Binary operation Boolean logic

1. Lecture 5
Binary Operation
Boolean Logic

2. Binary Operations
• Addition
• Subtraction
• Multiplication
• Division

3. Addition

4. Subtraction

5. Multiplication

6. Division

7. Boolean Logic Operations
Let x, y, z be Boolean variables. Boolean variables can only have binary values
i.e., they
can have values which are either 0 or 1.
For example, if we represent the state of a light switch with a Boolean
variable x, we will assign a value of 0 to x when the switch is OFF, and 1 when
it is ON
A few other names for the states of these Boolean variables
0 1
Off On
Low High
False True

8. Boolean Logic
• AND
• OR
• NOT

9. We define the following logic operations or functions
among the Boolean variables
Name Example Symbolically
NOT y = NOT(x) x´
AND z = x AND y x · y
OR z = x OR y x + y

10. Truth Table
A truth table defines the output of a logic function for all
possible inputs.
Number of rows in a truth table?
2n
n = number of input variables

11. NOT Operation
Truth Table for the NOT Operation
X y = x´
0 1
1 0

12. AND Operation
Truth Table for the AND Operation
X y z = x · y
0 0 0
0 1 0
1 0 0
1 1 1

13. OR Operation
Truth Table for the OR Operation
x y z = x + y
0 0 0
0 1 1
1 0 1
1 1 1

14. Examples
z = (x + y)´
x y x + y z = (x + y)´
0 0 0 1
0 1 1 0
1 0 1 0
1 1 1 0

15. Examples
z = y · (x + y)
x y x + y z = y · (x+ y)
0 0 0 0
0 1 1 1
1 0 1 0
1 1 1 1