Boolean algebra
From the Simple English Wikipedia, the free encyclopedia that anyone can change
Boolean algebra is algebra with variables (things which can be changed) that have only two states (or two numbers). 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.
[change] Rules of Boolean algebra
In Digital Electronics the signals of computer i.e given here true and false are denoted by 1 and 0 respectively.
TRUE + TRUE = TRUE TRUE + FALSE = TRUE FALSE + TRUE = TRUE FALSE + FALSE = FALSE
Hence the T.T. will be
1+1=1 1+0=1 0+1=1 0+0=0
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
1-1=0 1-0=1 0-1=1 0-0=0
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
1*1=1 1*0=0 0*1=0 0*0=0
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.
[change] 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.
