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