Microsoft Word - Digital Logic Design v_4_6a

2.5. Boolean Functions

 Pure form

X.Y.Z is called the product of terms when literals are ANDed together

X+Y+Z is called the sum of terms when literals are ORed together

 Mixed forms

(X+Y).(Z+Y+X)  this form is called the product of sums form (POS form)

X.Y + Y.Z  this form is called the sum of products form (SOP form)

 Truth table for a function

 Steps

 Identify all possible combination of “1s” and “0s”. For an “n” variable function, there will 2n

rows in the table counting from 0 to 2 (n-1).

 Evaluate the output function value for each set of input variable values.

 Example

Draw a system diagram and generate a truth table for the function, F(X, Y, Z) = X.Y + Y.Z + Z’.Y

System Diagram

Truth Table

X Y Z F(X,Y,Z)

0 0 0

0 0 1

0 1 0

0 1 1

1 0 0

1 0 1

1 1 0

1 1 1

0 0 1 1 0 0 1 1

System

F(X, Y, Z)

Input Output

X

Y

Z