## 2.7 Problems

1. Draw a circuit that will cause output D to go true when switch A and switch B are closed or when switch C is closed.

2. Draw a circuit that will cause output D to be on when push button A is on, or either B or C are on.

3. Design a circuit for a car that considers the variables below to control the motor M. Also add a second output that uses any outputs not used for motor control. 4. Make a simple circuit that will turn on the outputs with the binary patterns when the corresponding buttons are pushed. Inputs X, Y, and Z will never be on at the same time. 5. Convert the following Boolean equation to the simplest possible circuit. 6. Simplify the following boolean equations. 7. Simplify the following Boolean equations, 8. Simplify the Boolean expression below. 9. Given the Boolean expression a) draw a digital circuit and b) simplify the expression. 10. Simplify the following Boolean equation and write a corresponding circuit. 11. For the following Boolean equation, a) Write the logic circuit for the unsimplified equation.

b) Simplify the equation.

c) Write the circuit for the simplified equation.

12. a) Write a Boolean equation for the following truth table. (Hint: do this by writing an expression for each line with a true output, and then ORing them together.) b) Write the results in a) in a Boolean equation.

c) Simplify the Boolean equation in b)

13. Simplify the following Boolean equation, and create the simplest circuit. 14. Simplify the following boolean equation with Boolean algebra and write the corresponding circuit. 15. a) Develop the Boolean expression for the circuit below.

b) Simplify the Boolean expression.

c) Draw a simpler circuit for the equation in b). 16. Given a system that is described with the following equation, a) Simplify the equation using Boolean Algebra.

b) Implement the original and then the simplified equation with a digital circuit.

17. Simplify the following and implement the original and simplified equations with gates. 18. Simplify the following Boolean equation and implement it in a circuit. 19. Use Boolean equations to develop simplified circuit for the following truth table where A, B, C and D are inputs, and X and Y are outputs. 20. Convert the truth table below to a Boolean equation, and then simplify it. The output is X and the inputs are A, B, C and D. 21. Simplify the following Boolean equation. Convert both the unsimplified and simplified equations to a circuit. 