## 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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