1. Moore machine and Mealy machine (P.274)
School of Computing
Moore machine and Mealy machine (P.274)
Mealy machine: created by G. H. Mealy, 1955
Moore machine: created by E.F. Moore, 1956

2. Moore machine and Mealy machine (P.274)
School of Computing
Moore machine and Mealy machine (P.274)
Mealy machine: created by G. H. Mealy, 1955
Moore machine: created by E.F. Moore, 1956
Purpose: to design a mathematical model for sequential circuits.

3. Moore machine and Mealy machine (P.274)
School of Computing
Moore machine and Mealy machine (P.274)
Mealy machine: created by G. H. Mealy, 1955
Moore machine: created by E.F. Moore, 1956
Purpose: to design a mathematical model for sequential circuits.
Definition: A Moore machine is a collection of five things

4. Moore machine and Mealy machine (P.274)
School of Computing
Moore machine and Mealy machine (P.274)
Mealy machine: created by G. H. Mealy, 1955
Moore machine: created by E.F. Moore, 1956
Purpose: to design a mathematical model for sequential circuits.
Definition: A Moore machine is a collection of five things
A finite set of states qo q1 q2 … qo is the start state.

5. Moore machine and Mealy machine (P.274)
School of Computing
Moore machine and Mealy machine (P.274)
Mealy machine: created by G. H. Mealy, 1955
Moore machine: created by E.F. Moore, 1956
Purpose: to design a mathematical model for sequential circuits.
Definition: A Moore machine is a collection of five things
A finite set of states qo q1 q2 … qo is the start state.
An alphabet of letters for forming the input string Σ = {a, b, c, … }

6. Moore machine and Mealy machine (P.274)
School of Computing
Moore machine and Mealy machine (P.274)
Mealy machine: created by G. H. Mealy, 1955
Moore machine: created by E.F. Moore, 1956
Purpose: to design a mathematical model for sequential circuits.
Definition: A Moore machine is a collection of five things
A finite set of states qo q1 q2 … qo is the start state.
An alphabet of letters for forming the input string Σ = {a, b, c, … }
An alphabet of possible output characters Γ = {x, y, z, … }

7. Moore machine and Mealy machine (P.274)
School of Computing
Moore machine and Mealy machine (P.274)
Mealy machine: created by G. H. Mealy, 1955
Moore machine: created by E.F. Moore, 1956
Purpose: to design a mathematical model for sequential circuits.
Definition: A Moore machine is a collection of five things
A finite set of states qo q1 q2 … qo is the start state.
An alphabet of letters for forming the input string Σ = {a, b, c, … }
An alphabet of possible output characters Γ = {x, y, z, … }
A transition table that shows for each state and each input letter what state is reached next.

8. Moore machine and Mealy machine (P.274)
School of Computing
Moore machine and Mealy machine (P.274)
Mealy machine: created by G. H. Mealy, 1955
Moore machine: created by E.F. Moore, 1956
Purpose: to design a mathematical model for sequential circuits.
Definition: A Moore machine is a collection of five things
A finite set of states qo q1 q2 … qo is the start state.
An alphabet of letters for forming the input string Σ = {a, b, c, … }
An alphabet of possible output characters Γ = {x, y, z, … }
A transition table that shows for each state and each input letter what state is reached next.
An output table that shows what character from Γ is printed by each state as it is entered

9. Moore machine Transition and output table
School of Computing
Moore machine Transition and output table
Output by the
New State
Old State qo q1 q2 q3
Old State 1
Input a q1 q3 q0
Input b q3 q1 q2

10. School of Computing Moore machine – the pictorial representation a b a
qo /1 a
q1 /0 b a a b
q2 /0 b
q3 /1 a b

11. Moore machine – example Input: a b b a Output:
School of Computing
Moore machine – example
Input: a b b a
Output:
qo /1 a
q1 /0 b a a b
q2 /0 b
q3 /1 a b

12. Moore machine – example Input: a b b a Output: 1
School of Computing
Moore machine – example
Input: a b b a
Output: 1
qo /1 a
q1 /0 b a a b
q2 /0 b
q3 /1 a b

13. Moore machine – example Input: a b b a Output: 1
School of Computing
Moore machine – example
Input: a b b a
Output: 1
qo /1 a
q1 /0 b a a b
q2 /0 b
q3 /1 a b

14. Moore machine – example Input: a b b a Output: 1 0
School of Computing
Moore machine – example
Input: a b b a
Output: 1 0
qo /1 a
q1 /0 b a a b
q2 /0 b
q3 /1 a b

15. Moore machine – example Input: a b b a Output: 1 0
School of Computing
Moore machine – example
Input: a b b a
Output: 1 0
qo /1 a
q1 /0 b a a b
q2 /0 b
q3 /1 a b

16. Moore machine – example Input: a b b a Output: 1 0 0
School of Computing
Moore machine – example
Input: a b b a
Output: 1 0 0
qo /1 a
q1 /0 b a a b
q2 /0 b
q3 /1 a b

17. Moore machine – example Input: a b b a Output: 1 0 0
School of Computing
Moore machine – example
Input: a b b a
Output: 1 0 0
qo /1 a
q1 /0 b a a b
q2 /0 b
q3 /1 a b

18. Moore machine – example Input: a b b a Output: 1 0 0 0
School of Computing
Moore machine – example
Input: a b b a
Output:
qo /1 a
q1 /0 b a a b
q2 /0 b
q3 /1 a b

19. Moore machine – example Input: a b b a Output: 1 0 0 0
School of Computing
Moore machine – example
Input: a b b a
Output:
qo /1 a
q1 /0 b a a b
q2 /0 b
q3 /1 a b

20. Moore machine – example Input: a b b a Output: 1 0 0 0 1
School of Computing
Moore machine – example
Input: a b b a
Output:
qo /1 a
q1 /0 b a a b
q2 /0 b
q3 /1 a b

21. Moore machine – example Input: a b b a Output: 1 0 0 0 1
School of Computing
Moore machine – example
Input: a b b a
Output:
qo /1 a
q1 /0 b
No final state
Output is always one letter more than the input a a b
q2 /0 b
q3 /1 a b

22. Mealy machine School of Computing
Definition: A Mealy machine is a collection of four things
A finite set of states qo q1 q2 … qo is the start state.
An alphabet of letters for forming the input string Σ = {a, b, c, … }
An alphabet of possible output characters Γ = {x, y, z, … }
A pictorial representation with states represented by small circles and directed edges indicting transitions between states. Each edge is labeled with a compound symbol of the form i/o.

23. School of Computing Example: input abba output 0111 a/0 b/1 a/1 b/0q1
a/0
b/1 q0 q2
a/1
b/0
a/0
b/1
b/1 q3
a/1

24. School of Computing FSA NFSA Moore Mealy Start State 1 Final State
some or 1
none
Edge Labels
letters
i/o
# of edges
1 letter
arbitrary
Deterministic
yes no
Output