Simplifying Boolean Algebra

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In order to simplify Boolean algebra, it's important to understand the definitions, the notations and the laws. Discover how to simplify Boolean algebra, which is a deductive mathematical system closed over the value 0 and 1, with help from a math teacher in this free video on math help and algebra.

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Video Transcript

So how does one simplify boolean algebra? Hi, I'm Jimmy Chang, I've been teaching college mathematics for over 9 years and to simplify boolean algebra, it's important to understand the definitions, some of the notation and then the laws so that you are ready to simplify the various boolean algebra expressions that will come your way. So here's a review as to what it is. Now, just as a refresher, boolean algebra is a deductive mathematical system closed over the value 0 and 1. Remember boolean algebra is binary. They use the number 0 and 1, 0 generally stands for false, 1 stands for true. And the open circle typically is the generic symbol for the operation. This is a binary operator. Remember we have the symbols plus and prime, times which is multiplication, the product also stands for the word AND. so multiplication is associated with AND. So A times B, A AND B. Plus, which is the sum, stands for the word OR. So when you have A plus B you can also think of it as A OR B. And you also have the prime, which stands for compliment, so A prime is the compliment of A but also think of that as the negation of A or NOT A. So here are some laws involving boolean algebra. Now we have first the idempotent laws, X plus X is equal to X, X times X is equal to X. The commutative laws are pretty straightforward as regular algebra. X plus Y equal Y plus X and XY equals YX. The associative laws are the same idea. X plus (Y plus Z) equals (X plus Y plus Z) and the same goes with multiplication. We also have the identity laws, X plus 0 is equal to X, X times 1is equal to X, again pretty straightforward as in regular algebra. The complimentary laws, X plus X prime is equal to 1, X times X prime is equal to 0 and the prime of X prime is X. The primes cancel each other out. The dominance laws, X plus 1 is equal to 1, X times 0 is equal to 0, OK? And last but not least we have De Morgan's laws where if you have the prime of XY it becomes addition, X prime plus Y prime and if you have the prime of X plus Y, you end up having multiplication X prime times Y prime. So to simplify boolean algebra, knowing these rules are very important. So I'm Jimmy Chang and there are some foundations for simplifying boolean algebra.


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