These slides have full understanding about Equivalent Moore Mealy... Having Moore to Mealy conversion and Mealy to Moore conversion... These slides also describing the concept of Transducers as models of sequential circuits (both w.r.t Moore and Mealy)... All these concepts are explained with easy examples...

1. Moore, Mealy Machine
Conversions
&
Transducers as models
of sequential circuits
Presented By:
 Anum Ayub
 Sanobir Aslam
 Aiman Hafeez
 Tasbeeh Zahra

2. 2
SALAM!
I am Anum Ayub
I am here to present Conversion of Mealy
machine to Moore Machine.
Roll No: 101611047

3. Conversion of
Moore machine
to
Mealy Machine
Presented By:
Anum Ayub
(RollNo: 47 )
1

4. Introduction of Moore Machine
and Mealy Machine
A Mealy Machine is an FSM (Finite State Machine) whose output
depends on the present state as well as the present input.
The value of the output function is a function of the transitions and
the changes, when the input logic on the present state is done.
While,
A Moore machine is also an FSM (Finite State Machine) whose
outputs depend on only the present state.
The value of the output function is a function of the current state and
the changes at the clock edges, whenever state changes occur.
4

5. Conversion of Moore machine
to Mealy Machine
Moore machine cannot directly convert to its
equivalent Mealy machine because the length of
the Moore machine is one longer than the Mealy
machine for the given input.
To convert Moore machine to Mealy machine, state
output symbols are distributed into input symbol
paths.
5

6. STEPS to Convert
Moore machine to 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.
6

7. Example 1:
7
Transition table for above Moore machine is as follows:
Present
State
Next State
Output
State State
q0 q1 q0 0
q1 q1 q2 0
q2 q1 q0 1

8. 8
Present
State
Next State
a b
State Output State Output
q0 q1 0 q0 0
q1 q1 0 q2 1
q2 q1 0 q0 0
Transition table for above Mealy machine is as follows:

9. 9
Transition diagram for Mealy machine will be:

10. Example 2:
10
Transition table for above Moore machine is as follows:
Present State
Next State
a b
A B,0 A,0
B B,0 C,0
C B,0 D,1
D B,0 A,0
A B C D
b/0
a/0
a/0
a/0 a/0
b/0
b/0
b/1

11. Example 3:
11
Transition table for above Moore machine is as follows:
Present
State
Next State
Output
0 1
q0 q1 q2 1
q1 q3 q2 0
q2 q2 q1 1
q3 q0 Q3 1
1/1
0/1
q3
q0q1
q2
1/11/1 1/0
0/1
0/1
0/0
Present
State
0 1
q0 q1 , 0 q2 , 1
q1 q3 , 1 q2 , 1
q2 q2 , 0 q1 , 0
q3 q0 , 0 q3 , 1
Transition table for above Mealy machine is as
follows:

12. Conversion of
Mealy machine
to
Moore Machine
Presented By:
Sanobir Aslam
(RollNo: 79)
2

13. 13
SALAM!
I am Sanobir Aslam
I am here to present Conversion of Moore
machine to Mealy Machine.
Roll No: 101611079

14. Conversion of Mealy machine
to Moore Machine
To convert Mealy machine to Moore machine, we
will create a separate state for every new output
symbol and according to incoming and outgoing
edges are distributed.
14

15. STEPS to Convert
Mealy machine to Moore machine:
￮ Step 1:
For each state(Qi), calculate the number of different outputs
that are available in the transition table of the Mealy machine.
￮ Step 2:
Copy state Qi, if all the outputs of Qi are the same. Break qi
into n states as Qin, if it has n distinct outputs where n = 0, 1, 2....
￮ Step 3:
If the output of initial state is 0, insert a new initial state at
the starting which gives 1 output.
15

16. Example 1:
16
Transition table for above Mealy machine is
as follows:
Present
State
Next State
a b
State Output State Output
q1 q1 0 q2 0
q2 q2 1 q3 10
q3 q2 0 q3 1

17. 17
The state q1 has only one output. The state q2 and q3 have both output 0 and 1. So we will
create two states for these states. For q2, two states will be q20(with output 0) and q21(with
output 1). Similarly, for q3 two states will be q30(with output 0) and q31(with output 1).
Transition table for Moore machine will be:
Present
State
Next State
Output
State Output
q1 q1 q2 0
q20 q21 q30 0
q21 q21 q30 1
q30 q20 q31 0
q31 q20 q31 1

18. 18
Transition diagram for Moore machine will be:

19. Example 2:
19
Transition table for above Moory machine is as follows:
Present
State
Next State
a b
State Output State Output
q1 q1 1 q2 0
q2 q4 1 q4 1
q3 q2 1 q3 1
q4 q3 0 q1 1

20. 20
• For state q1, there is only one incident edge with output 0. So, we
don't need to split this state in Moore machine.
• For state q2, there is 2 incident edge with output 0 and 1. So, we will
split this state into two states q20( state with output 0) and q21(with
output 1).
• For state q3, there is 2 incident edge with output 0 and 1. So, we will
split this state into two states q30( state with output 0) and q31(
state with output 1).
• For state q4, there is only one incident edge with output 0. So, we
don't need to split this state in Moore machine.

21. 21
Transition table for Mealy machine will be:
Present
State
Next State
Output
State Output
q1 q1 q2 1
q20 q4 q4 0
q21 Ø Ø 1
q30 q21 q31 0
q31 q21 q31 1
q4 q3 q4 1

22. 22
Transition diagram for Mealy machine will be:

23. Transducers as
models of
Sequential
Circuits
3
Presented By:
Tasbeeh Zahra
(RollNo: 55 )
(Mealy Machine)

24. 24
SALAM!
I am Tasbeeh Zahra
I am here to present Transducers as models
of Sequential Circuits.
Roll No: 101611055

25. Transducers
Convert signal from one form to another
￮ E . g microphone, speaker etc.
25
NAND DELAY OR
OR
input outputA B
Transducer circuit
Mealy Machine

26. 26
Truth Tables
AND Gate
A B A.B
0 0 0
0 1 0
1 0 0
1 1 1
OR Gate
A B A.B
0 0 0
0 1 1
1 0 1
1 1 1
NAND Gate
A B A.B
0 0 1
0 1 1
1 0 1
1 1 0

27. 27
Transducer Circuit
NAND DELAY OR
OR
input outputA B
• Two Points A & B.
• Total No. OF points=2=
• No of states = 2^2 = 4 = q0 ,q1,q2,q3.
 Already available Points we say Old A & Old B.
 New Equation
• New A = input NAND (Old A OR Old B)
• New B = Old A
• Output = input OR Old B

28. Transducer-theory of Automata
28
New A = input NAND (Old A OR Old B)
New B = Old A
Output = input OR Old B
State Table
States Old A Old B
q0 0 0
q1 0 1
q2 1 0
q3 1 1

29. 29
Check on both input 0 and 1.
State q0 ,
Old A = 0 , Old B = 0
New A = input NAND (Old A OR Old B)
New A = 0 NAND (0 OR 0)
New A = 1
New B = Old A
New B = 0
Output = input OR Old B
Output = 0 OR 0
Output = 0
At input 0
State q0 ,
Old A = 0 , Old B = 0
New A = input NAND (Old A OR Old B)
New A = 1 NAND (0 OR 0)
New A = 1
New B = Old A
New B = 0
Output = input OR Old B
Output = 1 OR 0
Output = 0
At input 1

30. 30
Check on both input 0 and 1.
State q1 ,
Old A = 0 , Old B = 1
New A = input NAND (Old A OR Old B)
New A= 0 NAND (0 OR 1)
New A = 1
New B = Old A
New B = 0
Output = input OR Old B
Output = 0 OR 1
Output = 1
At input 0
State q1 ,
Old A = 0 , Old B = 1
New A = input NAND (Old A OR Old B)
New A = 1 NAND (0 OR 1)
New A = 0
New B = Old A
New B = 0
Output = input OR Old B
Output = 1 OR 1
Output = 1
At input 1

31. 31
Check on both input 0 and 1.
State q2 ,
Old A = 1 , Old B = 0
New A = input NAND (Old A OR Old B)
New A= 0 NAND (1 OR 0)
New A = 1
New B = Old A
New B = 1
Output = input OR Old B
Output = 0 OR 0
Output = 0
At input 0
State q2 ,
Old A = 1 , Old B = 0
New A = input NAND (Old A OR Old B)
New A = 1 NAND (1 OR 0)
New A = 0
New B = Old A
New B = 1
Output = input OR Old B
Output = 1 OR 0
Output = 1
At input 1

32. 32
Check on both input 0 and 1.
State q3 ,
Old A = 1 , Old B = 1
New A = input NAND (Old A OR Old B)
New A= 0 NAND (1 OR 1)
New A = 1
New B = Old A
New B = 1
Output = input OR Old B
Output = 0 OR 1
Output = 1
At input 0
State q3 ,
Old A = 1 , Old B = 1
New A = input NAND (Old A OR Old B)
New A = 1 NAND (1 OR 1)
New A = 0
New B = Old A
New B = 1
Output = input OR Old B
Output = 1 OR 1
Output = 1
At input 1

33. 33
State
At Input 0 At Input 1
A B Output A B Output
q0 1 0 0 1 0 1
q1 1 0 1 0 0 1
q2 1 1 0 0 1 1
q3 1 1 1 0 1 1
Transition Table
q0
Mealy Machine
1,1
q1
q2q3
1,1
1,1 1,1
0,0
0,0
0,1
0,1

34. Transducers as
models of
Sequential
Circuits
4
Presented By:
Aiman Hafeez
(RollNo: 53 )
(Moore Machine)

35. 35
SALAM!
I am Aiman Hafeez
I am here to present Transducers as models
of Sequential Circuits.
Roll No: 101611053

36. 36
NAND DELAY OR
OR
input outputA B
Transducer circuit
Moore Machine

37. 37
Truth Tables
AND Gate
A B A.B
0 0 0
0 1 0
1 0 0
1 1 1
OR Gate
A B A.B
0 0 0
0 1 1
1 0 1
1 1 1
NAND Gate
A B A.B
0 0 1
0 1 1
1 0 1
1 1 0

38. 38
Transducer Circuit
• Two Points A & B.
• Total No. OF points=2=
• No of states = 2^2 = 4 = q0 ,q1,q2,q3.
 Already available Points we say Old A & Old B.
 New Equation
• New A = input NAND (Old A OR Old B)
• New B = Old A
• Output = Old A OR Old B
NAND DELAY OR
OR
input outputA B

39. Transducer-theory of Automata
39
New A = input NAND (Old A OR Old B)
New B = Old A
Output = Old A OR Old B
State Table
States Old A Old B
q0 0 0
q1 0 1
q2 1 0
q3 1 1

40. 40
Check on both input 0 and 1.
State q0 ,
Old A = 0 , Old B = 0
New A = input NAND (Old A OR Old B)
New A = 0 NAND (0 OR 0)
New A = 1
New B = Old A
New B = 0
Output = Old A OR Old B
Output =0 OR 0
Output = 0
At input 0
State q0 ,
Old A = 0 , Old B = 0
New A = input NAND (Old A OR Old B)
New A = 1 NAND (0 OR 0)
New A = 1
New B = Old A
New B = 0
Output = Old A OR Old B
Output = 0 OR 0
Output = 0
At input 1

41. 41
Check on both input 0 and 1.
State q1 ,
Old A = 0 , Old B = 1
New A = input NAND (Old A OR Old B)
New A= 0 NAND (0 OR 1)
New A = 1
New B = Old A
New B = 0
Output = Old A OR Old B
Output = 0 OR 1
Output = 1
At input 0
State q1 ,
Old A = 0 , Old B = 1
New A = input NAND (Old A OR Old B)
New A = 1 NAND (0 OR 1)
New A = 0
New B = Old A
New B = 0
Output = Old A OR Old B
Output =0 OR 1
Output = 1
At input 1

42. 42
Check on both input 0 and 1.
State q2 ,
Old A = 1, Old B = 0
New A = input NAND (Old A OR Old B)
New A= 0 NAND (1 OR 0)
New A = 1
New B = Old A
New B = 1
Output = Old A OR Old B
Output = 1 OR 0
Output = 1
At input 0
State q2 ,
Old A = 1 , Old B = 0
New A = input NAND (Old A OR Old B)
New A = 1 NAND (1 OR 0)
New A = 0
New B = Old A
New B = 1
Output = Old A OR Old B
Output = 1 OR 0
Output = 1
At input 1

43. 43
Check on both input 0 and 1.
State q3 ,
Old A = 1 , Old B = 1
New A = input NAND (Old A OR Old B)
New A= 0 NAND (1 OR 1)
New A = 1
New B = Old A
New B = 1
Output = Old A OR Old B
Output = 1 OR 1
Output = 1
At input 0
State q3 ,
Old A = 1 , Old B = 1
New A = input NAND (Old A OR Old B)
New A = 1 NAND (1 OR 1)
New A = 0
New B = Old A
New B = 1
Output = Old A OR Old B
Output =1 OR 1
Output = 1
At input 1

44. 44
Transition Table
q0/0
Moore Machine
1
1
1
1
0
0
0
0
Present
State
Next State
Output
Input 0 Input 1
q0 (1,0) = q2 (1,0) = q2 0
q1 (1,0) = q2 (0,0) = q0 1
q2 (1,1) = q3 (0,1) = q1 1
q3 (1,1) = q3 (0,1) = q1 1
q1/1
q2/1q3/1

45. 45
Any questions?
If you have any then
GOOGLE IT… ! 😉