1. MINTERMS
AND
MAXTERMS
A binary variable may appear either in its normal
form x or in its complement form x . Let us consider two
binary variables x and y, connected with AND operator.
There are four possible combinations: xy, xy,xy and xy.
These four possible combinations of input variables x and
y can be represented on a venn diagram. A minterm is
the product of all the variables within the logic system,
complemented or not. Thus, if x and y are the variables,
the following are athe minterms: xy,
A venn diagram consistsof a rectangle, inside which
there are two overlapping circles, one for each variable x
and y. Such a venn diagram for two variables is shown
in this shows all the domains of the four possible
combinations of the input variables x and y.
Venn diagrams may be used to explain the laws of
Boolean algebra. Venn diagrams may be used to

2. explain the laws of Boolean algebra.
X=xy+x=xy+xy’.
Venn diagram for two variables x=xy+x.
A maxterm is of all the variables within the logic
system, complemented or not. If x,y and z are all the
variables within a system, the following are the
maxterms.
x+y+z
x+y+z’
x+y’+z
x+y’+z’
x’+y+z
x’+y+z’
x’+y’+z
x’+y’+z’

3. Boolean functions expressed either as a sum of
minterms or as product of maxterms are said to be in
canonical form.