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Chapter: Digital Electronics - Minimization Techniques and Logic Gates

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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:

 

               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)

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