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Boolean Algebra Simplifier Calculator

Work out boolean algebra simplifier instantly with clear inputs, formula shown and shareable results.

About Boolean Algebra Simplifier Calculator

Adjacent minterms differing in exactly one bit combine, because AB + AB' = A. Pairing every such neighbour is the first and most productive step of Quine-McCluskey reduction and of Karnaugh mapping.

Formula

Combining rule

X·Y + X·Y' = X, so minterms differing in one bit merge and drop that variable

Worked example

With the default values below, Boolean Algebra Simplifier Calculator returns Simplified sum of products of A'B' + A'C' + B'C + BC' + AC + AB. Change any input above and every figure here is recalculated in your browser.

Inputs used

Minterms that are true (decimal, for three variables)
0, 1, 2, 5, 6, 7
Number of variablesaccepts 1–4
3

Results

Simplified sum of products
A'B' + A'C' + B'C + BC' + AC + AB
Minterms given
6
Literals in the unsimplified form
18
Maxterms (rows that are false)
2

Step by step

  1. 1Values used
  2. 2Combining rule
  3. 3Simplified sum of products= A'B' + A'C' + B'C + BC' + AC + AB
  4. 4Minterms given= 6
  5. 5Literals in the unsimplified form= 18
  6. 6Maxterms (rows that are false)= 2

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Simplify minterms 0,1,2,5,6,7 of three variables.

The adjacent pairs collapse to a much shorter sum of products than the six four-literal terms you start with.

Why do minterms differing in one bit combine?

Because that variable appears in both polarities, so it cannot affect the outcome and factors out entirely.

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