2. 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
3. You will learn:
• Draw the Karnaugh Map for the function.
• Use the information from a Karnaugh Map to
determine the smallest sum-of-products function.
4. What Does a Karnaugh Map Look Like?
• A Karnaugh Map is a grid-like
representation of a truth table.
• Another way of presenting a truth table
• A Karnaugh map has zero and one entries
at different positions.
• Each position in a grid corresponds to a
truth table entry.
• An example is shown on the slide
5.
6. How Can a Karnaugh Map Help?
• In the case of the Karnaugh Map the
advantage is that the Karnaugh Map is
designed to present the information in a
way that allows easy grouping of terms
that can be combined.
• Take all ones in pairs and group them
7. Let's examine the map again.
• The term on the left in the gray area of
the map corresponds to:
• The term on the right in the gray area
of the map corresponds to:
• These two terms can be combined to
give
8. NOTE:
• The beauty of the Karnaugh Map is that it has
been cleverly designed so that any two
adjacent cells in the map differ by a change in
one variable.
• It's always a change of one variable any time
you cross a horizontal or vertical cell
boundaries.
• Notice that the order of terms isn't random.
Look across the top boundary of the Karnaugh
Map. Terms go 00, 01, 11, 10. However, in a
Karnaugh Map terms are not arranged in
9. Example 1
There is a small surprise in one grouping.
The lower left and the lower right 1s
actually form a group. They differ only in
having B and its' inverse. Consequently
they can be combined. You will have to
imagine that the right end and the left
end are connected.
10. Remember these basic rules
• In a Karnaugh Map of any size, crossing a
vertical or horizontal cell boundary is a change
of only one variable - no matter how many
variables there are.
• Each single cell that contains a 1 represents a
minterm in the function, and each minterm
can be thought of as a "product" term with N
variables.
• To combine variables, use groups of
2, 4, 8, etc. A group of 2 in an N-variable
