PC Basics

Boolean Logic and

Operators

PC Basics

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!

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Truth Values

Learn how to figure out Boolean Logic

Hello Bill how ya doin?

Not bad Steve but my hard drive’s

playing up a bit.

Some statements can be seen to be either true or falseFor example…• you are in a Computing lesson• this slide has a white background• it is the weekendOther statements are a matter of opinion, e.g.• it’s warm today• that’s a nice hat you’re wearingFor this lesson, we will only considered statements about which everyone will agree

TRUE

TRUE

FALSE

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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

LOPC Basics

NOT

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 = trueFor example…• you are NOT in a Computing lesson• this slide’s background is NOT blue• it is NOT Friday

FALSE

FALSE

TRUE

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OR

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 = trueFor 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

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AND

Learn how to figure out Boolean Logic

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 = trueFor 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

FALSE

FALSE

TRUE

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Is Anything Always True?

Learn how to figure out Boolean Logic

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

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What About Computers?

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 = off = 0

• False and true are also often represented by zero and non-zero numbers when programming.

FALSE

FALSE

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Logic Circuits

Learn how to figure out Boolean Logic

ANDit is dark

motion detectedlight

NXOR landing light

upstairs switch

downstairs switch

• The above circuit could operate a landing light (you could use OR if they were push switches)

LOPC Basics

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

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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

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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

PC Basics

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.

PC Basics

ANDit is dark

motion detectedlight

NXOR landing light

upstairs switch

downstairs switch

• The above circuit could operate a landing light (you could use OR if they were push switches)