Microsoft Word - Digital Logic Design v_4_6a

2.7. Canonical or Standard Form of Functions

 Typically, a function has to be written in one of the two standard forms before the minimization step.
The two standard forms are:

 Standard Sum of Products (SOP)


 Standard Product of Sums (POS)

 Obtaining Standard Sum of Products (SOP) Forms of Functions
In standard or canonical SOP form, all the variables are present in each product term.

 Example - for f(A,B) = A+B

1) System Diagram

2) Write the Truth table to see all the possible value of F(A,B)

Input Output

A B F(A,B)=A+B

0 0 0

0 1 1

1 0 1

1 1 1

3) Write the full product term for all the possible combinations

F(A,B) = F(0,0).A.B+ F(0,1). AB+ F(1,0). A.B+ F(1,1).A.B

F(A,B) = 0.A.B + 1. AB + 1.A.B + 1. A.B

F(A,B) = 1. AB + 1.A.B + 1.A.B  Canonical or Standard Form

A standard product or “min-term” is a product of all independent input variables for a function that

corresponds to a row of the truth table with output of 1. For example, A.B is a min term in the

above example.

System

A

B

F(A,B) = A + B