Activity 2.1.7
Introduction
Despite all of the work done by George Boole, there was still more work to be done. Expanding on Boole’s studies, Augustus DeMorgan (1806-1871) developed two additional theorems that now bear his name. Without DeMorgan’s Theorems, the complete simplification of logic expression would not be possible.
As we will seen in later activities, DeMorgan’s Theorems are the foundation for the NAND and NOR logic gates.
In this activity you will learn how to simplify logic expressions and digital logic circuits using DeMorgan’s two theorems along with the other laws of Boolean algebra.
Conclusion
1. Draw the gate equivalent for DeMorgan’s two theorems.
1. Draw the gate equivalent for DeMorgan’s two theorems.
2. How would you prove that the original Do-Nothing circuit and the simplified version are equivalent?
Simplify the original.
Your company was SO pleased with the money you saved them on the coffee vending machine project (last activity) that they’ve promoted you to VP of engineering and given you a raise to $100 per hour. Congratulations.
Your first decision as VP is to start manufacturing the simplified version of the Do-Nothing circuit. (Did we mention that the circuit doesn’t do anything?)
3. If each GATE cost 20¢ and you made 100,000 units, how much of the company’s money did you waste on your first project?
$120,000
Did you get fired?
YES
Simplify the original.
Your company was SO pleased with the money you saved them on the coffee vending machine project (last activity) that they’ve promoted you to VP of engineering and given you a raise to $100 per hour. Congratulations.
Your first decision as VP is to start manufacturing the simplified version of the Do-Nothing circuit. (Did we mention that the circuit doesn’t do anything?)
3. If each GATE cost 20¢ and you made 100,000 units, how much of the company’s money did you waste on your first project?
$120,000
Did you get fired?
YES