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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'
m0
X+Y+Z
M0
X'.Y'.Z
m1
X+Y+Z'
M1
X'.Y.Z'
m2
X+Y'+Z
M2
X'.Y.Z
m3
X+Y'+Z'
M3
X.Y'.Z'
m4
X'+Y+Z
M4
X.Y'.Z
m5
X'+Y+Z'
M5
X.Y.Z'
m6
X'+Y'+Z
M6
X.Y.Z
m7
X'+Y'+Z'
M7
Consider a function F= x'y'z+xy'z'+xyz=m1+m4+m7
If we take the complement of F then F'= (x+y+z')(x'+y+z)(x'+y'+z')=M1.M4.M7
Any Boolean function can be expressed as a product of Maxterms and Sum of Minterms.
Logic for multiplexer tree
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