Jung H. Kim Chapter 23 1

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SYEN 3330Digital Systems

• Chapter 2 Part 3

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Boolean Operator Precedence
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Review Duality Principle
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Duality In Proofs
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Useful Theorems

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Proof of Simplification

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Proof of Concensus

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Proof of DeMorgans Law

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Boolean Function Evaluation
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Expression Simplification

• Simplify to contain the smallest number of
  literals (complemented and uncomplemented
  variables)

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Complementing Functions

• This generate a lot of terms. You might want to
  simplify the expression first.

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Canonical Forms

• It is useful to specify Boolean functions of n
  variables in a manner that is easy to compare.
• Two such Canonical Forms are in common usage
• Sum of Minterms
• Product of Maxterms

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Minterms
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Maxterms
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Maxterms and Minterms
The index above is important for describing which
variables in the terms are true and which are
complemented.
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Standard Order
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Purpose of the Index

• The index for the minterm or maxterm, expressed
  as a binary number, is used to determine whether
  the variable is shown in the true form or
  complemented form.

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Index Example in Three Variables
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Four Variables, Index 0-7
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Four Variables, Index 8-15
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Minterm and Maxterm Relationship
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Function Tables for Both
Minterms of two variables
Maxterms of two variables
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Observations
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Minterm Function Example
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Minterm Function Example

• F(A, B, C, D, E) m2 m9 m17 m23

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Maxterm Function Example
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Maxterm Function Example

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Cannonical Sum of Minterms
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Another SOM Example
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Shorthand SOM Form
Note that we explicitly show the standard
variables in order and drop the m designators.
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Canonical Product of Maxterms
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Product of Maxterm Example
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Function Complements
Then
Or alternately
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Conversion Between Forms
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Review of Canonical Forms
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Review Indices
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Forms of Terms, Complements
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Review Sum of Minterms Form
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Review Product of Maxterms
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Review Complements, Conversions