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Logic Operations Lecture 9

Logic Operations Lecture 9. Boolean Logic Operations.

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Logic Operations Lecture 9

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  1. Logic Operations Lecture 9

  2. Boolean Logic Operations

  3. Letx, y, zbe Boolean variables. Boolean variables can only have binary valuesi.e., they can have values which are either 0 or 1For 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

  4. A few other names for the states of these Boolean variables

  5. We define the following logic operations or functions among the Boolean variables

  6. We’ll define these operations with the help of truth tableswhat is the truth tableof a logic functionA truth table defines the output of a logic function for all possible inputs ?

  7. Truth Table for the NOT Operation(y true whenever x is false)

  8. Truth Table for the NOT Operation

  9. Truth Table for the AND Operation(z true when both x & y true)

  10. Truth Table for the AND Operation

  11. Truth Table for the OR Operation(z true when x or y or both true)

  12. Truth Table for the OR Operation

  13. Truth Table for the XOR Operation(z true when x or y true, but not both)

  14. Truth Table for the XOR Operation

  15. Those 4 were the fundamental logic operations. Here are examples of a few more complex situations z = (x + y)´ z = y ·(x + y) z = (y · x) w STRATEGY: Divide & Conquer

  16. z = (x + y)´

  17. z = y ·(x + y)

  18. z = (y · x) w

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