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Boolean Algebra

Boolean Algebra. && how we might use it in spreadsheets. Belinda Kerchmar 2.24.11. Boolean Logic. Invented by George Boole Boolean logic is the basis for modern computer logic. Quick Review: Variables. Where are variables in excel held?

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Boolean Algebra

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  1. Boolean Algebra && how we might use it in spreadsheets Belinda Kerchmar 2.24.11

  2. Boolean Logic • Invented by George Boole • Boolean logic is the basis for modern computer logic.

  3. Quick Review: Variables • Where are variables in excel held? • What types of variables can we have? (In other words, what can be held in a cell?)

  4. What is a Boolean Variable? • A variable (cell) that holds either true or false • In excel, can also be seen as 1 or 0 • Can be thought of conceptually as yes or no

  5. Boolean Operations • In Math, there are operations: plus, minus, times, etc. • In Boolean Algebra, there are operations as well. • Boolean Operations: • AND • OR • NOT

  6. Boolean Logic • Boolean logic Basics: • AND • OR • NOT

  7. Intuitive vs. Excel • Over the course of the lecture, I’ll use a syntax like this: a AND b AND c • The same expression in excel would look like: AND(a,b,c)

  8. AND • If every boolean being “and-ed” is true, then the AND operator returns true. • true AND true AND true = true • true AND false AND true = false

  9. AND • In excel: AND (some list of arguments) • If everything in list of arguments is true, then AND returns true. Otherwise, AND returns false. • Did all students pass the course?

  10. OR • If some boolean being “or-ed” is true, then the OR operator returns true • false OR false OR false = false • false OR false OR true = true

  11. OR • In excel: OR(some list of arguments) • If at least one of the list of arguments is true, then OR returns true. • Did at least one student pass?

  12. NOT • NOT(one argument) • If p is true, then NOT p is false. • If p is false, then NOT p is true.

  13. NOT • NOT (circles) • blue & white • NOT(diagrams) • yellow & white • NOT(circles OR diagrams) • white • NOT(circles AND diagrams) • yellow, blue, white • Did neither student pass the course?

  14. Properties • Just as in Math, the operations in Boolean Algebra follow certain properties.

  15. Properties you’ve seen before…

  16. De Morgan’s Laws • NOT (P AND Q) = • (NOT P) OR (NOT Q) • NOT (P OR Q) = • (NOT P) AND (NOT Q)

  17. On your own (or in groups) • Download Spreadsheet from course website • Write formulas to determine the following information for each item: • Is it tasty and healthy? • Is it dinner, but not tasty? • Is it dinner, and healthy or tasty? • Is it healthy, but not tasty or a snack?

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