Boolean Expression Minimizer provides step-by-step simplification of Boolean algebraic expressions. Two modes are available:
1. Interactive algebraic reducer: In this mode, you are instructed to simplify an expression. Hints are provided and expressions are checked for validity and equivalence in each step.
2. Automatic algebraic reducer: In this mode, the expression is automatically simplified with all the steps explained.
Boolean expressions are entered in a prefix format, whereby the NOT operator continues 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:
→ Addition: (i) X + X’ = 1 (ii) XX’ = 0
→ Ideal level: (i) X + X = X (ii) XX = X
→ Join: X ” = X
→ Homogeneity: (i) X + 0 = X (ii) X1 = X
→ Empty element: (i) X + 1 = 1 (ii) X0 = 0
→ Absorption: (i) X + XY = X (ii) X (X + Y) = X
→ Advertising: (i) X + X’Y = X + Y (ii) X (X’ + Y) = XY
→ Merge: (i) XY + XY’ = X (ii) (X + Y) (X + Y’) = X
→ DeMorgan’s Law: (i) (X + Y) ‘= X’Y’ (ii) (XY) ‘= X’ + Y’
→ Commutative: (i) X + Y = Y + X (ii) XY = YX
→ Associative: (i) X + (Y + Z) = X + Y + Z (ii) X (YZ) = XYZ
→ Dispersibility: (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 application requires an Internet connection.