Simplifying Boolean expressions

Example 1: A two-level logic expression Z = A'BC + AB'C' + AB'C + ABC' + ABC = AB'C + AB'C' + A'BC + ABC' + ABC rearrange = AB'(C + C') + A'BC + AB(C' + C) distributive = AB' + A'BC + AB comp. = AB' + AB + A'BC rearrange = A(B' + B) + A'BC distributive = A + A'BC comp.
- Use absorption #2D {(X •Y')+Y=X+Y} with X=BC and Y=A
Z = A + BC

Example 1: A two-level logic expression Z = A'BC + AB'C' + AB'C + ABC' + ABC = AB'C + AB'C' + A'BC + ABC' + ABC rearrange = AB'(C + C') + A'BC + AB(C' + C) distributive = AB' + A'BC + AB comp. = AB' + AB + A'BC rearrange = A(B' + B) + A'BC distributive = A + A'BC comp.