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

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.

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

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.

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, … }

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, … }

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.

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

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

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

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

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

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

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

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

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

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

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: 1 0 0 0 qo /1 a q1 /0 b a a b q2 /0 b q3 /1 a b

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: 1 0 0 0 qo /1 a q1 /0 b a a b q2 /0 b q3 /1 a b

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: 1 0 0 0 1 qo /1 a q1 /0 b a a b q2 /0 b q3 /1 a b

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: 1 0 0 0 1 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

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.

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

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