Step-by-step Boolean function

Solve a Boolean function from a formula, value vector, or editable truth table with every transformation shown.
Boolean function

Truth table

ABCF
0001
0010
0101
0110
1001
1010
1101
1111

Step-by-step solution

  1. 1

    PDNF

    Join elementary conjunctions for every row where F = 1.

    ¬A∩¬B∩¬C ∪ ¬A∩B∩¬C ∪ A∩¬B∩¬C ∪ A∩B∩¬C ∪ A∩B∩C

  2. 2

    PCNF

    Intersect elementary disjunctions for every row where F = 0.

    (A∪B∪¬C) ∩ (A∪¬B∪¬C) ∩ (¬A∪B∪¬C)

  3. 3

    Minimized DNF

    Combine adjacent implicants using the Quine–McCluskey method.

    A∩B ∪ ¬C

  4. 4

    Zhegalkin polynomial

    Compute algebraic-normal-form coefficients with a modulo-2 Möbius transform.

    1 ⊕ C ⊕ A·B·C

  5. 5

    Shannon expansion

    Expand the function by variable A.

    (A∩(¬B∩¬C ∪ B∩¬C ∪ B∩C)) ∪ (¬A∩(¬B∩¬C ∪ B∩¬C))

Karnaugh map

A \ BC00011110
01001
11011

Logic circuit

Inputs: ABC
A∩B ∧
¬C ¬
∨ Function output
F

How to use this tool

Convert a Boolean function between its truth table, canonical forms, Zhegalkin polynomial, and a logic-circuit representation.

Steps

  1. Enter a formula or provide a function-value vector.
  2. Check or edit the truth table.
  3. Follow every transformation and copy the required form.

Useful for

  • Discrete mathematics
  • Boolean algebra
  • Digital logic

Limits and accuracy

  • Functions are limited to four variables.
  • The minimized DNF uses the Quine–McCluskey method.

Privacy

Your formula and all calculations stay in the browser.