## PRACTICE PROBLEMS

(Note: Problem solutions are available at http://sites.google.com/site/automatedmanufacturingsystems/)

1. Setup the Karnaugh map for the truth table below. 2. Use a Karnaugh map to simplify the following truth table, and implement it in ladder logic. 3. Write the simplest Boolean equation for the Karnaugh map below, 4. Given the truth table below find the most efficient ladder logic to implement it. Use a structured technique such as Boolean algebra or Karnaugh maps. 5. Examine the truth table below and design the simplest ladder logic using a Karnaugh map. 6. Find the simplest Boolean equation for the Karnaugh map below without using Boolean algebra to simplify it. Draw the ladder logic. 7. Given the following truth table for inputs A, B, C and D and output X. Convert it to simplified ladder logic using a Karnaugh map. 8. Consider the following truth table. Convert it to a Karnaugh map and develop a simplified Boolean equation (without Boolean algebra). Draw the corresponding ladder logic. 9. Given the truth table below a) find a Boolean algebra expression using a Karnaugh map.

b) draw a ladder diagram using the truth table (not the Boolean expression).

10. Convert the following ladder logic to a Karnaugh map. 11. a) Construct a truth table for the following problem.

i) there are three buttons A, B, C.

ii) the output is on if any two buttons are pushed.

iii) if C is pressed the output will always turn on.

b) Develop a Boolean expression.

c) Develop a Boolean expression using a Karnaugh map.

12. Develop the simplest Boolean expression for the Karnaugh map below,

a) graphically.

b) by Boolean Algebra 13. Consider the following boolean equation. a) Can this Boolean equation be converted directly ladder logic. Explain your answer, and if necessary, make any changes required so that it may be converted to ladder logic.

b) Write out ladder logic, based on the result in step a).

c) Simplify the equation using Boolean algebra and write out new ladder logic.

d) Write a Karnaugh map for the Boolean equation, and show how it can be used to obtain a simplified Boolean equation.