Boolean Algebra

Any equation must be within the <math> </math> tags. For Boolean alegbra the main issue is how to negate a term like:

[math] \overline{a}[/math] or [math] \overline{\overline{a}+b}[/math]

this can be done by adding the following around any term you wish to negate.:

<math> \overline{} </math>  

[math] \overline{a}[/math]

is

 <math> \overline{a} </math>

[math] \overline{\overline{a}+b}[/math]

is

 <math> \overline{\overline{a}+b} </math>.

Identities

AND Identities

The logic gate AND is represented by the "." symbol. Some examples of an equation containing this operation is:

[math] A.B [/math]

This expression means "A AND B = 1".

[math] \overline{A.B} [/math]

The line above the equation means "NOT", therefore this expression means " NOT A AND B = 1".

OR Identities

The logic gate 'OR' in Boolean algebra is represented by a '+' symbol. For example, if I was to represent "A or B" in Boolean algebra, it would look like this: [math] a+b [/math]

Laws

Commutative Law

The Commutative Law is where equations are the same no matter what way around the letters are written. For example

<math> A + B = B + A </math>

Equations

Solving equations is a matter of applying the laws of boolean algrebra, followed by any of the identities you can find: