Digital Circuits
Boolean Algebra
67 questions By Tony R. Kuphaldt
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Question 46 of 67
Use DeMorgan’s Theorem, as well as any other applicable rules of Boolean algebra, to simplify the following expression so there are no more complementation bars extending over multiple variables:
$$\overline{\overline{XY\overline{Z}}Y}$$
Reveal answerSimplified expression:
$$\overline{Y} + X\overline{Z}$$
Notes:Have your students demonstrate exactly what they did (step by step) to simplify this expression, sharing their problem-solving strategies with the whole class.
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Question 47 of 67
Use DeMorgan’s Theorem, as well as any other applicable rules of Boolean algebra, to simplify the following expression so there are no more complementation bars extending over multiple variables:
$$\overline{\overline{J+K}JL}$$
Reveal answerSimplified expression:
(Expression is always equal to 1) Notes:Have your students demonstrate exactly what they did (step by step) to simplify this expression, sharing their problem-solving strategies with the whole class.
Ask your students to determine what a non-variable solution means for a circuit such as this in a practical sense. What would they suspect if they tried to simplify a digital circuit and obtained this kind of result?
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Question 48 of 67
Use Boolean algebra to simplify the following logic gate circuit:

Reveal answer
Notes:Have your students explain the entire process they used in simplifying the gate circuit: developing the Boolean expression, simplifying that expression using Boolean algebra techniques, and then developing a new gate circuit from the simplified Boolean expression. By having your students share their thought processes with the whole class, you will increase the level of learning on the parts of presenter and viewer alike. Students presenting their solutions will gain a better understanding of how it works because the act of presenting helps consolidate what they already know. Students viewing the presentation will get to see another person’s technique (rather than just the instructor’s), which will allow them to see examples of how to do these processes cast in slightly different terms.


Question 29, answer 3 has a typo - should be A*B + !(D)*E not A*B+!(D*E)