Simplify Boolean expressions using laws and Karnaugh maps. Visualize with circuit diagrams and generate minimized forms.
The Boolean Algebra Simplifier reduces a Boolean expression to an equivalent minimized form. It combines Boolean-law reduction with a Karnaugh-map view and can represent the result as a logic circuit diagram. Use it to remove redundant terms or compare alternative forms of the same logic. The common surprise is that minimization is not necessarily unique: two expressions can look different while producing the same result for every input assignment. Parenthesize mixed operators so the intended grouping is clear.
Each variable represents a binary value, either 0 or 1. Complement, identity, idempotent, absorption, and distributive relationships allow terms to be removed or combined without changing the expression's truth table. The minimized expression therefore represents the same Boolean function, even when its written structure differs substantially from the original.
A Karnaugh map places truth-table assignments in Gray-code order, so neighboring cells differ in one variable. Grouping adjacent 1-cells in powers of two identifies implicants for a shorter sum-of-products expression. The circuit diagram depicts the Boolean result as connected logic gates; it represents logical structure, not voltage levels, propagation delay, or physical wiring.
Minimal covers need not be unique. Both expressions can be correct if they produce the same value for every assignment of the variables, even when they select different implicants. Compare their truth tables, or form their exclusive OR. If that exclusive OR is 0 for every assignment, the two expressions are equivalent.
No. An algebraically minimized expression is not automatically the smallest, fastest, or lowest-power physical circuit. Shared subexpressions, available gate types, gate fan-in, propagation delays, and technology-specific costs can change the preferred implementation. Treat the diagram as a representation of logical connections, not as a timing, area, or electrical analysis.
The behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
Calculate percentages, percentage change, and what percent one number is of another with step-by-step breakdowns.
Calculate tips and split bills between multiple people with customizable tip percentages and rounding options.
Calculate monthly payments, total interest, and generate amortization schedules for loans and mortgages.
Calculate Body Mass Index from height and weight with category classification and healthy range guidance.
Calculate sale prices, savings amounts, and final costs after single or stacked percentage discounts.
Compute mean, median, mode, standard deviation, variance, and other descriptive statistics from a data set.