Use A–D, 0, 1, !, &, ^, | and parentheses. Precedence: NOT, AND, XOR, OR.
Your result
Click Calculate
Every assignment is displayed after you submit an expression.How this calculator helps
This Boolean algebra calculator evaluates a bounded logical expression and displays every possible truth-table row. Use variables A through D, constants zero and one, parentheses and the explicit operators !, &, ^ and |. The outputs classify the expression as always true, always false or contingent on its inputs. The page does not promise a shortest symbolic expression or optimal gate circuit. Truth-table evaluation is a concrete way to inspect a Boolean statement before comparing it with a proposed simplification.
How to use it
- 1
Read the labeled input units and select the supported calculation mode where available.
- 2
Enter the values established from the source records described below; do not substitute a different measurement basis.
- 3
Click Calculate result to calculate from the supplied inputs.
- 4
Read the main output together with the checks and limitations. After editing inputs, click Calculate again to update the stored result.
Formula and methodology
! means NOT, & means AND, ^ means XOR and | means OR. Precedence is NOT, AND, XOR, OR; parentheses override it. N variables produce 2^N complete input assignments.
The calculator applies the displayed arithmetic to the values entered on this device. It does not silently load a local tax rate, currency conversion or commercial assumption.
Worked calculation example
A & !B is true only for A=1, B=0. A | !A is a tautology; A & !A is a contradiction. A ^ B differs from A | B when both inputs are one.
How to interpret your result
The first output contains the complete assignment-to-result mapping. Read its variable heading before interpreting each row. The classification summarizes the entire table rather than just the first assignment. A correct table can still represent the wrong intended condition if the expression was transcribed incorrectly, so check syntax and grouping as well as the output.
For different inputs or formulas, use Binary Calculator; Hex Calculator; Substitution Calculator.
Related questions this calculator covers
- boolean algebra calculator
Scenario comparison
| Scenario | What it shows |
|---|---|
| A|!A | all rows output one. |
| A&!A | all rows output zero. |
| A^B | only differing input rows output one. |
Common mistakes to avoid
- Using inclusive OR where exclusive OR was intended.
- Omitting parentheses when changing the source notation.
- Claiming two expressions are equivalent after checking one row.
For two variables, list 00, 01, 10 and 11 by hand and apply the supported operator definitions. Test a tautology and contradiction, then an XOR example. To assess a proposed rewrite, compare every assignment with matching variable order; do not infer gate optimality from equivalent output.
Authoritative reference. Standard propositional truth-table definitions; the exact bounded operator grammar and classification are disclosed by SolvePilot.What can affect the result?
Use the supported syntax explicitly
Write A&B rather than AB, because implicit multiplication or adjacent variable syntax is not supported. The letters are case-insensitive and become uppercase internally. Use ! before a variable or parenthesized expression for negation. Plus, apostrophe notation and words such as AND are deliberately excluded so the parser has one unambiguous operator vocabulary. A rejected expression does not mean the underlying Boolean problem is invalid; it means the expression needs to be rewritten in this page’s disclosed syntax.
Read precedence before relying on a table
NOT binds most tightly, followed by AND, XOR and OR. For example, A|B&C means A|(B&C). If your source uses another convention or you intend a different grouping, add parentheses explicitly. The parser evaluates every input assignment with that same grouping. Expressions are capped at two hundred characters and thirty-two nesting levels. Those bounds keep the browser operation predictable and do not restrict the mathematical subject to only short expressions in general.
XOR is different from inclusive OR
Inclusive OR is true when either input or both inputs are true. XOR is true when the two inputs differ. Confusing the operators changes a table even when most rows happen to agree. The two-input row with both values one is a useful distinguishing test. Likewise, negating A&B produces a different expression from !A&B. Evaluate the intended grouping rather than judging equivalence from one convenient input example or from how similar two expressions look.
Inspect all rows for equivalence
Up to four distinct variables produce at most sixteen rows. The rows are ordered as binary assignments with the variable names sorted alphabetically. To compare two expressions, calculate each and align assignments for the same set of variables. Matching outputs across every assignment establish equivalence on those variables; matching one row does not. If an expression omits a variable used by the other, consider both values of that extra variable when comparing. No automatic symbolic minimizer is claimed.
Classification does not validate an application
A tautology is true for every displayed assignment, and a contradiction false for every assignment. A contingent expression has a mixture. Those classifications describe formal logic under the chosen syntax, not whether a real hardware system or business rule is safe or correct. The calculator does not model propagation delay, electrical behavior, sequential state or unknown HDL values. All processing is local; the input string is parsed without JavaScript eval or execution of user-supplied code.
Privacy and browser processing
Values entered on this page are processed in the current browser session. SolvePilot does not require an account and does not receive the values entered into the calculator. Refreshing or closing the page clears the working values unless the browser itself restores a previous session. Avoid entering identifying or account information because the calculation needs summary values only.
Accuracy and verification
Accuracy depends first on input quality. Confirm definitions, scales, dates and source information before entering a value. Keep an independent record of any result used for planning because this page does not create an official statement or retain a calculation history.
Limits of this estimate
The first output contains the complete assignment-to-result mapping. Read its variable heading before interpreting each row. The classification summarizes the entire table rather than just the first assignment. A correct table can still represent the wrong intended condition if the expression was transcribed incorrectly, so check syntax and grouping as well as the output. A tautology is true for every displayed assignment, and a contradiction false for every assignment. A contingent expression has a mixture. Those classifications describe formal logic under the chosen syntax, not whether a real hardware system or business rule is safe or correct. The calculator does not model propagation delay, electrical behavior, sequential state or unknown HDL values. All processing is local; the input string is parsed without JavaScript eval or execution of user-supplied code.
Sources and review information
Frequently asked questions
Does the calculator simplify expressions?＋
It evaluates a complete truth table and classification. It does not claim minimum symbolic form or minimum gate count.
Which operators are accepted?＋
Use ! for NOT, & for AND, ^ for XOR and | for OR, plus parentheses, A–D and constants 0 or 1.
How many variables are supported?＋
At most four named variables, producing at most sixteen rows. The expression length and nesting are also bounded.
Why is A|B&C grouped that way?＋
AND has higher precedence than OR. Use parentheses if another grouping is intended.
Does it execute pasted code?＋
No. The bounded parser accepts the listed Boolean tokens and does not use eval or execute JavaScript.