Lesson 0011: Simplifying Boolean Expressions
Boolean algebra follows some of the same patterns as regular algebra.
The AND and OR operations can be changed according to the commutative
property, the associative property, and the distribuitive property.
- Commutative Property
- Associative Property
- Distribuitive Property
De Morgans Laws
There is a very important rule that applies to the NOR and NAND functions.
It is called De Morgans Law. It states that:
Some other laws state that:
- (because it means A OR 0, which the 0 cancels out, leaving A)
- (because 0 AND-ed with anything is false.)
- (because 1 OR anything is true.)
- (because 1 AND any constant is the same as the constant. The 1 cancels out.)
- (because either A or ~A is true, and a true OR a false is true, or 1.)
- (because either A or ~A is false and a false AND a true is false, or 0.)
- (because A OR itself is the same as A.)
- (because if A is true, the result will be true and if A is false the result will be false.)
- (because A negated is ~A, and this result negated will be the same as the original.)
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