Boolean Operators

Starter - Riddles
AND
OR
NOT
Combining Logic Gates
Practice
Plenary

Knights and Knaves Riddle 1

You have been shipwrecked on the Knights and Knaves island. On this island there are only three types of people:

Knights, who always tell the truth.
Knaves, who always lie.
Spies, who can either tell the truth or lie.

You are walking down a footpath and are approached by two people Amy and Bill.

Bob says “At least one of use is a Knave.”
You know that one is a knight and one is a knave.

Who is Amy and who is Bill?

Knights and Knaves Riddle 2

You are sunbathing on the beach when you are approached by three people.

You know that one is a knight, one is a knave and one is a spy. However, you don’t know who is who.

Alfred says “Charlie is a Knave”
Beatrix says “Alfred is a Knight”
Charlie says “I am a spy”

Who is who?

AND Gates

AND Gates

Boolean AND gates are one most common logic gates used in programming. The work by returning True, only if both inputs are true.

Truth Table

Input A	Input B	Output
FALSE	FALSE	FALSE
FALSE	TRUE	FALSE
TRUE	FALSE	FALSE
TRUE	TRUE	TRUE

Python AND gates

In python we can use and gates easily within our programs(in fact you probably already have!).

	print(True and True)
	print(True and False)
	print(False and False)

view raw andgate.py hosted with

by GitHub

The example above is a pretty pointless example! Below are some more sensible uses of And gates…

Example – Password checker

In login systems both the username and password need to be correct in order for a user to be gained access.

	username = input("Please enter your username:")
	password = input("Please enter your password:")
	if username == "aladin" and password == "abracadabra":
	print("You can enter the cave of many shiny treasures")

view raw aladdinscave.py hosted with

by GitHub

Practice Activities

Practice 1

Write a python program that asks the users for..

Practice 2

Use comparison operators with and

OR Gates

or gate python

OR Gates

OR gates are another commonly used gate. They are less picky that AND gates – if either of the inputs is True (or both) then the gate will output True.

OR Gate Truth Table

Input A	Input B	Output
FALSE	FALSE	FALSE
FALSE	TRUE	TRUE
TRUE	FALSE	TRUE
TRUE	TRUE	TRUE

Python or gates

Or gates are easy to use in Python. Here is a simple example.

	fav = input("What's your favourite color?")
	if fav == "green" or fav == "brown":
	print("That's one of my favourite colors too!")

view raw favcolororgateexample.py hosted with

by GitHub

Practice

Practice 3

Practice 4

NOT Gates

not gate

Not Gates

Not gates are the simplest form of gate. It’s job is simply to reserve whatever input it is given.

If the input is True, the output is False.
If the input is False, the output is True.

Not gate Truth Table

Input A	Output
FALSE	TRUE
TRUE	FALSE

Python NOT gates

Not gates are commonly used in Python code. Here is a simple example:

	movie = input("What's your favourite movie?")
	if not movie == "Monty Python's Life of Brian":
	print("You father was a hamster and your mother smelled of elderberries!")

view raw montypythonnotgateexample.py hosted with

by GitHub

Practice 3

Practice 5

Practice 6

Combining Logic Gates

Input 1 AND ( Input 2 OR Input 2)

As well as using Boolean Gates on their own you can also combine logic gates together. Order to work out how to solve combined logic gates you need to solve each of the left hand gates first, and then feed the outputs to the next gate along the line.

Example 1 - NOT with AND gate

Example 1 – NOT with AND gate (NAND gate)

NAND gate

Truth Table

Have a go at writing out the truth table for this combined gate.

Input 1	Input 2	Output
FALSE	FALSE	??
FALSE	TRUE	??
TRUE	FALSE	??
TRUE	TRUE	??

Answer

Input 1	Input 2	Output
FALSE	FALSE	TRUE
FALSE	TRUE	TRUE
TRUE	FALSE	TRUE
TRUE	TRUE	FALSE

Example 2 - Combined OR gates

OR OR gate

Truth Table

Have a go at writing the truth table for this combined OR gate.

Input 1	Input 2	Input 3
FALSE	FALSE	FALSE
FALSE	FALSE	TRUE
FALSE	TRUE	FALSE
FALSE	TRUE	TRUE
TRUE	FALSE	FALSE
TRUE	FALSE	TRUE
TRUE	TRUE	FALSE
TRUE	TRUE	TRUE

Answer

Input 1	Input 2	Input 3	Output
FALSE	FALSE	FALSE	FALSE
FALSE	FALSE	TRUE	TRUE
FALSE	TRUE	FALSE	TRUE
FALSE	TRUE	TRUE	TRUE
TRUE	FALSE	FALSE	TRUE
TRUE	FALSE	TRUE	TRUE
TRUE	TRUE	FALSE	TRUE
TRUE	TRUE	TRUE	TRUE

Combining gates using Python

Combining gates in Python

If you ever need to combine logic gates in Python, the easiest way to do so is to use brackets. This makes writing and reading the gates much easier.

print(not (True and True))

view raw pythoncompoundgateexample1.py hosted with

by GitHub

In the example above an AND gate is added, with the output feeding in to a NOT gate.

Practice - Python Questions

Take a look at these statements and work out whether they will output True or False!

Python Questions

True and True
True and False
True or True
False or False
False == True
False != False
not True
(True and True) and True
(True and False) and True
(False or False) or True

Practice - Logic Symbols

Logic Symbols

qn1

qn2

qn3

qn4

qn5

http://learnpythonthehardway.org/book/ex28.html