Simplify the given Boolean function into minimal SOP form, type your answer below, and verify against the Quine–McCluskey truth engine!
Automatically maps your active Solver function F onto MUX data lines (I0, I1...) using MSB select lines.
| Law | AND form | OR form |
|---|---|---|
| Identity | A·1 = A | A+0 = A |
| Null | A·0 = 0 | A+1 = 1 |
| Idempotent | A·A = A | A+A = A |
| Inverse | A·A' = 0 | A+A' = 1 |
| Commutative | AB = BA | A+B = B+A |
| Associative | (AB)C = A(BC) | (A+B)+C = A+(B+C) |
| Distributive | A(B+C) = AB+AC | A+BC = (A+B)(A+C) |
| Absorption | A(A+B) = A | A+AB = A |
De Morgan: (A+B)' = A'·B' and (A·B)' = A' + B'. Break the bar, change the operator.
| SOP | POS | |
|---|---|---|
| Form | OR of AND terms | AND of OR terms |
| Canonical term | Minterm m (output 1) | Maxterm M (output 0) |
| Notation | Σm(...) | ΠM(...) |
| K-Map groups | Adjacent 1s | Adjacent 0s |
| Literal rule | Variable=1 → A, 0 → A' | Variable=0 → A, 1 → A' |
Canonical → minimal: list minterms/maxterms, plot on the map, group, write each group, then OR (SOP) or AND (POS) the terms. Σm and ΠM of the same function use complementary index sets.
K-Map axes use 00, 01, 11, 10 so neighbouring cells differ in exactly one bit; that single change is what lets a group drop a variable.
Static-1 hazard: output should stay 1 but glitches 1 → 0 → 1 when a single input change moves between two adjacent groups with unequal gate delays. Static-0 is the dual: 0 → 1 → 0 in POS circuits.
Fix: add a redundant consensus term that covers the two adjacent cells straddling the groups, so some product stays high throughout the transition. Example: AB + A'C gains + BC.