Designing Sequential Circuits: Examples, and State Minimization

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Designing Sequential CircuitsExamples, and
State Minimization

• CS 231
• L.V. Kale

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Example

• Sequence analysis
• Output 1 whenever you see 1001, AND the total
  number of 1s seen is odd.

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State minimization I

• Two states can be merged
• if they have the same output and same next state
• Consider the example from last week detection of
  1001, with an extra state E.

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State minimization II

• Two states are equivalent (and can be merged) if
• They have the same outputs, and their next states
  are equivalents
• Method construct a 2-D matrix of all states
• Loop through them, marking off states if they are
  not equivalent
• All the unmarked pairs are equivalent (?)

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Limits of Finite State Machines

• Make a circuit that will give out 1 whenever
  the total number of 1s is equal to total number
  of 0s seen so far