Boolean Expression Minimizer

About: Boolean Expression Minimizer

Boolean Expression Minimizer provides step-by-step simplification of Boolean algebra expressions. Two modes are available:

1. Interactive Algebraic Minimizer: In this mode, you are guided to simplify an expression. Hints are provided and expressions are tested for validity and equivalence in each step.
2. Automatic Algebraic Minimizer: In this mode, the expression is automatically simplified with all steps explained.




Boolean expressions are entered in the infix format whereby the NOT operator proceeds the term and the AND operator is implied e.g. A' + BC. Up to 26 variables are supported from A to Z. The following laws and theorems are used:

→ Complementarity: (i) X + X' = 1 (ii) XX' = 0
→ Idempotency: (i) X + X = X (ii) XX = X
→ Involution: X'' = X
→ Identity: (i) X + 0 = X (ii) X1 = X
→ Null Element: (i) X + 1 = 1 (ii) X0 = 0
→ Absorption: (i) X + XY = X (ii) X(X+Y) = X
→ Adsoption: (i) X + X'Y = X + Y (ii) X(X' + Y) = XY
→ Unity: (i) XY + XY' = X (ii) (X+Y)(X+Y') = X
→ DeMorgan's Laws: (i) (X + Y)' = X'Y' (ii) (XY)' = X' + Y'
→ Commutativity: (i) X + Y = Y + X (ii) XY = YX
→ Associativity: (i) X + (Y + Z) = X + Y + Z (ii) X(YZ) = XYZ
→ Distributivity: (i) X(Y+Z) = XY + XZ (ii) X+YZ = (X+Y)(X+Z)
→ Consensus: (i) XY + X'Z + YZ = XY + X'Z (ii) (X + Y)(X' + Z)(Y + Z) = (X + Y)(X' + Z)
→ XOR Gate: X ^ Y = X'Y + XY'
→ XNOR Gate: X = Y ≡ X'Y' + XY

Note: This app requires an Internet connection.