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Karnaugh Maps 1

1) A Karnaugh map (K-map) is a visual method to simplify Boolean logic expressions without complex theorems or manipulations. 2) A K-map represents a truth table with the variables arranged in a grid and makes it easier to group adjacent ones to find simplified expressions. 3) Rules for grouping in a K-map include: only grouping powers of 2, groups should be as large as possible, overlapping and wrapping are allowed, and the fewest number of groups should be used.

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Antoinette V.
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70 views18 pages

Karnaugh Maps 1

1) A Karnaugh map (K-map) is a visual method to simplify Boolean logic expressions without complex theorems or manipulations. 2) A K-map represents a truth table with the variables arranged in a grid and makes it easier to group adjacent ones to find simplified expressions. 3) Rules for grouping in a K-map include: only grouping powers of 2, groups should be as large as possible, overlapping and wrapping are allowed, and the fewest number of groups should be used.

Uploaded by

Antoinette V.
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as ODP, PDF, TXT or read online on Scribd
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KARNAUGH MAPPING

What is a K-map?
● A Karnaugh map (K-map) is a visual method used to
simplify the algebraic expressions in Boolean functions
without having to resort to complex theorems or equation
manipulations. A K-map can be thought of as a special
version of a truth table that makes it easier to map out
parameter values and arrive at a simplified Boolean
expression.
K-Maps Rules
● The Karnaugh map uses the following rules for
the simplification of expressions by grouping
together adjacent cells containing ones
● Groups may wrap around the table. The
leftmost cell in a row may be grouped with the
rightmost cell and the top cell in a column may
be grouped with the bottom cell.
● There should be as few groups as possible, as
long as this does not contradict any of the
previous rules.
SUMMARY!
1) No zeros allowed.
2) No diagonals.
3) Only power of 2 number of cells in each group.
4) Groups should be as large as possible.
5) Every one must be in at least one group.
6) Overlapping allowed.
7) Wrap around allowed.
8) Fewest number of groups possible.
Example: Use K-map to represent the truth table
below into Boolean Logic

A B C F
0 0 0 0
0 0 1 0
0 1 0 1
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 0
Example: Use K-map to represent the truth table
below into Boolean Logic

A B C F
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 0
Example: Write a function that represents
the following 4-variable K-map below.
AB
00 01 11 10
CD

00 0 0 1 0

01 0 0 1 1

11 0 0 0 1

10 1 1 0 0
Example: Write a function that represents
the following 4-variable K-map below.
AB
00 01 11 10
CD

00 1 1 0 0

01 1 0 1 1

11 1 0 1 1

10 1 1 0 0
Example: Create a K-map for the
following expression

F=AC+AB’
Example: Create a K-map for the
following expression

F=C+AD’+A’BC’D

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