Boolean Expressions & Functions



Boolean algebra developed by George Boole in 1847. Before to start the topic look at see the basic terms (i.e. Boolean Algebra, Boolean Expressions and Boolean Functions). 

  • A Boolean Algebra deals with binary variables (i.e. A, B, C), Binary Constants (0,1) and logic operation (i.e. NOT, AND, OR).
  • Boolean Function is described by an algebraic expression called Boolean expression.
  • Boolean Expression consists of binary variables, the constants (0 and 1), and the logic operation symbols. 

Boolean Functions and Expressions

The Boolean Expression is an INPUT and Boolean Function is an OUTPUT.

Note: Output of Boolean algebra function, on the given value of variables, can be either TRUE (1) or FALSE(0)  Let explain the following Boolean functions.

Symbolic Representation Of Boolean Expressions/Functions

Symbolically the Boolean functions can be represented through Logic gates. Consider the function  F = (x.y) + (y’.z). The symbolically representation of this function is given under. 

Symbolic Representation of Boolean expressions and functions

OUTPUT of Boolean Expressions/Functions

To find the output of any Boolean function, the Binary value of each variable is already given as a INPUT. SO, Simply replace the variables with their respective input values.




Let suppose a Boolean function  F(x,y,z) = (x.y) + (y’.z) and its input values are X=0, Y=1, Z=0 then the values of the Boolean function. The Output of given function is 

 F(x,y,z) = (x.y) + (y'.z)
As Y= 1 then, Y’ = 0
F(x,y,z)= (0.1) + (0.0)  
F(x,y,z)= (0) + (0)
F(x,y,z)= 0

Truth Table of Boolean Function

To represent a function in a truth table, we require a list of the 2(N) combinations, where N is the number of binary variables. If there are 3 variables (x, y and z) then 2(3) = 8 combinations will required. For batter understanding about Boolean Truth table look read the topic of logic gates.

The truth table for the Boolean function F = (x.y) + (y’.z) is given under

Truth Table of Boolean expressions and Functions

Boolean Functions with Truth Tables 

Let explain some examples of Boolean Algebra Functions with their Truth Tables

Example 01: F(X,Y)= (X+Y). Z

Block diagram for the Boolean function F(X,Y)= (X+Y). Z

Boolean Function Diagram
The truth table for the Boolean function F(X,Y)= (X+Y). Z

Truth Table of Example 01 of Boolean Function

Example 02: F(X,Y)= (X’.Y’) + (X’.Z)

Block diagram for the Boolean function F(X,Y)= (X’.Y’) + (X’.Z)

Boolean Function Example 02 in COA

The truth table for the Boolean function F(X,Y)= (X’.Y’) + (X’.Z)

Truth Table of Boolean Function Example 02

Example 03: F(X,Y) = (x’y’z) + (x’yz) + (xy’)

Block diagram for the Boolean function F(X,Y) = (x’y’z) + (x’yz) + (xy’)

Boolean Function of Example 03 in COA

The truth table for the Boolean function F(X,Y) = (x’y’z) + (x’yz) + (xy’)

 

Help Other’s By Sharing…

Contact Us

Burewala, Vehari, Punjab, Pakistan

cstaleem1@gmail.com

Website: CStaleem.com

Pin It on Pinterest