Lecture 5
0 likes42 views
This document discusses binary operations and Boolean logic. It defines binary operations like addition, subtraction, multiplication and division. It then explains Boolean logic operations such as NOT, AND and OR. Boolean variables can only have binary values of 0 or 1. Truth tables are provided to show the output for each Boolean logic operation based on all possible input combinations. Examples of Boolean logic expressions and their corresponding truth tables are also given.
1 of 15
Download to read offline
Lecture 5
- 1. Lecture 5 Binary Operation Boolean Logic
- 2. Binary Operations • Addition • Subtraction • Multiplication • Division
- 3. Addition
- 4. Subtraction
- 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