Question

In: Electrical Engineering

Derive a state diagram and table for a single-input and single-output Moore-type FSM that produces an...

Derive a state diagram and table for a single-input and single-output Moore-type FSM that produces an output of 1 if an input sequence of 101 is detected

Expert Solution

FSM - Finite State Machine

There are two types of machines, namely

Moore Machine : A finite state machine for which the output depends only on the states.
Mealy Machine : A finite state machine for which the input depends on the states and the inputs.

Now, let us break down the problem.

Tasks

A state table.
A state diagram.

1. STATE TABLE

Let us explore the question deeper.

Firstly, what is the objective of the machine?

TO PROVIDE AN OUTPUT OF "1" IF A SEQUENCE OF "101" IS DETECTED.

Secondly, what other information do we have about the machine?

It has 'SINGLE' input, i.e. we have one input port to our machine
It has 'SINGLE' output, i.e. we have one output port to our machine

Let us start at some initial state S. This state S could be any random state, or to look at it from another perspective, S could be the current state of the machine.

Now, we have a sequence of input arriving at the input port of machine. (Say 00010101000111)

t = 0 ; INPUT = 0
t = 1 ; INPUT = 0
t = 2 ; INPUT = 0
t = 3 ; INPUT = 1
t = 4 ; INPUT = 0
t = 5 : INPUT = 1
t = 6 ; INPUT = 0

Say we just started the machine. the input to the FSM changes with every clock pulse.

If an input of "1" arrivies at the input while the machine is in state S

The machine has to start detecting for a sequence of "101", and the first "1" in the sequecnce (xx1) has arrived.
This takes the machine to a different state S1 (say).
The output for the machine is "0" since a sequence of "101" has not been detected.

If an input of "0" arrivies at the input while the machine is in state S

The system stays in S.
The output for the machine is "0" since a sequence of "101" has not been detected.

If an input of "1" arrivies at the input while the machine is in state S1

The sequence becomes "11".
But, this "1" that arrived now could be the first in the sequence for a "101".
Hence, we stay in S1.
The output for the machine is "0" since a sequence of "101" has not been detected.

If an input of "0" arrivies at the input while the machine is in state S1

With the arrival of "0" we have two bits of the sequence (x10).
The system transitions to S2.
The output for the machine is "0" since a sequence of "101" has not been detected.

If an input of "1" arrivies at the input while the machine is in state S2

We have a sequence of "101".
The machine transitions to state S3.
The output for the machine is "1" since a sequence of "101" has been detected.

If an input of "0" arrivies at the input while the machine is in state S2

The input sequence becomes "100".
A state transition happens from S3 to S.
The output for the machine is "0" since a sequence of "101" has not been detected.

If an input of "1" arrivies at the input while the machine is in state S3

State S3 is when the current input has already made a sequence of "101"
We another "1" arrives the sequence becomes "011", which is not the output we are looking for.
But, the "1" that arrives could be the beginning of a sequence(xx1).
Hence, a state transition from S3 to S1 happens.
The output for the machine is "0" since a sequence of "101" has not been detected.

If an input of "0" arrivies at the input while the machine is in state S3

The sequence becomes "010", where we have 2 bits in the sequence(x10).
The state transition happens from S3 to S2.
The output for the machine is "0" since a sequence of "101" has not been detected.

1. STATE DIAGRAM

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