Boolean Logic In today’s lesson we will look at: what we mean by truth values what we mean by Boolean Operators how to use AND, OR and NOT how computers use these ideas!

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 pale blue background it is Sunday 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 consider statements about which everyone will agree TRUE FALSE

Mathematical Truths They might involve a variable, e.g. if x = 10: Most of the “truths” that you are likely to come across as a programmer will be mathematical. These are usually easier to determine, e.g. 1 is equal to 1 2 is more than 5 3 is NOT equal to 5 They might involve a variable, e.g. if x = 10: x is equal to 1 x is more than 5 x is NOT equal to 5 TRUE FALSE FALSE TRUE

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

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 Sunday FALSE TRUE

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 Friday OR this is a Computing lesson FALSE TRUE

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 blue AND the text is orange it is Friday AND this is a Computing lesson FALSE TRUE

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 blue AND NOT blue Think about this next time you hear someone say, “…whether or not…”! TRUE FALSE

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.

Logic Circuits The above circuit could operate a security light AND it is dark motion detected light The above circuit could operate a security light OR landing light upstairs switch downstairs switch The above circuit could operate a landing light (if push switches were using)

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