Combinational Circuits

Boolean Eqution Forms

A Boolean algebra is the combinations of variables and operators.Typically, it has one or more inputs and produces an output in the range of 0 or 1.

All Boolean eqution can be represented in two forms:

Ø  Sum-of-products (SOP)

-          Combination of input values that produce 1s is the convert into equivalent variables ANDed together then ORed with other combination variables with the same output.

-          SOP is easier to derive from truth table.

SOP expression

F= (A’B’C’D’) + (A’B’C’D) + (A’B’CD) + (ABC’D)

Ø  Product-of-sums (POS)

-Input combinations that produces 0 in sum terms

-Covert input values that produces 0s into equivalent variables,ORed the variables,then ANDed with other ORed forms.

-Usually use if more 1s produces in output function.

Example:-

F=(A+B+C)(A+B+C’)(A+B’+C)(A’+B+C)

The truth table:

 POS expression:

F=(A+B+C)(A+B+C’)(A+B’+C)(A’+B+C)

By  Nazirul Anwar B. Jamil