Enter your Boolean Expression into the Boolean Algebra Simplifier and get a fully Simplified Expression alongside the Reduction in term count between your Original Terms and Simplified Terms. Toggle Show Simplification Steps, choose your Output Format, and enable Calculate Normal Forms to dig deeper into the logic.
Simplified Expression
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Original Terms
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Simplified Terms
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Reduction
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The calculator applies commutative law, distributive law, absorption law, De Morgan's theorem, idempotent law, complement law, identity law, and double negation law to simplify expressions step-by-step.
Use + for OR operations, · (dot) for AND operations, and ! for NOT operations. Use parentheses to group terms. Variables should be single letters A-Z. Example: (A + B) · (!C + D)
DNF (Disjunctive Normal Form) expresses the Boolean function as a sum of products, while CNF (Conjunctive Normal Form) expresses it as a product of sums. Both are standard canonical forms used in Boolean algebra.
Yes, the calculator can simplify complex Boolean expressions with multiple levels of nesting and parentheses. It processes expressions systematically using established Boolean algebra rules.
Simplifying Boolean expressions reduces circuit complexity, improves performance in digital systems, makes logic easier to understand, and can reduce implementation costs in hardware design.
The basic calculator supports AND (+), OR (·), and NOT (!). Advanced versions may include XOR, NAND, and NOR operations. Check the help documentation for complete operator support.
The calculator uses proven Boolean algebra laws and produces mathematically correct simplifications. All transformations preserve the logical equivalence of the original expression while reducing complexity.