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• What we mean by truth values
• What we mean by Boolean Operators
• How to use AND, OR and NOT
• How computers use these ideas!
Some statements can be seen to be either true or false
For example…
Not bad
TRUE
• you are in a Computing lesson
Steve but my
TRUE
Hello
how background
• this slide has
a Bill
white
hard drive’s
ya doin?
playing up a
FALSE
• it is the weekend
bit.
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
Learn how to figure out Boolean Logic
• 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
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 FALSE
• this slide’s background is NOT blue FALSE
• it is NOT Friday
TRUE
Learn how to figure out Boolean Logic
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
Learn how to figure out Boolean Logic
FALSE
TRUE
TRUE
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 whiteAND the text is black
• it is Monday AND this is a Computing lesson
Learn how to figure out Boolean Logic
FALSE
FALSE
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
FALSE
– this slide is white AND NOT white
FALSE
• Think about this next time you hear someone
say, “…whether or not…”!
Learn how to figure out Boolean Logic
• 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
– false = off = 0
FALSE
• False and true are also often represented by
zero and non-zero numbers when programming.
Learn how to figure out Boolean Logic
it is dark
motion detected
AND
light
NXOR
landing
light
upstairs switch
downstairs switch
• The above circuit could operate a landing
light (you could use OR if they were push
switches)
Learn how to figure out Boolean Logic
• 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
• 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
• 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
• “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.
it is dark
motion detected
AND
light
NXOR
landing
light
upstairs switch
downstairs switch
• The above circuit could operate a landing
light (you could use OR if they were push
switches)