Simplification of Boolean Functions
In order to simplify Boolean functions, it's important to have a foundational understanding of the identity laws and complimentary laws. Learn about idempotent laws, commutative laws and associative laws in math with help from a math teacher in this free video on math help and algebra.
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So what is involved in the simplification of Boolean Functions? Hi, I'm Jimmy Chang. I've been teaching college mathematics for over nine years. Now to be able to simplify Boolean Functions, it's really important to have a foundation of what the laws are. So before you even simplify any Boolean functions. You know, we definitely need to go over them. Just to be sure that you know what they are. Now at this particular point, you already know the, the multiplication, the addition and the compliment symbols. And understanding that they are And, Or and Not. The negation symbols, respectively. So in the next couple of minutes, we're just going to go over those laws. And just be sure that you know them. And then you'll be able to simplify. Use these laws to simplify Boolean Functions. Now first, we have the Identity Laws. Now the Identity Laws are pretty straightforward. In that you have X plus 0 equals to X. X times one is equal to X. And then you get to the complimentary laws. Those involve in the Compliment symbol. Now remember, X plus X prime is equal to one. X times X prime is equal to zero. And then we have X prime of prime. So the prime of X prime, that gets you back to X. Now we have the so called Dominance laws which talk about X plus one is equal to one. And X times zero is equal to zero. We then move to the Idempotent Laws. Where we have X plus X is equal to X. And X times X is equal to X. Then we have the Commutative Laws. Which are pretty self explanatory. And that they're just like regular algebra. The X plus y is equal to Y plus X. And X times Y is equal to Y times X. The Associative laws are very straightforward as well. they kind of have the same connotation as the regular Algebra laws. X plus parenthesis Y plus Z, is equal to the parenthesis X plus Y. And then plus Z. And then the same thing with multiplication. There as you can tell. And then you get to the De Morgan?s laws. Where you have the prime of XY becomes the addition. X prime plus Y prime and the prime of X plus Y gives you X prime times Y prime. But you won't be using these laws over and over again. when it comes to simplification Boolean functions. So it's imperative that you know these inside and out. So, I'm Jimmy Chang and these are some rules on Simplifying of Boolean Functions.