Define Minterm and the Maxterm - Canonical Form?
Any Boolean expression perhaps expressed in terms of either minterms or maxterms. The literal is a single variable within a term which may or may not be complemented. For an expression with the N variables, minterms and maxterms are defined as follows:
A minterm is the product of the N distinct literals where each literal occurs exactly once.
A maxterm is the sum of the N distinct literals where each literal occurs exactly once.
For the two-variable expression, the maxterms and minterms are as follows
X
Y
Minterm
Maxterm
0
X'.Y'
X+Y
1
X'.Y
X+Y'
X.Y'
X'+Y
X.Y
X'+Y'
For a three-variable expression, the maxterms and minterms are as follows
Z
Designation
Designtion
X'.Y'.Z'
m_{0}
X+Y+Z
M_{0}
X'.Y'.Z
m_{1}
X+Y+Z'
M_{1}
X'.Y.Z'
m_{2}
X+Y'+Z
M_{2}
X'.Y.Z
m_{3}
X+Y'+Z'
M_{3}
X.Y'.Z'
m_{4}
X'+Y+Z
M_{4}
X.Y'.Z
m_{5}
X'+Y+Z'
M_{5}
X.Y.Z'
m_{6}
X'+Y'+Z
M_{6}
X.Y.Z
m_{7}
X'+Y'+Z'
M_{7}
Consider a function F= x'y'z+xy'z'+xyz=m_{1+}m_{4}+m_{7}
If we take the complement of F then F'= (x+y+z')(x'+y+z)(x'+y'+z')=M_{1}.M_{4}.M_{7 }
Any Boolean function can be expressed as a product of Maxterms and Sum of Minterms.