Boolean Expression Simplifier
Type any expression in A–D and get the exact minimal SOP — supports ', !, ·, +, ^ and parentheses.
Boolean Expression Simplifier computes any boolean expression in A–D reduced to its exact minimal sum-of-products — free, instant and private in your browser. Students checking homework and firmware authors collapsing nested conditionals use it to skip the datasheet algebra: type your numbers, read the answer with the substituted formula shown step by step, and share an exact permalink of the calculation.
About Boolean Expression Simplifier
Boolean Expression Simplifier computes any boolean expression in A–D reduced to its exact minimal sum-of-products using the standard engineering relation: truth-table expansion → Quine–McCluskey exact minimisation. Worked live: A·B + A·B′·C + A′·B·C simplifies to A·B + B·C + A·C — wait, run it: the tool gives the true minimum. The result recalculates on every keystroke, the worked-example panel shows your numbers substituted into the formula, and the Copy permalink button encodes the inputs in the URL so a colleague opens exactly your calculation. Everything runs client-side — nothing you type leaves your device.
How to use Boolean Expression Simplifier
- 1Enter your values — the tool starts with realistic defaults for this exact use case, so the worked example is meaningful immediately.
- 2Read the live result and the worked-example panel, which substitutes your numbers into the formula step by step.
- 3Adjust any input to compare scenarios, then use Copy result or Copy permalink to share the calculation.
Why use Boolean Expression Simplifier?
- ✓Implements the real formula — truth-table expansion → Quine–McCluskey exact minimisation — with the substitution shown, not a black box
- ✓Built for students checking homework and firmware authors collapsing nested conditionals
- ✓Copy result and permalink buttons — share the exact calculation in a README, forum answer or design review
- ✓100% free, no sign-up, runs entirely in your browser (works offline once loaded)
Frequently asked questions
How do you calculate boolean expression?+
Any boolean expression in A–D reduced to its exact minimal sum-of-products follows truth-table expansion → Quine–McCluskey exact minimisation. For example, A·B + A·B′·C + A′·B·C simplifies to A·B + B·C + A·C — wait, run it: the tool gives the true minimum. The calculator applies the same relation and shows the substituted arithmetic so you can verify every step.
Is the result guaranteed minimal?+
Yes, in product-term count for two-level SOP — Quine–McCluskey is exact, unlike heuristics (Espresso) used for huge inputs. With ≤4 variables exactness is cheap. A product-of-sums form can occasionally use fewer literals; solve the complement to compare.
Why did my XOR-style expression get BIGGER after simplifying?+
XOR has no compact SOP: A⊕B⊕C needs 4 product terms, period. If the minimal SOP looks bulkier than your original, your expression is parity-flavoured and was already optimal in XOR form — keep the ⊕ operators in code and hardware.
Is the Boolean Expression Simplifier free and private?+
Yes — completely free with no sign-up or usage limits, and it runs entirely in your browser: the values you enter are never uploaded or stored on a server.
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