Boolean algebra

From Wikipedia, the free encyclopedia
(Redirected from Boolean logic)
Jump to: navigation, search

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 after its creator George Boole.[1]

NOT gate[change | change source]

0 1
1 0


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

It means the output is not the input.

AND gate[change | change source]

AND 0 1
0 0 0
1 0 1


The AND operator is written as like this:

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

OR gate[change | change source]

OR 0 1
0 0 1
1 1 1


The OR operator is written as like this:

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

XOR gate[change | change source]

XOR 0 1
0 0 1
1 1 0


XOR basically means "exclusive or", meaning one input or the other must be true, but not both.

The XOR operator is written as like this:

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

Identities[change | change source]

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 laws[change | change source]

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 pages[change | change source]

References[change | change source]

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

Other websites[change | change source]