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# Standard POS Form & Maxterms

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

STANDARD POS FORM & MAXTERMS:

â€˘               POS  expressions  containing  all  Variables  in  the  Domain  in  each  term  are  in Standard Form.

â€˘               Standard sum terms are also called Maxterms. A Maxterm is a NOT Minterm.

â€˘               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 ORâ€™ed with the original term

## 2. CHARACTERISTICS OF A MAXTERM:

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

â€˘               Represents exactly one combination of the binary variables in a truth table for which the function produces a â€ś0â€ť output. That is the binary representation or value.

â€˘               Has value of 0 for that combination and 1 for all others

â€˘               For n variables, there are 2n distinct maxterms

Example: Why Standard SOP and POS Forms?

â€˘               Direct mapping of Standard Form expressions and Truth Table entries.

â€˘               Alternate Mapping methods for simplification of expressions

â€˘               Minimal Circuit implementation by switching between Standard SOP or POS

â€˘               PLD based function implementation Express the Boolean function as

1)          POS form

2)          SOP form

D=(Aâ€˛+B)(Bâ€˛+C)

### POS form:

Given

D=(Aâ€˛+B)(Bâ€˛+C)

=Aâ€˛Bâ€˛+Aâ€˛C+BBâ€˛+BC

=             Aâ€˛Bâ€˛+Aâ€˛C+BC

=             Aâ€˛+Bâ€˛+ Aâ€˛C+BC

=             Aâ€˛(1+C)+Bâ€˛+BC

=             Aâ€˛+Bâ€˛+BC

D= Aâ€˛Bâ€˛+BC

Using missed terms formulae;

=             Aâ€˛Bâ€˛(C+Câ€˛)+(A+Aâ€˛)BC

=             Aâ€˛Bâ€˛C+ Aâ€˛Bâ€˛Câ€˛+ABC+Aâ€˛BC

D(A,B,C)= ÎŁ m(1,0,7,3) D= Aâ€˛Bâ€˛+BC

### SOP form:

D(A,B,C)= Ď€M(1,0,7,3) Dâ€˛=(Aâ€˛+Bâ€˛)(B+C)

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Digital Electronics : Minimization Techniques and Logic Gates : Standard POS Form & Maxterms |