Standard POS Form & Maxterms

STANDARD POS FORM & MAXTERMS:

•               POS  expressions  containing  all  Variables  in  the  Domain  in  each  term  are  in Standard Form.

•               Standard sum terms are also called Maxterms. A Maxterm is a NOT Minterm.

•               Any non-standard POS expression may be converted to Standard form by applying Boolean Algebra Rule 8 and Rule 12 A+BC=(A+B)(A+C) to it.

1. STANDARD POS FORM:

Example:

SHORTCUT: Introduce all possible combinations of the missing variables OR’ed with the original term

2. CHARACTERISTICS OF A MAXTERM:

•               Maxterm is a standard sum term in which all variables appear exactly once (complemented or uncomplemented)

•               Represents exactly one combination of the binary variables in a truth table for which the function produces a “0” output. That is the binary representation or value.

•               Has value of 0 for that combination and 1 for all others

•               For n variables, there are 2n distinct maxterms

Example:

Why Standard SOP and POS Forms?

•               Direct mapping of Standard Form expressions and Truth Table entries.

•               Alternate Mapping methods for simplification of expressions

•               Minimal Circuit implementation by switching between Standard SOP or POS

•               PLD based function implementation Express the Boolean function as

1)          POS form

2)          SOP form

D=(A′+B)(B′+C)

POS form:

Given

D=(A′+B)(B′+C)

=A′B′+A′C+BB′+BC

=             A′B′+A′C+BC

=             A′+B′+ A′C+BC

=             A′(1+C)+B′+BC

=             A′+B′+BC

D= A′B′+BC

Using missed terms formulae;

=             A′B′(C+C′)+(A+A′)BC

=             A′B′C+ A′B′C′+ABC+A′BC

D(A,B,C)= Σ m(1,0,7,3)

D= A′B′+BC

SOP form:

D(A,B,C)= πM(1,0,7,3)

D′=(A′+B′)(B+C)