Convert a Boolean expression to disjunctive normal form:

Convert x⊻y to some common forms:

Convert x⊻y⊻z using the condition that x∧(y∨z) is true:

Show that the output is equivalent to the input when x∧(y∨z):

Convert a Boolean expression to different forms:

Disjunctive normal form:

Conjunctive normal form:

Exclusive sum of products:

Algebraic normal form:

Two-level Nand and Not :

Two-level Nor and Not :

Two-argument Nand :

Two-argument Nor :

Two-level And and Not :

Two-level Or and Not :

Implies and Not :

If and constants:

Boolean function form:

Boolean decision tree:

Show that they are all equivalent:

Convert a Boolean function using a "care set" or condition:

The resulting forms are equivalent when cond is true:

They are not equivalent without the condition:

Typically the forms are longer without conditions:

The output from BooleanConvert is equivalent to its input:

The output from BooleanConvert with condition is conditionally equivalent to its input:

The forms f and g are equivalent when cond is true:

They are not equivalent on their own:

Use BooleanMinimize to get the minimal length form:

The forms are equivalent: