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Back to Class Notes (M326)

Truth Table Design

1. Create a truth table star design for at least three propositions.  Make sure that your design has at least two regions with edges in common (so that the "canonical" logic functions can be simplified).  If your truth function has four or more simple statements the you can use the Gray Code-Venn diagram or color the vertices of a hypercube.

2. Write out the truth table for this design.

3. Determine the "canonical" logic function (sum of products) for the truth table.

4. Draw a Karnaugh Map corresponding to the canonical logic function.

5. Use the Karnaugh map to simplify the canonical logic function.

6. Simplify the canonical logic function algebraically. (Use the Karnaugh map to help you to see the necessary algebraic operations.)

7. Assign the value 1 and 0 to the true and false statements, respectively, in your truth table.  Show that the Boolean algebra, B(+,.,',0,1) with two elements {0,1} satisfies the logic function.

8. Create a logic network using AND, OR, and NOT gates corresponding to the simplified logic function.

9. Exta Credit: Try to find a physical situation governed by your logic network.