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Mainpulate Boolean Expressions

You can transform one boolean expression into an equivalent expression by applying the postulates and theorems of boolean algebra. Minimizing the expression allows the designer to use fewer electrical components and, therefore, can reduce the cost of the system.

Excellent Video (goes through the laws and how to manipulate expressions)

Additional reading and useful links

Boolean Expression Calculator (Electronics)

Boolean Algebra Calculator (Wolfram)

Boolean Expression Simplification

The following shows an example of using algebraic techniques to simplify a boolean expression

~(A * B) * (~A + B) * (~B + B)  
~(A * B) * (~A + B) * 1 6 - Complement law
~(A * B) * (~A + B) 5 - Identity law
(~A + ~B) * (~A + B) 8 - DeMorgan's law
~A + ~B * B 4 - Distributive law
~A + 0 6 - Complement law
~A 5 - Identity law