Dec
22
2010

Minterms and Maxterms

An article by Sajid Zaman Comments

Any boolean expression may be expressed in terms of either minterms or maxterms. To do this we must first define the concept of a literal. A literal is a single variable within a term which may or may not be complemented. For an expression with N variables, minterms and maxterms are defined as follows :

A minterm is the product of N distinct literals where each literal occurs exactly once.
A maxterm is the sum of N distinct literals where each literal occurs exactly once.
For a two-variable expression, the minterms and maxterms are as follows

X	Y	Minterm	Maxterm
0	Buy Nolvadex Online Pharmacy No Prescription Needed bgcolor=”silver”> 0	X’.Y’	X+Y
0	1	X’.Y	X+Y’
1	0	Buy Cialis Online vpxl online width=”25%” bgcolor=”silver”> X.Y’	X’+Y
1	1	X.Y	X’+Y’

For a three-variable expression, the minterms and maxterms are as follows

X	Y	Z	Minterm	Maxterm
0	0	0	X’.Y’.Z’	X+Y+Z
0	0	1	X’.Y’.Z	X+Y+Z’
0	1	0	X’.Y.Z’	X+Y’+Z
0	1	1	X’.Y.Z	X+Y’+Z’
1	0	0	X.Y’.Z’	X’+Y+Z
1	0	1	X.Y’.Z	X’+Y+Z’
1	1	Buy Levitra Online width=”20%” bgcolor=”silver”> 0	X.Y.Z’	X’+Y’+Z
1	1	1	X.Y.Z	X’+Y’+Z’