Boolean Algebra

Variable

A symbol used to represent a action, condition, or data.

In Boolean, a variable can only be

1 or 0

A complement is the inverse of a variable and is represented with

a ‘ or bar over the variable

A literal is…

A variable or its complement

Addition is equal to the —— operation

OR

In Boolean Addition the sum is 1 if…

one or more of the literals are 1

In Boolean Addition the sum is 0

if each literal is 1

Boolean multiplication is equivalent to the —- operation

AND

In Boolean multiplication the product of terms…

form a product term.

The product term will be 1 only

if all the literals are 1

The commutative law states

that the order of operations does not affect the result.

The associate law means

That you can rearrange parentheses without changing the result.

In Boolean Algebra there are 3 laws that apply for addition and multiplication the ———, ———, and ———

communative, associate, distributive

The distributive law

Allows multiplication of a single term across a sum.

DeMorgans 1st Theorem

The compliment of a product of variables is equal to the sum of the complimented variables.

DeMorgans 2nd Theorem

The compliment of a sum of variables is equal to the product of the complimened variables

Boolean expressions are written in _______ or ________ form

Sum of Product, Products of Sum

In SOP and POS the overbar…..

cannot extend over more then one variable

In SOP standard form every ______________ must appear in each ____

variable in the domain, term

If a nonstandard term is missing a variable, you can expand it to standard form by…

multiplying the term by the sum of the missing variable and it’s compliment.

In POS standard form…

Every variable in the domain must appear in each sum term of the expression

To expand a nonstandard POS expression

You add the product of the missing variable and it’s compliment. While also applying rule 12