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KMaps and Circuit Reduction

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Maurice Karnaugh developed K-Maps in the 1950s. ... Disjunction ( ) A circuit is a collection of logic gates. Why Circuit Reduction? ... – PowerPoint PPT presentation

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Title: KMaps and Circuit Reduction


1
K-Maps and Circuit Reduction
  • Presented By
  • Anthony Coln

2
K stands for Karnaugh
  • Maurice Karnaugh developed K-Maps in the 1950s.
  • These maps provided an alternate way of
    representing Boolean functions.

3
Boolean Functions Circuits
  • Major functions used
  • Negation ()
  • Conjunction ()
  • Disjunction ()
  • A circuit is a collection of logic gates

4
Why Circuit Reduction?
  • Circuit reduction is need to cut costs

5
Why Circuit Reduction? (cont.)
  • See the physical reduction?

6
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.

7
Circuits to K-Maps The Link
  • Given a circuit, a truth table can be made. From
    that truth table comes a K-Map.

8
K-Map Breakdown
  • How the inputs of the circuit determine the size
    of the K-Map

9
Circuit Reduction
  • Sum-of-products needed

10
Circuit Reduction (cont.)
  • Truth table values put into K-Map and reduced

11
Minterm Grouping Examples
12
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.

13
Questions??????
14
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?
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