with a label\(\left( {{\bf{x,y}}} \right)\), then we write it down \({{\bf{s}}_{\bf{j}}}\) in the row \({{\bf{s}}_{\bf{i}}}\)and in column x under “f input”.

If there is an arrow from \({{\bf{s}}_{\bf{i}}}\) to \({{\bf{s}}_{\bf{j}}}\) with a label\(\left( {{\bf{x,y}}} \right)\), then we write down y in the row \({{\bf{s}}_{\bf{i}}}\)and in column x under “g input”.

The state table is shown below.

Therefore, the result shows the table of a finite-state machine.

Give the state table for the given state diagram

Given that, a state diagram is shown below.

Using the state diagram create the state table for the finite-state machines.

Construction:

Let us create the table.

The table consists of state, f input, and g input.

State the nodes as\({{\bf{s}}_{\bf{0}}}{\bf{,}}{{\bf{s}}_{\bf{1}}}{\bf{,}}{{\bf{s}}_{\bf{2}}}\).

If there is an arrow from \({{\bf{s}}_{\bf{i}}}\) to \({{\bf{s}}_{\bf{j}}}\) with a label\(\left( {{\bf{x,y}}} \right)\), then we write it down \({{\bf{s}}_{\bf{j}}}\) in the row \({{\bf{s}}_{\bf{i}}}\)and in column x under “f input”.

If there is an arrow from \({{\bf{s}}_{\bf{i}}}\) to \({{\bf{s}}_{\bf{j}}}\) with a label\(\left( {{\bf{x,y}}} \right)\), then we write down y in the row \({{\bf{s}}_{\bf{i}}}\)and in column x under “g input”.

The state table is shown below.

Hence, the result shows the table of a finite-state machine.

Give the state table for the given state diagram

Given that, a state diagram is shown below.

Using the state diagram create the state table for the finite-state machines.

Construction:

Let us create the table.

The table consists of state, f input, and g input.

State the nodes as\({{\bf{s}}_{\bf{0}}}{\bf{,}}{{\bf{s}}_{\bf{1}}}{\bf{,}}{{\bf{s}}_{\bf{2}}}{\bf{,}}{{\bf{s}}_{\bf{3}}}\).

If there is an arrow from \({{\bf{s}}_{\bf{i}}}\) to \({{\bf{s}}_{\bf{j}}}\) with a label\(\left( {{\bf{x,y}}} \right)\), then we write it down \({{\bf{s}}_{\bf{j}}}\) in the row \({{\bf{s}}_{\bf{i}}}\)and in column x under “f input”.

If there is an arrow from \({{\bf{s}}_{\bf{i}}}\) to \({{\bf{s}}_{\bf{j}}}\) with a label\(\left( {{\bf{x,y}}} \right)\), then we write down y in the row \({{\bf{s}}_{\bf{i}}}\)and in column x under “g input”.

The state table is shown below.

So, the result shows the table of a finite-state machine.