rel="nofollow" href="#fb3_img_img_51d312cf-30bc-5b9d-88a3-a54cdef6be7d.jpg" alt="image"/> = 1, Figure 4.26: State table of four inputs
For Row 3: Given A = 0, B = 0, C = 1, and D = 0, so
For Row 4: Given A = 0, B = 0, C = 1, and D = 1, so
Continue the evaluation of each row to complete the state table as shown in Figure 4.26.
Review Questions
1.Describe the binary principle.
2. Explain how “1” and “0” are used to represent two binary states.
3. What are the two configurations to which a switch or a relay contact can be wired?
4. Describe positive logic elements.
5. Describe negative logic elements.
6. What are the three basic logic functions?
7. Explain the operation principle of the AND function.
8. What is a true table?
9. How many possible input combinations are there for the logic gate having 2, 3, and 4 inputs, respectively?
10. Describe the operation principle of the OR function.
11. Describe the operation principle of the NOT function.
12. What is Boolean algebra?
13. What symbol is used to represent the AND function between two inputs?
14. What symbol is used to represent the OR function between two inputs?
15. What symbol is used to represent the NOT function of an input?
16. Convert the circuit given in the logic gates (Figure 4.27) to its Boolean equations.
Figure 4.27: Review Question 16
17. Convert the logic gate circuit (Figure 4.28) to its Boolean equations.
Figure 4.28: Review Question 17
18. Convert the following Boolean equations into a ladder diagram.
19. Convert the following Boolean equations into a ladder diagram.
20. What is a state table?
21. Summarize the procedure for constructing a state table for a logic circuit.
22. Construct a state table for the following Boolean equations.
Simplifying Logic Circuits
Most logic circuits should be developed in their simplest forms in order to (1) reduce the amount of wiring and the number of components if hard-wired relay ladder circuits are used and (2) shorten the scanning cycle time in PLC applications. Additional benefits include a reduced number of hard-wired connections, reduced cost of the product, and, finally, a reduction in errors because the circuit is simpler.
Two common methods used to simplify logic equations using logic equations are Boolean laws and Karnaugh maps. This chapter explains these two logic circuit simplification methods in detail. The chapter starts with Boolean algebra postulates and laws, followed by tips for using Boolean algebra laws successfully. The second half of the chapter is devoted to the construction of Karnaugh maps, and applying the simplification principle of Karnaugh maps.
5.1 Boolean Algebra Postulates
