2.7: Exercises
- Page ID
- 27623
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- DeMorgan’s Law:
- Show that DeMorgan’s Law is correct for two variables, (A’B’)’ = A+B by using a truth table.
- Does DeMorgan’s Law hold for 3 variables? What about 4 variables?
- Simplify the following Boolean expressions using Boolean algebra
- A + AB
- A + A’B
- AB’C’ + ABC’
- AC + AC’ + A’B + A’B’
- The operations AND, OR, and NOT are universal in that any Boolean function can be implemented using just these three gates.
- Prove by construction that the NAND gate is universal by creating AND, OR, and NOT gates using only the NAND gate.
- Prove by construction that the NOR gate is also universal.
- Why are the AND and OR gate not universal? (e.g. what simple operation cannot be created with just an AND or OR gate?)
- For inputs A and B, show how to use an XOR gate to create a NOT gate if B is 1, and a buffer if B is 0.
- XOR is sometimes called an “odd” function because the result of an XOR is 1 if the number of 1’s the minterm is odd, the xor is 1, otherwise it is 0. Show that this is true for 3 and 4 variable XOR functions, e.g. A ⊕ B ⊕ C, and A ⊕ B ⊕ C ⊕ D.
- For the following truth table:
- Give the DNF equation for the table.
- Minimize the equation using a K-map.
- Show that the DNF is equivalent to the minimum representation using Boolean algebra.
A
B
C
F(A,B,C)
0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 0
- For the following truth table
- Give the DNF equation for the table.
- Minimize the equation using a K-map.
- Show that the DNF is equivalent to the minimum representation using Boolean algebra.
A
B
C
F(A,B,C)
0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1
- For the following truth table
- Give the DNF equation for the table.
- Minimize the equation using a K-map.
- Show that the DNF is equivalent to the minimum representation using Boolean algebra.
A
B
C
F(A,B,C)
0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1
- Solve the 7-segment display problem for segments b, d, and f.