KMaps and Circuit Reduction

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K-Maps and Circuit Reduction

• Presented By
• Anthony Coln

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K stands for Karnaugh

• Maurice Karnaugh developed K-Maps in the 1950s.
• These maps provided an alternate way of
  representing Boolean functions.

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Boolean Functions Circuits

• Major functions used
• Negation ()
• Conjunction ()
• Disjunction ()
• A circuit is a collection of logic gates

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Why Circuit Reduction?

• Circuit reduction is need to cut costs

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Why Circuit Reduction? (cont.)

• See the physical reduction?

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Algebraic Alternative

• (a b c) (a b c)
• (a b c) a (a b c) b (a
  b c) c
• (a a) (a b) (a c) (b a) b (b
  c) (c a) c
• (b c)
• DONT THINK YOU WANT TO DO ALL THAT.

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Circuits to K-Maps The Link

• Given a circuit, a truth table can be made. From
  that truth table comes a K-Map.

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K-Map Breakdown

• How the inputs of the circuit determine the size
  of the K-Map

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Circuit Reduction

• Sum-of-products needed

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Circuit Reduction (cont.)

• Truth table values put into K-Map and reduced

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Minterm Grouping Examples
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References

• Maxfield Montrose. Karnaugh Maps 101. Bebop
  to the Boolean Boogie. www.maxmon.com. 2004.
• Schneider, G. Michael and Judith L. Gersting.
  Invitation to Computer Science C Version. 3rd
  ed. Course Technology. 2004. pp. 151-163.
• Tan, Soo Tang. Finite Mathematics. 6th ed.
  Brooks/Cole. 2000. pp. 597-616.

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Questions??????
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You might want to know this

• If a circuit has 5 inputs, how many boxes will
  its K-Map have?
• If a circuit has 6 inputs, how many boxes will
  its K-Map have?