Define minterm and the maxterm - canonical form, Computer Engineering

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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

0

X'.Y'

X+Y

0

1

X'.Y

X+Y'

1

0

X.Y'

X'+Y

1

1

X.Y

X'+Y'

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

X

Y

Z

Minterm

Designation

Maxterm

Designtion

0

0

0

X'.Y'.Z'

m0

X+Y+Z

M0

0

0

1

X'.Y'.Z

m1

X+Y+Z'

M1

0

1

0

X'.Y.Z'

m2

X+Y'+Z

M2

0

1

1

X'.Y.Z

m3

X+Y'+Z'

M3

1

0

0

X.Y'.Z'

m4

X'+Y+Z

M4

1

0

1

X.Y'.Z

m5

X'+Y+Z'

M5

1

1

0

X.Y.Z'

m6

X'+Y'+Z

M6

1

1

1

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.


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