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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.
Boolean Expression Calculator (Electronics)
Boolean Algebra Calculator (Wolfram)
https://www.allaboutcircuits.com/textbook/digital/chpt-7/boolean-rules-for-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 |
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