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  Mealy & Moore Machines

Mealy & Moore Machines:

There are two fundamental ways to design clocked sequential circuits. These are using following machine:

1. Mealy Machine
2. Moore Machine

Mealy Machine:

In the theory of computation (TOC), a Mealy machine is a finite-state machine whose output values are finds out both by its current state and the current inputs. It is a deterministic finite state transducer: for each of the state and input, at most one transition is achievable.

1103_mealy machine.jpg

A Mealy machine refers a six tuple:

(Q, Σ, Δ, δ, λ, qo)

Here,
Δ: is the output alphabet

λ: is a mapping from Q X Σ to Δ giving output λ(q, a) attached with the transitions from state q and input each state.

Output in response to input a1, a2, ..an is λ(qo, a1) λ(q1, a2) λ(q2, a3) ... λ(qn-1, an)

Here qo, q1, ..qn is the sequence of states such that δ(qi-1, ai)=qi

Moore machine:

In the TOC, a Moore machine is a finite-state machine whose output values are find out solely by its current state. It is on the contrary to Mealy machine, whose output values are find out both by its current state and by the values of its inputs.

1640_moore machine.jpg

A Moore machine refer six tuple

(Q, Σ, Δ, δ, λ, qo)

Δ: is the output alphabet

λ: is a mapping from Q to Δ giving output associated with each state.

Output in response to input a1, a2, ..an is λ(qo) λ(q1)... λ(qn)

where qo, q1, ..qn is the sequence of states such that δ(qi-1, ai)=qi

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