H2: Logic Circuits

Time Estimate1-2 hours   Grade Impact1%   DueSep 14 @ 12pm  

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Helpful Tip
The free CircuiTikZ Designer provides an intuitive GUI that can help you typeset beautiful circuit diagrams in CircuiTikZ, a professional way to typeset circuits in $\LaTeX$ documents. It’s what I used to generate the figures on this page. Circuit simulators are also helpful, there is a list on the Resources page.

Also, WaveDrom is an easy place to generate timing diagrams. It’s what I used to generate diagrams for this assignment.

Show your work

You must show all steps of your work for full credit. While calculators can perform these conversions, demonstrating your process ensures understanding and mastery of the concepts.

Exercises

1. Draw a circuit that evaluates the formula $\lnot(A \lor B) \land (C \land \lnot D) = E$.

2. Write a formula that corresponds to the following circuit:

   

3. Write a formula that corresponds to the following timing diagram:

   

4. Draw a circuit that corresponds to the following timing diagram:

   

5. Complete a truth table for $F = (\lnot A \land B \lor C) \land (D \lor \lnot E) \lor (A \land \lnot D)$.

6. Complete a truth table for $G = (A \lor \lnot B) \land (C \lor D) \land (\lnot A \lor \lnot C)$.

7. Complete a timing diagram for $E = (\lnot A \lor B \land C) \lor (D \land \lnot B) \land (\lnot B \lor A)$.

8. Draw a circuit that evaluates $E = (A \land B) \lor (\lnot C \land D) \lor (B \land \lnot D)$.

9. Design your own circuit! Write a logical formula that your circuit will evaluate. It must contain at least 4 inputs and 1 output. Draw and label a circuit diagram that corresponds to your formula. Construct a truth table for your formula, showing all possible input combinations and the corresponding output. Create a timing diagram that illustrates the behavior of your circuit for interesting input combinations.

10. Try to draw a circuit that evaluates $A = (\lnot A \land B)$. Do you think it is possible to construct this circuit using only AND, OR, and NOT gates? Why or why not? If it is not possible, what would make it possible?