k-map, k-map topic in digital electronicss.pdf

k-map

1. Karnaugh Maps(K- Map)
•A Karnaugh map is a graphical representation of the logic system.

•It can be drawn directly from either minterm (sum-of-products) or
maxterm (product-of-sums) Boolean expressions

•It is desired to have a minimized sum-of-products or a minimized
product-of-sums expression.
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Types of K- Map
Two-variable Karnaugh map.

2. •Construction of a Karnaugh Map(K- Map)
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An n-variable Karnaugh map has 2n squares
In the case of a minterm Karnaugh map,
‘1’ is placed in all those squares for which the output is ‘1’,
‘0’ is placed in all those squares for which the output is ‘0’. 0s are omitted for
simplicity.
An ‘X’ is placed in squares corresponding to ‘don’t care’
conditions.
In the case of a maxterm Karnaugh map,
‘1’ is placed in all those squares for which the output is ‘0’,
‘0’ is placed for input entries corresponding to a ‘1’ output. Again, 0s
are omitted for simplicity,
an ‘X’ is placed in squares corresponding to ‘don’t care’ conditions.

3. •Two-variable Karnaugh map.



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Three-variable Karnaugh map.

4. •Four-variable K- map.

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five-variable K- map.

5. •six-variable K- map.

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•For minterms (sum of product )table .

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•For maxterms (product of sum )table .

8. Three-variable K map.
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For minterms (sum of product )table.

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–If we consider the minterm of K map. Then
Grouping of adjacent one pair.

Output of the K map is Y = B

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Output of the K map is Y =
Output of the K map is Y =
Three variable K map
Output of the K map is Y =
Output of the K map is Y =

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Output of the K map is Y =
Output of the K map is Y = C
Output of the K map is Y = B Output of the K map is Y =

12. Four-variable K- map.
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A B C D F
0 0 0 0 0
1 0 0 0 1
2 0 0 1 0
3 0 0 1 1
4 0 1 0 0
5 0 1 0 1
6 0 1 1 0
7 0 1 1 1
8 1 0 0 0
9 1 0 0 1
10 1 0 1 0
11 1 0 1 1
12 1 1 0 0
13 1 1 0 1
14 1 1 1 0
15 1 1 1 1
Example:
Minimize the flowwing function using K – map. Right
truth table and Drow the logic ckt diagram,

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Example:
Minimize the flowing function using K – map. Right truth
table and Drown the logic ckt diagram,

16. Five-variable K- map.
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Example:
Minimize the flowing function using K – map. Right truth table
and Drown the logic ckt diagram,

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Example:
Minimize the flowing function using K – map. Right truth table
and Drown the logic ckt diagram,