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 1 1 0

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