Mathematics
Boolean Algebra Representation Methods

Boolean Algebra



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Boolean Algebra Representation Methods
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Boolean algebra is a type of algebra that deals with the logic and connections of statements. Boolean algebra is typically used in computational mathematics used in computer science and electrical engineering courses. This type of algebra can be represented in many ways but first lets describe how the values are actually found.

Every value in Boolean algebra is either a 1 or 0; where 1 = yes/true and 0 = no/false. To find these values one will evaluate whether a given statement is true or false and then enter a 1 or 0 corresponding in a relating truth table. Then you can combine these numbers together to state when certain operations and computational tasks will be initiated. For example if we say if Statement 1 AND Statement 2 are both true then do this; or if Statement 1 OR Statement 2 is false don’t do this. These statements always have one key component in common and that is they all say IF this happens THEN do this; and the name we use to describe these statements are “Logic Gates”. This is simply because computers do not think they simply are told when something happens it should react in a certain way. Many people know that computers operate in binary or large matrixes of 1s and 0s but not many people know how exactly it works; which is why I will cover some basic logic gate functions.

^ = * = Conjunction = AND
= + = Disjunction = OR

ab = ba
This statement means if either a OR b is true then…

a^b = b^a
This statement means if a AND b are true then…

a(bc) = (ab) c
This statement means if a OR b OR c is true then…

a^ (b^c) = (a^b) ^c
This statement means if a AND b AND c is true then…

a(a^b) = a
This means if a is true OR if a AND b are true then; which could loosely translate to as long as a is true then…

From these examples one can get a general feel about the basics of how to read the statements and actually think out the logic in their mind. When you look at these examples as a whole their output is either they do something or do not do something; and how they operate this is they send an output of a 1 or a 0 which then is plugged into a bunch of different operations. All of these operations connect into a very complex web that maintains a properly functioning computer; but when you break down each operation piece by piece it is very simple. Everything involving a computer can be broken down into countless individual operations and we use these equations and Logic Gates to describe each of these individual operations and how they connect with each other.

Now since you have a basic foundation of understanding of how a computer can check if these thinks are true or false you can focus more on the actual logic itself. Logic plays a large role into computer programming due to the basis of technology is based off of binary and without logic gates like these computers would not exist.

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