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Chapter: Digital Electronics - Minimization Techniques and Logic Gates

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Standard SOP Form & Minterms

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

STANDARD SOP FORM & MINTERMS:

 

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

 

               Standard product terms are also called Minterms.

 

               Any non-standard SOP expression may be converted to Standard form by applying Boolean Algebra Rule 6 to it.

 

Example:



Example: Determine Standard SOP expression

 


Introduce all possible combinations of the missing variables AND’ed with the original term

 

CHARACTERISTICS OF A MINTERM:

 

               Minterm is a standard product 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 “1” output. That is the binary representation or value.

 

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

 

               For n variables, there are 2n distinct minterms

 

Example:



Express the Boolean function F=A+B′C in sum of min terms.

 

Given

 

F=A+B′C

=A(B+ B′)(C+C′)+ B′C(A+A′)

=(AB+A B′)(C+C′)+B′C(A+A′)

=ABC+ABC′+AB′C+AB′C′+AB′C+A′B′C

= ABC+ABC′+AB′C+AB′C+A′B′C

F=m1+m4+m5+m6+m7

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