Binary Operation Boolean Logic
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The document discusses binary operations and Boolean logic. It defines binary operations like addition, subtraction, multiplication and division. It then explains Boolean logic operations like AND, OR and NOT. Truth tables are provided to define the output for all inputs of the NOT, AND and OR operations. Examples of Boolean logic expressions and their corresponding truth tables are also given.
Binary Operation Boolean Logic
- 1. Lecture 5 Binary Operation Boolean Logic Lecturer: Sumaira Hussain S.M.I university
- 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