Find the minimal disjunctive normal form:

A Boolean counting function in disjunctive normal form:

Find a minimal disjunctive normal form:

A Boolean function of five variables represented in DNF:

Minimal-length DNF:

Minimal-length CNF:

Minimal-length NAND form:

Minimal-length NOR form:

Minimal-length ANF:

Show that all the forms are equivalent:

Minimize 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 BooleanMinimize is equivalent to its input:

The output from BooleanMinimize 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:

The minimal lengths "DNF", "CNF", "NAND", or "NOR" are not unique:

BooleanMinimize will produce an expression of length 3:

Another equivalent expression of length 3 is given by exchanging b and c:

Similar examples for "CNF", "NAND", and "NOR":

Use BooleanConvert when the minimal length form is not required:

BooleanConvert can also convert to additional forms: