Boolean algebra, a logic algebra, allows the rules used in the algebra of numbers to be applied to logic. It formalizes the rules of logic. Boolean algebra is used to simplify Boolean expressions which represent combinational logic circuits. It reduces the original expression to an equivalent expression that has fewer terms which means that less logic gates are needed to implement the combinational logic circuit.
Use the calculator to find the reduced boolean expression or to check your (intermediate) answers.
The following example shows how to use 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 |
Each line (or step) gives a new expression and the rule or rules used to derive it from the previous one. There can be several ways to arrive at the final result. You can use our calculator to check the intermediate steps of your answer. Equivalent means your answer and the original boolean expression have the same truth table.
Boolean Algebra Laws are used to simplify boolean expressions.
Each law is described by two parts that are duals of each other. The Principle of duality is
Combinational Logic Circuit Design comprises the following steps
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