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Karnaugh Mapping
17 questions By Tony R. Kuphaldt
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Question 16 of 17
Use a Karnaugh map to generate a simple Boolean expression for this truth table, and draw a relay circuit equivalent to that expression:
A B C D Output
0 0 0 0 1
0 0 0 1 0
0 0 1 0 0
0 0 1 1 0
0 1 0 0 1
0 1 0 1 0
0 1 1 0 1
0 1 1 1 0
1 0 0 0 1
1 0 0 1 0
1 0 1 0 0
1 0 1 1 0
1 1 0 0 1
1 1 0 1 0
1 1 1 0 1
1 1 1 1 0
Reveal answerSimple expression and relay circuit:
$$B \overline{D}+\overline{C}\ \overline{D}$$
Follow-up question: although the relay circuit shown above does satisfy the minimal SOP Boolean expression, there is a way to make it simpler yet. Hint: done properly, you may eliminate one of the contacts in the circuit!
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.
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Question 17 of 17
Use a Karnaugh map to generate a simple Boolean expression for this truth table, and draw a relay circuit equivalent to that expression:
A B C D Output
0 0 0 0 1
0 0 0 1 0
0 0 1 0 1
0 0 1 1 0
0 1 0 0 1
0 1 0 1 1
0 1 1 0 1
0 1 1 1 1
1 0 0 0 1
1 0 0 1 0
1 0 1 0 1
1 0 1 1 0
1 1 0 0 1
1 1 0 1 1
1 1 1 0 1
1 1 1 1 1
Reveal answerSimple expression and relay circuit:
$$B +\overline{D}$$
Notes:Given the preponderance of 1’s in this truth table, it is rational to try developing a POS expression rather than an SOP expression. However, your students may find that the elegance of Karnaugh mapping makes it easy enough to do it both ways! This is one question where you definitely want to have your students explain their methods of solution in front of the class, and you definitely want them to see how Karnaugh maps could be used both ways (SOP and POS).
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.
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