Moore and Mealy Machines
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Finite automata may have outputs corresponding to each transition. There are two types of finite state machines
that generate output
Mealy Machine
Moore machine
Mealy Machine
A Mealy Machine is an FSM whose output depends on the present state as well as the present input.
It can be described by a 6 tuple (Q, , O, , X, q0) where
Q is a finite set of states.
is a finite set of symbols called the input alphabet.
O is a finite set of symbols called the output alphabet.
is the input transition function where : Q Q
X is the output transition function where X: Q O
q0 is the initial state from where any input is processed (q0 Q).
The state table of a Mealy Machine is shown below
Next state
Present state input = 0 input = 1
State Output State Output
a b x1 c x1
b b x2 d x3
c d x3 c x1
d d x3 d x2
The state diagram of the above Mealy Machine is
Moore Machine
Moore machine is an FSM whose outputs depend on only the present state.
A Moore machine can be described by a 6 tuple (Q, , O, , X, q0) where
Q is a finite set of states.
is a finite set of symbols called the input alphabet.
O is a finite set of symbols called the output alphabet.
is the input transition function where : Q Q
X is the output transition function where X: Q O
q0 is the initial state from where any input is processed (q0 Q).
The state table of a Moore Machine is shown below
Next State
Present state Output
Input = 0 Input = 1
a b c x2
b b d x1
c c d x2
d d d x3
The state diagram of the above Moore Machine is
Mealy Machine vs. Moore Machine
The following table highlights the points that differentiate a Mealy Machine from a Moore Machine.
Mealy Machine Moore Machine
Output depends both upon present state
Output depends only upon the present state.
and present input.
Generally, it has fewer states than Moore
Generally, it has more states than Mealy Machine.
Machine.
Input change can cause change in output change as soon as logic is
Output changes at the clock edges.
done.
In Moore machines, more logic is needed to decode the outputs
Mealy machines react faster to inputs
since it has more circuit delays.
Moore Machine to Mealy Machine
Algorithm 4
Input Moore Machine
Output Mealy Machine
Step 1 Take a blank Mealy Machine transition table format.
Step 2 Copy all the Moore Machine transition states into this table format.
Step 3 Check the present states and their corresponding outputs in the Moore Machine state table; if for a
state Qi output is m, copy it into the output columns of the Mealy Machine state table wherever Qi appears in the
next state.
Example
Let us consider the following Moore machine
Next State
Present State Output
a=0a=1
a d b 1
b a d 0
c c c 0
d b a 1
Now we apply Algorithm 4 to convert it to Mealy Machine.
Step 1 & 2
Next State
Present State a=0 a=1
State Output State Output
a d b
b a d
c c c
d b a
Step 3
Next State
Present State a=0 a=1
State Output State Output
=> a d 1 b 0
b a 1 d 1
c c 0 c 0
d b 0 a 1
Mealy Machine to Moore Machine
Algorithm 5
Input Mealy Machine
Output Moore Machine
Step 1 Calculate the number of different outputs for each state (Qi) that are available in the state table of the
Mealy machine.
Step 2 If all the outputs of Qi are same, copy state Qi. If it has n distinct outputs, break Qi into n states as Qin
where n = 0, 1, 2.......
Step 3 If the output of the initial state is 1, insert a new initial state at the beginning which gives 0 output.
Example
Let us consider the following Mealy Machine
Next State
Present State a=0 a=1
Next State Output Next State Output
a d 0 b 1
b a 1 d 0
c c 1 c 0
d b 0 a 1
Here, states a and d give only 1 and 0 outputs respectively, so we retain states a and d. But states b and
c produce different outputs 1and0 . So, we divide b into b0, b1 and c into c0, c1.
Next State
Present State Output
a=0a=1
a d b1 1
b0 a d 0
b1 a d 1
c0 c1 C0 0
c1 c1 C0 1
d b0 a 0
