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Karnaugh map

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This presentation has the details about the Karnaugh map

This presentation has the details about the Karnaugh map


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  • 1. Karnaugh Map
  • 2. Introduction
    A karnaugh map is a visual display of the fundamental products needed for a sum of products solution.
    By using this map we can easily simplify the Boolean equations in sum of product form.
  • 3. Two – variable map Truth table
  • 4. Karnaugh map
    B
    A
    B
    10
    11
    03
    02
    A
  • 5. Explanation
    The vertical column has A followed by , and the horizontal row B followed by .
    Then take the combination of inputs which produce the output as 1.
    A
    B
  • 6. Cont.,
    In the given truth table, the output is 1 at and
    input combinations.
    Enter 1 in the spaces of and at the karnaugh map, because the corresponding outputs are high. The remaining spaces are entered with 0’s.
    B
    A
    B
    A
    A
    B
    A
    B
  • 7. Three variable map Truth table
  • 8. Karnaugh map
    C
    10
    11
    B
    A
    B
    A
    02
    13
    A
    B
    C
    A
    B
    06
    07
    04
    05
  • 9. Explanation
    The vertical column is labeled as , , ,
    This order is not a binary progress of 00,01,10 and 11.
    A
    B
    A
    B
    A
    B
    A
    B
  • 10. Cont.,
    In the karnaugh map the variables order are assigned in a sequence of only one variable changes from complemented to un complemented form.
    The horizontal row is marked as and
    C
    C
  • 11. Cont.,
    The fundamental products for these 1 outputs are
    , and
    Enter ‘1’ on these variables positions of the karnaugh map.
    The remaining spaces are filled with 0’s.
    C
    A
    B
    C
    A
    B
    A
    B
    C
  • 12. Four variable map
    Many digital systems process data in 4 bits (nibbles).
    Some digital IC chips will work with nibbles like 0000, 0001 and so on.
  • 13. Cont.,
    For this reason, logic circuit are often designed to handle four input variables and their complements.
    This is done by using 4 variable karnaugh map.
  • 14. Four variable karnaugh map Truth Table
  • 15. Cont.,
  • 16. Karnaugh map
    10
    11
    03
    02
    04
    05
    07
    16
    012
    013
    015
    114
    18
    19
    011
    110
    A
    B
    A
    B
    A
    B
    A
    B
    C
    D
    C
    D
    C
    D
    C
    D
  • 17. Explanation
    The vertical column is , , and .
    The horizontal row is , , and .
    A
    B
    A
    B
    A
    B
    A
    B
    C
    D
    C
    D
    C
    D
    C
    D
  • 18. Cont.,
    The output 1 is appeared at the input combinations of
    , , , ,
    , and
    Enter ‘1’ on these spaces of the karnaugh map, and the remaining spaces are filled with 0’s.
    C
    D
    A
    B
    C
    D
    A
    B
    C
    D
    A
    B
    C
    D
    A
    B
    C
    D
    A
    B
    C
    D
    A
    B
    C
    D
    A
    B
  • 19. The End
    …… Thank You ……