Why
Do You Need To Know About Karnaugh Maps?
Karnaugh Maps are used for many small design problems. It's true
that many larger designs are done using computer implementations of different
algorithms. However designs with a small number of variables occur
frequently in interface problems and that makes learning Karnaugh Maps
worthwhile. In addition, if you study Karnaugh Maps you will gain
a great deal of insight into digital logic circuits.
In this section we'll examine some Karnaugh Maps for three and four variables.
As we use them be particularly tuned in to how they are really being used
to simplify Boolean functions.
The goals for this lesson include the following.
Given a Boolean function described by a truth table or logic function,
Draw the Karnaugh Mapfor
the function.
Use the information from a Karnaugh Map to determine the smallest sum-of-products
function.
What
Does a Karnaugh Map Look Like?
A Karnaugh Map is a grid-like representation of a truth table. It
is really just another way of presenting a truth table, but the mode of
presentation gives more insight. A Karnaugh map has zero and one
entries at different positions. Each position in a grid corresponds
to a truth table entry. Here's an example taken from the voting circuit
presented in the lesson on Minterms. The truth table is shown first.
The Karnaugh Map for this truth table is shown after the truth table.
|
A
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B
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C
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V
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0
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0
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0
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0
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0
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0
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1
|
0
|
|
0
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1
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0
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0
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0
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1
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1
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1
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|
1
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0
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0
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0
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|
1
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0
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1
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1
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1
|
1
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0
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1
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1
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1
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1
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1
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