Boolean Logic and Operators

1. Boolean Logic and Operators

2. Today’s Learning Objective • What we mean by truth values • What we mean by Boolean Operators • How to use AND, OR and NOT • How computers use these ideas!

3. Truth Values Some statements can be seen to be either true or false For example… • you are in a Computing lesson • this slide has a white background • it is the weekend Other statements are a matter of opinion, e.g. • it’s warm today • that’s a nice hat you’re wearing For this lesson, we will only considered statements about which everyone will agree Not bad Steve but my hard drive’s playing up a bit. TRUE TRUE FALSE Hello Bill how ya doin? Learn how to figure out Boolean Logic

4. Boolean Operators • Arithmetic operators, e.g. +, -, X and ÷, tell us how to combine two numbers • Everyone agrees on the results – e.g. 2 + 3 = 5 • Boolean (also called logical) operators tell us how to combine truth values in a standard way • You might also have seen them used in database searches • Boolean operators include: • NOT • AND • OR Learn how to figure out Boolean Logic

5. NOT The NOT operator toggles the truth value to its opposite value, e.g. • NOT true = false • NOT false = true For example… • you are NOT in a Computing lesson • this slide’s background is NOT blue • it is NOT Friday FALSE FALSE TRUE Learn how to figure out Boolean Logic

6. OR The OR operator gives a true result if any of the input values is true, e.g. • false OR false = false • false OR true = true • true OR false = true • true OR true = true For example… • it is Saturday OR Sunday • it is a weekday OR a weekend • it is Monday OR this is a Computing lesson FALSE TRUE TRUE Learn how to figure out Boolean Logic

7. AND The AND operator gives a true result if everything is true, e.g. • false AND false = false • false AND true = false • true AND false = false • true AND true = true For example… • it is evening AND it is Monday • this slide is whiteANDthe text is black • it is Monday AND this is a Computing lesson FALSE FALSE TRUE Learn how to figure out Boolean Logic

8. Is Anything Always True? Are there operations that are always true (or false)? • X OR NOT X is always true, e.g. • it is Monday OR NOT Monday • this slide is blue OR NOT blue • X AND NOT X is always false, e.g. • it is Monday AND NOT Monday • this slide is white AND NOT white • Think about this next time you hear someone say, “…whether or not…”! FALSE FALSE Learn how to figure out Boolean Logic

9. What About Computers? • Computers don’t understand the idea of truth, but they can detect whether a circuit or switch is on or off. • Circuits being on and off can also represent 1 and 0 as we learnt in the binary lesson. • When designing logic circuits for computers: • true = on = 1 • false = off = 0 • False and true are also often represented by zero and non-zero numbers when programming. FALSE FALSE Learn how to figure out Boolean Logic

10. Logic Circuits AND it is dark light motion detected upstairs switch landing light NXOR • The above circuit could operate a landing light (you could use OR if they were push switches) downstairs switch Learn how to figure out Boolean Logic

11. Combining Operators • Just like BODMAS or BIDMAS for Maths, there is a correct order to perform AND and OR • AND is often written as a dot – e.g. A AND B could be written as A.B – and is done first, like multiplication in Maths • OR is often written as a + - e.g. A OR B could be written as A+B – and is done second, like addition • e.g. with A OR B AND C you would do the AND first and then the OR • You can also use brackets, e.g. (A OR B) AND C Learn how to figure out Boolean Logic

12. Task • Use the help sheet called “Decoding Binary Numbers” to decode the secret message that has been emailed to you. • Copy and paste the email into a Word document and write the real message underneath. Learn how to decode binary numbers

13. Extension Task • Play the Binary Game yourself and see what score you get: forums.cisco.com/CertCom/game/binary_game.swf Learn how to decode binary numbers

14. Today’s Learning Objective • “Learn how to decode binary numbers”. • Put  or  onto your Self Assessment sheet to show whether or not you have achieved today’s learning objective.

15. AND it is dark light motion detected upstairs switch landing light NXOR downstairs switch • The above circuit could operate a landing light (you could use OR if they were push switches)