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.
SHORTCUT: Introduce all possible combinations of the missing variables OR’ed with the original term
• 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
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
= A′+B′+ A′C+BC
Using missed terms formulae;
= A′B′C+ A′B′C′+ABC+A′BC
D(A,B,C)= Σ m(1,0,7,3)
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