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Karnaugh Mapping
17 questions By Tony R. Kuphaldt
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Question 13 of 17
Use a Karnaugh map to generate a simple Boolean expression for this truth table, and draw a relay logic circuit equivalent to that expression:
A B C Output
0 0 0 0
0 0 1 0
0 1 0 1
0 1 1 0
1 0 0 0
1 0 1 0
1 1 0 1
1 1 1 0
Reveal answerSimple expression and relay circuit:
$$B\overline{C}$$
Notes:One of the things you may want to have your students share in front of the class is their Karnaugh maps, and how they grouped common output states to arrive at Boolean expression terms. I have found that an overhead (acetate) or computer-projected image of a blank Karnaugh map on a whiteboard serves well to present Karnaugh maps on. This way, cell entries may be easily erased and re-drawn without having to re-draw the map (grid lines) itself.
Ask your students to compare using a Karnaugh map versus using standard SOP/Boolean simplifications to arrive at the simplest expression for this truth table. Which technique would they prefer to use, and why?
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Question 14 of 17
Use a Karnaugh map to generate a simple Boolean expression for this truth table, and draw a gate circuit equivalent to that expression:
A B C D Output
0 0 0 0 0
0 0 0 1 0
0 0 1 0 0
0 0 1 1 0
0 1 0 0 0
0 1 0 1 0
0 1 1 0 1
0 1 1 1 0
1 0 0 0 0
1 0 0 1 0
1 0 1 0 1
1 0 1 1 1
1 1 0 0 0
1 1 0 1 0
1 1 1 0 1
1 1 1 1 1
Reveal answerSimple expression and gate circuit:
$$AC+BC\overline{D}$$
Challenge question: use Boolean algebra techniques to simplify the table’s raw SOP expression into minimal form without the use of a Karnaugh map.
Notes:One of the things you may want to have your students share in front of the class is their Karnaugh maps, and how they grouped common output states to arrive at Boolean expression terms. I have found that an overhead (acetate) or computer-projected image of a blank Karnaugh map on a whiteboard serves well to present Karnaugh maps on. This way, cell entries may be easily erased and re-drawn without having to re-draw the map (grid lines) itself.
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Question 15 of 17
Use a Karnaugh map to generate a simple Boolean expression for this truth table, and draw a gate circuit equivalent to that expression:
A B C D Output
0 0 0 0 0
0 0 0 1 0
0 0 1 0 0
0 0 1 1 0
0 1 0 0 0
0 1 0 1 0
0 1 1 0 0
0 1 1 1 0
1 0 0 0 1
1 0 0 1 0
1 0 1 0 1
1 0 1 1 1
1 1 0 0 0
1 1 0 1 0
1 1 1 0 1
1 1 1 1 1
Reveal answerSimple expression and gate circuit:
$$AC+A\overline{B}\ \overline{D}$$
Challenge question: use Boolean algebra techniques to simplify the table’s raw SOP expression into minimal form without the use of a Karnaugh map.
Notes:One of the things you may want to have your students share in front of the class is their Karnaugh maps, and how they grouped common output states to arrive at Boolean expression terms. I have found that an overhead (acetate) or computer-projected image of a blank Karnaugh map on a whiteboard serves well to present Karnaugh maps on. This way, cell entries may be easily erased and re-drawn without having to re-draw the map (grid lines) itself.
This is one of those situations where an important group “wraps around” the edge of the Karnaugh map, and thus is likely to be overlooked by students.
I am studying for my midterms, and this helped me a lot. The author is trying to share the information through pure comprehension, explaining the origin and target of each and every rule, which most teachers tend not to do… Thank you so much !!
question 16 circuit is not fully simplified