Enter Boolean Expression
Example Data Table
| Example expression | Variables | Expected simplified form | Notes |
|---|---|---|---|
| A'B + AB' + AB | A, B | A + B | Combines mutually covering minterms. |
| (A + B)(A + B') | A, B | A | Uses absorption through equivalent truth values. |
| A XOR B | A, B | A'B + AB' | Returns exclusive difference states. |
Formula Used
This calculator evaluates the Boolean function over every input combination, then builds minterms for output 1 and maxterms for output 0.
Canonical sum of products uses F = Σm(i), where each listed index represents a truth-table row producing 1. Canonical product of sums uses F = ΠM(j), where each listed index represents a row producing 0.
For reduction, the page applies exact implicant combining similar to the Quine-McCluskey method. Terms differing in one bit merge into broader implicants until no further exact combination remains.
Final simplified SOP selects essential prime implicants and the smallest additional covering set. Simplified POS follows the same logic using the zero-output rows.
How to Use This Calculator
- Enter a Boolean expression using letters for variables.
- Use
!or apostrophe for NOT,*for AND, and+for OR. - Wrap grouped logic inside parentheses whenever precedence matters.
- Click Simplify Expression to compute canonical and reduced forms.
- Review the generated truth table, implicants, and simplified expressions.
- Use the CSV and PDF buttons to export your results.
Frequently Asked Questions
1. What expressions can this calculator simplify?
It accepts variables, parentheses, NOT, AND, OR, XOR, NAND, NOR, and constants 0 or 1. It also supports implicit multiplication such as AB.
2. Why is there a six-variable limit?
Exact truth tables and exact implicant selection grow quickly with each variable. Limiting variables keeps the output readable and the simplification method dependable.
3. What is the difference between SOP and POS?
SOP groups the true rows into summed product terms. POS groups the false rows into multiplied sum terms. Both represent the same function.
4. Are apostrophe and exclamation mark both NOT?
Yes. You can write A' or !A for negation. The calculator normalizes both styles before evaluating and simplifying the function.
5. Does the tool show how the answer was built?
Yes. It shows the normalized token stream, evaluation order, prime implicants, essential implicants, and the full truth table for verification.
6. Can I use multi-character variable names?
Yes. Names like X1, IN1, or Enable are supported as long as they start with a letter and then use letters, numbers, or underscores.
7. What does canonical SOP notation mean?
The notation Σm lists the truth-table row numbers where the function becomes 1. Those row numbers define the canonical sum-of-products form.
8. When should I export CSV or PDF?
CSV is useful for analysis, documentation, and spreadsheet review. PDF works well for reports, assignments, or sharing a fixed version of results.