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A’(A + B) + (AA + B)(A + B’)
= A’A+A’B+(AA+B)(A+B’) Applying Distributive Law
= A’B+(AA+B)(A+B’) Rule 8 A.A’ = 0
= A’B+(A+B)(A+B’) Rule 7 A.A = A
= A’B + (AA+AB’+AB+BB’) Distributive Law
= A’B +(A+AB’+AB) Rule 7 & 8 AA=A A.A’=0
=A’B + (A+B+AB) Rule 11 A+A’B=A+B
= A’B+A+B Rule 10 A+A.B=A
=A+B+B Rule 11 A=A’B=A+B
=A+B Rule 5 A+A=A
A simpler mapping method uses Karnaugh maps to simplify general expressions.
Mapping of all the terms in a SOP form expression and the sum terms in a POS form can be
easily done if standard forms of SOP and POS expressions are used. Karnaugh maps will be
discussed latter in the chapter.
Lastly, the PLDs are implemented having a general purpose structure based on ANDOR
arrays. A function represented by an expression in Standard SOP form can be readily
programmed.
Minterms and Maxterms
The Product terms in the Standard SOP form are known as Minterms and the Sum
terms in the Standard POS form are known as Maxterms.
A B C Minterms Maxterms
0 0 0 A.B.C A +B + C
0 0 1 A.B.C A +B + C
0 1 0 A.B.C A +B + C