1. 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!

2. 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

3. 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

4. Boolean Operators
Arithmetic operators, e.g. +, -, X and ÷, tell us how to combine two numbers
Everyone agrees on the results – e.g = 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

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 Sunday
FALSE
TRUE

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 Friday OR this is a Computing lesson
FALSE
TRUE

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

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

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.

10. 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)

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