Logical Algebra Calculator

Test Boolean expressions with tables and canonical logic forms. Review variables, operators, and truth patterns instantly. Make complex reasoning checks easier every single time.

Calculator Input

Use A-Z variables and operators: !, &, |, xor, nand, nor, ->, <->.
Optional. Evaluate one chosen row directly.
Loads a sample into the expression box.

Example Data Table

Expression Variables Sample Assignment Expected Output
(A & B) | !C A, B, C A=1, B=1, C=0 1
(A xor B) -> C A, B, C A=1, B=0, C=1 1
(A nand B) <-> D A, B, D A=1, B=1, D=0 1
!(A | B) | (C & D) A, B, C, D A=0, B=0, C=1, D=1 1

Formula Used

Core evaluation idea
Each row assigns every variable either 0 or 1. The expression is then evaluated with Boolean operator rules to produce output F.
Operator formulas
NOT: ¬A = 1 when A = 0. AND: A ∧ B = 1 only when both are 1. OR: A ∨ B = 1 when at least one is 1. XOR: A ⊕ B = 1 when inputs differ. Implication: A → B = ¬A ∨ B. Equivalence: A ↔ B = 1 when both inputs match.
Canonical forms
SOP joins all true rows as minterms. POS joins all false rows as maxterms. This calculator builds both directly from the truth table.

How to Use This Calculator

  1. Enter a Boolean expression using variables like A, B, C, and D.
  2. Choose supported operators such as NOT, AND, OR, XOR, NAND, NOR, implication, or equivalence.
  3. Optionally add one focused assignment like A=1, B=0, C=1.
  4. Click the calculate button to generate the truth table and derived outputs.
  5. Review true count, false count, minterms, maxterms, and canonical SOP or POS.
  6. Use the CSV button for spreadsheet work and PDF for reporting.

FAQs

1. What does this logical algebra calculator do?

It evaluates Boolean expressions, builds a full truth table, counts true and false outputs, and generates canonical SOP and POS forms from the resulting rows.

2. Which operators can I use?

You can use NOT, AND, OR, XOR, NAND, NOR, implication, and equivalence. Symbol and word-style inputs are both supported for easier entry.

3. How many variables are supported?

This version supports up to six variables. That keeps the truth table readable while still covering many advanced classroom and design problems.

4. What are minterms and maxterms?

Minterms identify row numbers where the expression becomes true. Maxterms identify row numbers where it becomes false. They are useful for canonical forms.

5. What is canonical SOP?

Canonical SOP is a sum of products form created from all truth table rows that output 1. Each row contributes one minterm.

6. What is canonical POS?

Canonical POS is a product of sums form created from all truth table rows that output 0. Each false row contributes one maxterm.

7. Why use the focused assignment field?

It lets you test one exact variable combination quickly. This is useful when checking a design state, homework step, or a single expected condition.

8. Can I export my results?

Yes. You can download the generated truth table as CSV and save the full displayed report as a PDF for sharing or documentation.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.