Boolean algebra

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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.

[change] See Also

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