QuineMcCluskey Method

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Quine-McCluskey Method

• ECE-331, Digital Design
• Dr. Ron Hayne
• Electrical and Computer Engineering

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Quine-McCluskey Minimization

• wrt to minimization, K-maps Only good for
• Small functions (lt5variables)
• Single output function at a time
• Not Implementable on Computer
• Subjective Interpretation, Different Coverings
• Q-M (Tabular Minimization) Solves These Problems

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Basic Definitions

• Prime Implicant
• A group of adjacent 1s that is not contained
  within any larger implicant
• Essential Prime Implicant
• A prime implicant which includes a minterm that
  is covered by only one Prime Implicant

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Basic Definitions

• Complete Sum
• A representation of a function by the sum of ALL
  possible prime implicants
• Not necessarily irredundant
• Irredundant Sum
• The representation of a function by A sum of PIs
  such that the removal of any one of the PIs
  changes the value of the function for some
  combination of input values

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Basic Definitions

• Cost Function
• A measure of the effort or hardware associated
  with the implementation of something or the
  accomplishment of a task
• Digital Design Cost Functions
• Number of terms
• Number of occurrences of a literal (not the
  number of distinct literals).

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Quine-McCluskey Method

• Construct the Implicant Table
• Group minterms by number of 1s
• Apply Adjacency Theorem to pairs of implicants
• Mark all implicants that are used in larger groups

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Q-M Example

Karim-Johnson, p. 59
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Step 1a Implicant Table
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Step 1b,c Adjacency Theorem
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Step 1b,c Adjacency Theorem
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Step 1b,c Adjacency Theorem
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Quine-McCluskey Method

• Construct the Covering Table
• Prime Implicants and Minterms
• Mark rows and columns
• Identify Essential Prime Implicants
• Construct the Reduced Covering Table
• Secondary Prime Implicants
• Mark rows and columns
• Minimum cover for remaining minterms
• Simplified Logic Expression

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Step 2a Covering Table
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Step 2b Covering Table
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2c Essential Prime Implicants
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Step 2c Covering Table
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3a,b Reduced Covering Table
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3c Reduced Covering Table
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4 Simplified Logic Expression
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Summary

• Q-M
• Implicant Table
• Covering Table
• Essential Prime Implicants
• Simplified Logic Expression