Activity 2.2.1 Karnaugh mapping
Introduction
At this point you have the capability to apply the theorems and laws of Boolean algebra to simplify logic expressions to produce simpler and more cost effective digital logic circuits. You may have also realized that simplifying a logic expression using Boolean algebra, though not terribly complicated, is not always the most straightforward process. There isn’t always a clear starting point for applying the various theorems and laws, nor is there a definitive end in the process.
Wouldn’t it be nice to have a process for simplifying logic expressions that was more straightforward, had a clearly defined beginning, middle, and end, and didn’t required you to memorize all of the Boolean theorems and laws? Well there is, and it is called Karnaugh mapping. Karnaugh mapping, or K-Mapping, is a graphical technique for simplifying logic expressions containing up to four variables.
In this activity you will learn how to utilize the Karnaugh mapping technique to simplify two, three, and four variable logic expressions. Additionally, logic expressions containing don’t care conditions will be simplified using the K-Mapping process.
Conclusion
much cleaner than boolean
simpler than boolean
2.The three variable K-maps shown below can be completed with three groups of two. The two groups shown (cells #1 & #3; cells #4 & #6) are required. The third group, needed to cover the one in cell #2, could be cells #2 & #3 or cells #2 & #6.
Write the two possible logic expressions for the function F1.
-AC+-ABC+A-C
-AB+-A-BC+A-C
These logic expressions are considered to be equivalent (not equal). Explain what this means.
Some logic expressions can have the same output and inputs but they can use less or more chips or wire.
At this point you have the capability to apply the theorems and laws of Boolean algebra to simplify logic expressions to produce simpler and more cost effective digital logic circuits. You may have also realized that simplifying a logic expression using Boolean algebra, though not terribly complicated, is not always the most straightforward process. There isn’t always a clear starting point for applying the various theorems and laws, nor is there a definitive end in the process.
Wouldn’t it be nice to have a process for simplifying logic expressions that was more straightforward, had a clearly defined beginning, middle, and end, and didn’t required you to memorize all of the Boolean theorems and laws? Well there is, and it is called Karnaugh mapping. Karnaugh mapping, or K-Mapping, is a graphical technique for simplifying logic expressions containing up to four variables.
In this activity you will learn how to utilize the Karnaugh mapping technique to simplify two, three, and four variable logic expressions. Additionally, logic expressions containing don’t care conditions will be simplified using the K-Mapping process.
Conclusion
- Give three advantages of using K-mapping to simplify logic expressions over Boolean algebra.
much cleaner than boolean
simpler than boolean
2.The three variable K-maps shown below can be completed with three groups of two. The two groups shown (cells #1 & #3; cells #4 & #6) are required. The third group, needed to cover the one in cell #2, could be cells #2 & #3 or cells #2 & #6.
Write the two possible logic expressions for the function F1.
-AC+-ABC+A-C
-AB+-A-BC+A-C
These logic expressions are considered to be equivalent (not equal). Explain what this means.
Some logic expressions can have the same output and inputs but they can use less or more chips or wire.