Open main menu

Boolean algebra

variant of ordinary elementary algebra

Boolean algebra is algebra for binary (0 means false and 1 means true). It uses normal maths symbols, but it does not work in the same way. It is named for George Boole,[1] who invented it in the middle 19th century. In the 20th century boolean algebra came to be much used for logic gates.

Contents

NOT gateEdit

NOT
0 1
1 0

[2]

The NOT operator is written with a bar over numbers or letters like this:

 
 
 

It means the output is not the input.

AND gateEdit

AND 0 1
0 0 0
1 0 1

[2]

The AND operator is written as   like this:

 
 
 
 

The output is true only if one and the other input is true.

OR gateEdit

OR 0 1
0 0 1
1 1 1

[2]

The OR operator is written as   like this:

 
 
 
 

One or the other input can be true for the output to be true.

XOR gateEdit

XOR 0 1
0 0 1
1 1 0

[2]

XOR basically means "exclusive or", meaning one input or the other must be true, but not both. It is also sometimes called NOR, which means the same thing.

The XOR operator is written as   like this:

 
 
 
 

To make it more simple, one or the other input must be true, but not both.

IdentitiesEdit

Different gates can be put together in different orders:

  is the same as an AND then a NOT. This is called a NAND gate.

It is not the same as a NOT then an AND like this:  

 
 

which is called XOR identity table

XOR 1 0 Any
1 TRUE 0 0
0 0 0  
Any 0    

, if  .[source?]


or if  =TRUE, TRUE.,

DeMorgan's lawsEdit

Augustus De Morgan found out that it is possible to change a   sign to a   sign and make or break a bar. See the 2 examples below:

 
 

"Make/break the bar and change the sign."

Related pagesEdit

ReferencesEdit

  1. "Boolean algebra | Define Boolean algebra at Dictionary.com". Dictionary.reference.com. 1997-02-27. Retrieved 2010-08-12.
  2. 2.0 2.1 2.2 2.3 "Logic Gates". Kpsec.freeuk.com. Retrieved 2010-08-12.

Other websitesEdit