Post on 02-Jan-2016
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Moore machine and Mealy machine (P.274)
Mealy machine: created by G. H. Mealy, 1955Moore machine: created by E.F. Moore, 1956
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Moore machine and Mealy machine (P.274)
Mealy machine: created by G. H. Mealy, 1955Moore machine: created by E.F. Moore, 1956
Purpose: to design a mathematical model for sequential circuits.
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Moore machine and Mealy machine (P.274)
Mealy machine: created by G. H. Mealy, 1955Moore 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
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Moore machine and Mealy machine (P.274)
Mealy machine: created by G. H. Mealy, 1955Moore 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 things1.A finite set of states qo q1 q2 … qo is the start state.
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Moore machine and Mealy machine (P.274)
Mealy machine: created by G. H. Mealy, 1955Moore 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 things1.A finite set of states qo q1 q2 … qo is the start state.2.An alphabet of letters for forming the input string Σ = {a, b, c, … }
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Moore machine and Mealy machine (P.274)
Mealy machine: created by G. H. Mealy, 1955Moore 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 things1.A finite set of states qo q1 q2 … qo is the start state.2.An alphabet of letters for forming the input string Σ = {a, b, c, … }3.An alphabet of possible output characters Γ = {x, y, z, … }
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Moore machine and Mealy machine (P.274)
Mealy machine: created by G. H. Mealy, 1955Moore 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 things1.A finite set of states qo q1 q2 … qo is the start state.2.An alphabet of letters for forming the input string Σ = {a, b, c, … }3.An alphabet of possible output characters Γ = {x, y, z, … }4.A transition table that shows for each state and each input letter what state is reached next.
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Moore machine and Mealy machine (P.274)
Mealy machine: created by G. H. Mealy, 1955Moore 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 things1.A finite set of states qo q1 q2 … qo is the start state.2.An alphabet of letters for forming the input string Σ = {a, b, c, … }3.An alphabet of possible output characters Γ = {x, y, z, … }4.A transition table that shows for each state and each input letter what state is reached next.5.An output table that shows what character from Γ is printed by each state as it is entered
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Moore machine Transition and output table
Old State
qo
q1
q2
q3
Old State
1
0
0
1
Input a
q1
q3
q0
q3
Input b
q3
q1
q3
q2
Output by the New State
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Moore machine – the pictorial representation
qo /1
q2 /0 q3 /1
a
aa b
b
b
q1 /0
b
a
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Moore machine – example Input: a b b a Output:
qo /1
q2 /0 q3 /1
a
aa b
b
b
q1 /0
b
a
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Moore machine – example Input: a b b a Output: 1
qo /1
q2 /0 q3 /1
a
aa b
b
b
q1 /0
b
a
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qo /1
q2 /0 q3 /1
a
aa b
b
b
q1 /0
b
a
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qo /1
q2 /0 q3 /1
a
aa b
b
b
q1 /0
b
a
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qo /1
q2 /0 q3 /1
a
aa b
b
b
q1 /0
b
a
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qo /1
q2 /0 q3 /1
a
aa b
b
b
q1 /0
b
a
1. No final state2. Output is always
one letter more than the input
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Mealy machine
Definition: A Mealy machine is a collection of four things1.A finite set of states qo q1 q2 … qo is the start state.2.An alphabet of letters for forming the input string Σ = {a, b, c, … }3.An alphabet of possible output characters Γ = {x, y, z, … }4.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.
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Example: input abba output 0111
q0 q2
q3
q1
a/0
b/1
b/1
a/1
a/1
a/0b/0
b/1
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FSA NFSA Moore Mealy
Start State 1 1 1 1
Final State some or 1 some or 1 none none
Edge Labels letters letters letters i/o
# of edges 1 for @ letter arbitrary 1 for @ letter 1 for @ letter
Deterministic yes no yes yes
Output no no yes yes