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Boolean Algebra
67 questions By Tony R. Kuphaldt
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Question 40 of 67
Use Boolean algebra to simplify the following relay (ladder logic) circuit:
Reveal answer
Notes:Have your students explain the entire process they used in simplifying the relay circuit: developing the Boolean expression, simplifying that expression using Boolean algebra techniques, and then developing a new relay 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.
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Question 41 of 67
Use Boolean algebra to simplify the following relay (ladder logic) circuit:
Reveal answer
Notes:Have your students explain the entire process they used in simplifying the relay circuit: developing the Boolean expression, simplifying that expression using Boolean algebra techniques, and then developing a new relay 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.
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Question 42 of 67
Complete truth tables for the following gates, and also write the Boolean expression for each gate:
The results should be obvious once the truth tables are both complete. Is there a general principle at work here? Do you think we would obtain similar results with Negative-OR and NAND gates? Explain.
Reveal answer
Negative-AND gate: \(\overline{A} \ \overline{B}\)
NOR gate: \(\overline{A+B}\)
Notes:Just a preview of DeMorgan’s Theorem here!
Question 29, answer 3 has a typo - should be A*B + !(D)*E not A*B+!(D*E)