Boolean Algebra Simplifier

Minimize a Boolean function from minterm and don't-care masks using Quine-McCluskey for up to four variables.

Scratchpad (not saved)

Save to create a persistent, shareable workspace.

What This Calculator Does

This calculator minimizes a Boolean function from minterms and don't-care states using a Quine-McCluskey style workflow, then shows the resulting implicants and a compact K-map view. It is aimed at small logic-design problems where exact simplification is still tractable.

It combines Variable Count, Minterm Mask (decimal), Don't-Care Mask (decimal) to estimate Simplified SOP, Prime Implicants, K-Map.

Formula & Method

Core equations: A sum-of-products form is written as F=\sum m(i) over the selected minterms, then adjacent minterms are combined by replacing one differing bit with a dash until a minimum prime-implicant cover is found.

Notation used in the formulas: R = Simplified SOP; x_{1} = Variable Count; x_{2} = Minterm Mask (decimal); x_{3} = Don't-Care Mask (decimal).

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use it when simplifying a truth-table driven logic expression, checking a hand-drawn Karnaugh map, or preparing a sum-of-products form for a small digital logic design.

Inputs Used

Variable Count: Used directly in the calculation.
Minterm Mask (decimal): Bit i = 1 means minterm i is included.
Don't-Care Mask (decimal): Bit i = 1 marks minterm i as don't care.

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