Boolean Algebra Calculator

Category: Algebra and General

Evaluate boolean expressions, create truth tables, and simplify logical statements. Supports AND (&), OR (|), NOT (!), XOR (โŠ•), NAND, NOR operations with variables A-Z and constants 0/1.

Expression Input

Use A-Z for variables, &(AND), |(OR), !(NOT), โŠ•(XOR), parentheses for grouping
Expression Builder

Variable Values

Analysis Options

Specify variables for truth table (auto-detected if empty)

Common Boolean Logic Formulas:

  • AND: \( A \land B = A \cdot B \)
  • OR: \( A \lor B = A + B \)
  • NOT: \( \lnot A \)
  • XOR: \( A \oplus B \)
  • NAND: \( \lnot (A \cdot B) \)
  • NOR: \( \lnot (A + B) \)

What Is the Boolean Algebra Calculator?

The Boolean Algebra Calculator is a simple yet powerful tool that helps you work with logical expressions. Whether you're a student learning about digital circuits or a professional dealing with logic gates, this calculator lets you evaluate boolean expressions, generate truth tables, and simplify logic formulas in seconds.

What You Can Do With This Tool

Hereโ€™s what this calculator helps you achieve:

  • Evaluate logic expressions instantly with support for AND, OR, NOT, XOR, NAND, and NOR operations
  • Auto-generate truth tables for up to 4 variables
  • Convert logic statements to Disjunctive Normal Form (DNF) and Conjunctive Normal Form (CNF)
  • Simplify expressions using common boolean laws
  • Visualize Karnaugh Maps for minimization

How to Use the Calculator

Follow these steps to use the Boolean Algebra Calculator effectively:

  1. Enter a logic expression in the input field (e.g., (A & B) | !C)
  2. Select the format youโ€™re comfortable with: symbolic (&, |, !), text (AND, OR, NOT), programming style (&&, ||, !), or mathematical symbols (โˆง, โˆจ, ยฌ)
  3. Use the on-screen buttons to build your expression quickly
  4. Assign values (0 or 1) to the variables if you want to evaluate the expression for specific inputs
  5. Click Evaluate Expression to see results, simplification steps, and truth table
  6. Enable extra options to view DNF, CNF, or Karnaugh Map if needed

Why Use This Calculator?

This tool saves time and reduces error when analyzing boolean logic. Whether you're checking your homework or designing logic gates, this tool ensures:

  • Accurate evaluation of logical conditions
  • Clear visualization through truth tables and Karnaugh Maps
  • Step-by-step simplification using standard laws
  • Quick generation of DNF and CNF forms, useful in logic design and programming

Related Concepts and Tools

If you're interested in logic or math calculators, you might also benefit from:

Frequently Asked Questions

What kind of expressions can I input?

You can use variables A-Z and logical operators such as AND (&), OR (|), NOT (!), XOR (โŠ•), NAND (โ†‘), and NOR (โ†“). You can also use parentheses to group parts of your expression.

How many variables can I use?

The calculator supports up to 4 variables for truth tables and Karnaugh maps, though expressions with more variables can still be evaluated.

Can I simplify any logic expression?

Yes. The tool applies standard boolean algebra laws like De Morganโ€™s laws, identity, null, and idempotent rules to simplify your expression.

Is this useful for programming or circuit design?

Absolutely. This calculator is valuable for programming conditions, logic gate design, and studying digital electronics or computer Science principles.

Conclusion

The Boolean Algebra Calculator is a fast and reliable solution for evaluating logical statements and simplifying boolean expressions. With features like truth tables, Karnaugh maps, and step-by-step simplification, itโ€™s a practical logic analysis tool suitable for learners and professionals alike. Combine it with tools like a percent error calculator or a scientific calculator to enhance your understanding across math and logic topics.