Boolean algebra
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Boolean algebra is algebra with variables (things which can be changed and represent other things) that have only two states. To make things easy, in this article they will be called TRUE or 1, and FALSE or 0. Boolean algebra is named after its creator, George Boole.
[edit] Rules of Boolean algebra
TRUE + TRUE = TRUE TRUE + FALSE = TRUE FALSE + TRUE = TRUE FALSE + FALSE = FALSE
This is the equivalent of an OR gate, which is why + is considered a binary OR operator
TRUE - TRUE = FALSE TRUE - FALSE = TRUE FALSE - TRUE = TRUE FALSE - FALSE = FALSE
This is the equivalent of an XOR gate, which is why - is considered a binary XOR operator.
TRUE * TRUE = TRUE TRUE * FALSE = FALSE FALSE * TRUE = FALSE FALSE * FALSE = FALSE
This is the equivalent of an AND gate, which is why * is considered a binary AND gate.
NOT (FALSE) = TRUE NOT (TRUE) = FALSE
Division is best thought of as the reverse of multiplication, for now.
[edit] De Morgan's Laws
De Morgan's Laws as applied to boolean algebra say that:
NOT(A + B) = (NOT(A) * NOT(B))
And, a bit like this:
NOT(A * B) = (NOT(A) + (NOT(B))
These are the startings of harder boolean algebra, which are not good for a simple book.