Boolean Algebra
Description
Have you ever had an idea that you thought was so unique that when you told someone else about it, you simply could not believe they thought you were wasting your time? If so, you know how the mathematician George Boole felt in the 1800s when he designed a math system that, at the time, had no practical application. Today, however, his math system is the most important mathematical tool used in the design of digital logic circuits. Boole introduced the world to Boolean algebra when he published his work called “An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities.” In the same way that normal algebra has rules that allow you to simplify algebraic expressions, Boolean algebra has theorems and laws that allow you to simplify expressions used to create logic circuits. By simplifying the logic expression, we can convert a logic circuit into a simpler version that performs the same function. The advantage of a simpler circuit is that it will contain fewer gates, will be easier to build, and will cost less to manufacture. In this activity you will learn how to apply the theorems and laws of Boolean algebra to simplify logic expressions and digital logic circuits. The moral of the story is to keep dreaming. Someday your grandchildren may be using something that you’re thinking about right now. When your grandparents were kids, do you think that they imagined someday that we would all have 10,000 songs in our pockets or a telephone in our backpacks?
Conclusion Questions
1. In order to simplify a Logic Expression, you must take the given equation and put them through the different theorems to simplify them.
2. You know you are finished when no more theorems fit the given expression.
3. You could prove two expressions are equal by using one of the three laws; associative, commutative, or distributive.
4. ROI = (75,000 / 450,000) x 100%
ROI = 16.666 %
No, this was not a good investment.
2. You know you are finished when no more theorems fit the given expression.
3. You could prove two expressions are equal by using one of the three laws; associative, commutative, or distributive.
4. ROI = (75,000 / 450,000) x 100%
ROI = 16.666 %
No, this was not a good investment.