Question

Find the output string generated by the Moore machine in Exercise 21 with each of the input strings in Exercise 22.

Short answer

(a): So, the output is 11111.

(b): Hence, the output is 1000000.

(c): Therefore, the output is 100011001100.

Step-by-step solution

General form

Moore machine (Definition):

A Moore machine\({\bf{M = }}\left( {{\bf{S,}}\,\,{\bf{I,}}\,\,{\bf{O,}}\,\,{\bf{f,}}\,\,{\bf{g,}}\,\,{{\bf{s}}_0}} \right)\)consists of a finite set of states, an input alphabet I, an output alphabet O, a transition function fthat assigns a next state to every pair of a state and an input, an output function g that assigns an output to every state, and a starting state\({{\bf{s}}_0}\). A Moore machine can be represented either by a table listing the transitions for each pair of state and input and the outputs for each state, or by a state diagram that displays the states, the transitions between states, and the output for each state. In the diagram, transitions are indicated with arrows labelled with the input, and the outputs are shown next to the states.

Concept of input string and output:

An input string takes the starting state through a sequence of states, as determined by the transition function. As we read the input string symbol by symbol (from left to right), each input symbol takes the machine from one state to another. Because each transition produces an output, an input string also produces an output string.

Step 2: Generate the output using state diagram

Referring to Exercise 22:An input string 0101

Referring to Exercise 21: The state diagram is shown below:

Using the diagram generate the output.

Let us use the input string to find the output.

The output obtained is 11111. The successive states and outputs are shown below table:

So, the output is 1111.

Generate the output using state diagram

Referring to Exercise 22: An input string 111111

Using the table generate the output.

Let us use the input string to find the output.

The output obtained is 1000000. The successive states and outputs are shown below table:

Hence, the output is 100000.

Referring to Exercise 22: An input string 11101110111

Using the table generate the output.

Let us use the input string to find the output.

The output obtained is 10001100110. The successive states and outputs are shown below table:

Therefore, the output is 10001100110.