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= P'.Q+0 [Complement law]
= P'.Q [Properties of 0 and 1]
1.10 MAXTERM, MINTERM, SUM OF PRODUCT AND PRODUCT OF SUM
Let us consider a Boolean expression having two variables X and Y. All the possible combinations of the product terms
of their variables in normal and complemented forms are X'.Y', X'.Y, X.Y' and X.Y whereas all the possible combinations
of the sum terms of their variables are (X+Y), (X+Y'), (X'+Y'), (X'+Y). All these product terms are called minterms and all
these sum terms are called maxterms.
Definition
Minterm can be defined as the product terms of all the variables present in the expression both in complemented
and normal forms.
Maxterm can be defined as the sum terms of all the variables present in the expression both in complemented and
normal forms.
Let us now consider a three-variable Boolean expression having variables A, B and C. Their corresponding maxterms
and minterms are shown with the help of a truth table given below. We can see that while generating minterm, if the
input bit (variable) is 1, it is used in its normal form, and if the input bit (variable) is 0, then it is complemented so that
the final product is 1 in each case.
Similarly, in the case of maxterm, the input bits, which are 0, are used in normal form while input bit 1 is complemented
so that the resulting sum is 0 in each case.
The last column contains the decimal equivalent of the binary digits and is termed the cardinal number.
A B C Minterm Maxterm Cardinal Number
0 0 0 A'.B'.C' A+B+C 0
0 0 1 A'.B'.C A+B+C' 1
0 1 0 A'.B.C' A+B'+C 2
0 1 1 A'.B.C A+B'+C' 3
1 0 0 A.B'.C' A'+B+C 4
1 0 1 A.B'.C A'+B+C' 5
1 1 0 A.B.C' A'+B'+C 6
1 1 1 A.B.C A'+B'+C' 7
In the same way, the maxterms and the minterms of a four-variable Boolean expression represented by A, B, C and D
are as follows:
A B C D Minterm Maxterm Cardinal Number
0 0 0 0 A'.B'.C'.D' A+B+C+D 0
0 0 0 1 A'.B'.C'.D A+B+C+D' 1
0 0 1 0 A'.B'.C.D' A+B+C'+D 2
0 0 1 1 A'.B'.C.D A+B+C'+D' 3
0 1 0 0 A'.B.C'.D' A+B'+C+D 4
0 1 0 1 A'.B.C'.D A+B'+C+D' 5
0 1 1 0 A'.B.C.D' A+B'+C'+D 6
0 1 1 1 A'.B.C.D A+B'+C'+D' 7
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