Egyptian Numerals Conversions

Posted on March 25, 2021 by Administrator Posted in Computer Science, Computing Concepts

In this blog post we will investigate how Egyptians used to write numbers (Ancient Egypt civilisation) and we will use an algorithm to convert decimal numbers into Egyptians numerals.

By completing this challenge, we will compare two different numerical notations:

Positional Notation (a.k.a Place Value Notation) as used by the decimal system (Hindu-Arabic numeral system)
Additive Notation as used by the Ancient Egypt numeral system as well as the Roman numeral system

Positional Notation (a.k.a Place Value Notation)

The notation we use nowadays when writing decimal numbers is based on the Hindu-Arabic numeral systems where each digit of a number has a value corresponding to the value of the digit multiplied by a factor (a power of 10) determined by the position of the digit in the number.

For instance:

With this number, the least significant digit (on the right: 5) represents units, the next digit (2) represents tens, the next digit (4) represents hundreds and the most significant digit (on the left: 3) represents thousands.

This notation is called a Place Value notation because the value of a digit varies based on its position/place in the number. So, for instance the digit 3 in the above number (3,425) has a value of 3,000 but in the number 2,536 its value is now 30.

Additive Notation

Ancient civilisations such as the Ancient Egypt Civilisation used a different notation to represent numbers. In the additive notation each symbol has a unique value which does not change based on its position in the number. The value of a number if calculated by adding the value of each of the symbols used in this number.

So, let’s investigate the symbols (Hieroglyphs) used in Ancient Egypt to represent numbers:

Symbol/Hieroglyph	𓏺	𓎆	𓏲	𓆼	𓂭	𓆐	𓁨
Value	1	10	100	1,000	10,000	100,000	1,000,000

Using the above symbols we can easily calculate the value of a number as follows:

Using this approach can you convert the following numbers in decimal?

Online conversions

Use our online convertor to check your answers…

Roman Numerals: Additive and Subtractive Notation

Roman Numerals use an additive notation combined with a subtractive notation.
The symbols used in Roman numerals are as follows:

Symbol	M	D	C	L	X	V	I
Value	1,000	500	100	50	10	5	1

Using this approach can you convert the following numbers in decimal?

Online conversions

Use our online convertor to check your answers…

UPC Barcodes

Posted on March 23, 2021 by Administrator Posted in Computer Science, Computing Concepts, Cryptography

A barcode is a visual representation of data that can easily be read by an optical barcode scanner/reader. Barcodes are used to facilitate and speed up the identification of different types of products. Using a barcode reader speed up the input/data entry process and and is a more reliable method generating less data entry errors than when a product code is entered manually.

There are different types/formats of barcodes such as ISBN barcodes used to identify books/publications or UPC (Universal Product Codes) or EAN (European Article Number) barcodes to uniquely identify products/trade items.

You can visit this wikipedia page to find out a about a range of linear barcodes (1D) and matrix barcodes (2D) such as QR codes.

UPC Encoding

Let’s focus on UPC barcodes. UPC barcodes are widely used in America, Europe, Australia, New Zealand, and other countries for tracking trade items in stores. A UPC barcode is a linear barcode consisting of a series of black and white stripes of different thickness. They are used to encode 12 numerical digits in two groups/segments of 6 digits: the left segment and the right segments.

A UPC barcode is delimited using guards: specific patterns that appear at the start, at the end and also in the middle of the barcode to separate the left and right segment:

With UPC barcodes, the first and last digits are often displayed before and after the left and right hand side guards of the barcode (even though the stripes representing these digits are still within the guards patterns):

Each numerical digit is encoded using a specific pattern. However the patterns used are different on the left and right segments. This feature is necessary to ensure that barcode readers can read a barcode in both directions (in case a barcode is presented upside down). In fact the patterns used on the right segments for each digit are the exact opposite to the patterns used for the digits on the left segment. Each pattern is seven stripes wide:

Decoding a barcode

Use the information provided above to decode the following barcodes and check your UPC codes using barcodespider.com to identify the corresponding products.

#	Barcode	Product	UPC?
#1		Raspberry Pi Model 3B
#2		32GB SD Card
#3		Optical Cordless Mouse

Barcode Generator

Check digits

The last digit of a UPC-A barcode is the check digit. A check digit is used to minimise the risk of errors when scanning a barcode. A check digit calculation is used to confirm that a barcode being scanned is valid or not. You can read more about check digit validation on this blog post.

Perseverance’s Parachute Secret Message Encoder

Posted on March 18, 2021 by Administrator Posted in Computer Science, Computing Concepts, Cryptography, Solved Challenges

On February 18, 2020, NASA successfully landed its rover “Perseverance” on planet Mars. To slow down its descent the rover deployed a parachute. The whole operation was filmed and relayed on the Internet. You can watch the official NASA video on youtube.

The internet community quickly noticed the unusual red and white pattern on the parachute resembling the pattern of a barcode:

Source: NASA/JPL-Caltech

In just a few hours, internauts successfully decoded the “secret message” encoded on the parachute. The message read:

“Dare Mighty Things – 34° 11’58” N 118° 10’31 W”

The numbers in this message correspond to the GPS coordinates of the JPL centre (NASA’s Jet Propulsion Laboratory in located in California), whereas “Dare Mighty Things” is the moto used by JPL.

The encoding process is fairly basic:

The 3 concentric inner rings of the parachute represent one word per ring.
Each character of a given word is represented by a number between 1 and 26 corresponding to its position in the alphabet (A is 1, B is 2, up to Z is 26). These numbers are then converted in binary using 7 bits per character followed by “000” as a delimiter between each character.
E.g. The word DARE is encoded in the inner circle. D=4 A=1 R=18 E=5 becomes in binary:
000-0000100-000-0000001-000-0010010-000-0000101-000
The pattern consists of red and white stripes. A white stripe represent a 0, a red stripe a 1. e.g.

Character	Value	64	32	16	8	4	2	1
D	4	0	0	0	0	1	0	0
A	1	0	0	0	0	0	0	1
R	18	0	0	1	0	0	1	0
E	5	0	0	0	0	1	0	1

The message is encoded clockwise.
A ring consists of 80 stripes (to encode a word of a maximum of 8 characters. All unused stripes appear as a large red block.
Using a similar approach, the outer ring of the parachute is used to encore the GPS coordinates in DMS (Degrees, Minutes, Seconds) format. Each coordinate being encoded in binary using 7-bits.

Let’s apply this to decode NASA’s Perseverance Secret Message:

“Dare Mighty Things – 34° 11’58” N 118° 10’31 W”

Online Encoder

You can use our online secret message encoder to design your own parachute. To do so you will need to:

Choose 3 words of maximum 8 letters each.
Identify the GPS coordinates (using the DMS format: Degrees, Minutes, Seconds) of a given location on planet earth. (You can use this website (www.gps-coordinates.net) to retrieve the required coordinates)
Input this information below to generate your parachute. You can then print or take a screenshot of your parachute.

Decoding Tasks

We have encoded a few messages using the same approach. Well you be able to decode these messages and identify the exact location using the following parachutes?

Parachute #1: Somewhere in Europe…

Parachute #2: Somewhere in America…

Parachute #3: Somewhere in Asia…

To complete this activity on paper, you can download and print the worksheet (PDF file).

Solution...

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➤ Members' Area

Tagged with: cryptography, encryption

Mars Perseverance Rover

Posted on March 16, 2021 by Administrator Posted in Computer Science, Python - Beginner, Python - Intermediate, Python Challenges, Solved Challenges

On February 18, 2020, NASA’s rover called “Perseverance” successfully landed on Mars. The mission of this high-tech 6-wheel rover is to explore the surrounding areas, analyse the Martian soil on different locations, take high definition pictures as well as audio recordings. The ultimate hope for NASA is that this rover may find evidence that there was once a form of life on planet Mars. You can read more about this rover on the official NASA website.

The rover and all its various sensors and electromechanical devices are controlled using a range of preloaded algorithms. New algorithms can also be transmitted to the rover via ultra high frequency (UHF) radio transmission.

The NASA is asking you to write a few new algorithms that will be used to explore a new specific zone on planet Mars. You will have to design, implement and test 7 algorithms to compete the different missions set by NASA. You will be able to test your algorithms using our Mars Perseverance Simulator Environment (MPSE).

Mission 1Mission 2Mission 3Mission 4Mission 5Mission 6Mission 7

Mission 1: Delimiting the area

The area, the rover will cover is a square of 400m by 400m situated in the North-West area of the Jezero Crater. Your first mission is to implement an algorithm to direct the rover around the perimeter of this area: The path to follow has been traced in white on the Mars Perseverance Simulator Environment.

mars-path-1

The code used to initialise the rover for this mission has already been completed for you (line 1 to 20) and you will not need to update this code. However, you will need to complete this code from line 22.

Note that the rover can respond to the following instructions:

rover.forward(distance)
rover.left(angle)
rover.right(angle)

For instance, you can try the following code to get you started:

rover.forward(200)
rover.left(45)
rover.forward(100)

Mars Perseverance Simulator Environment (MPSE):

Mission 2: Code Optimisation

The rover being located more than 240 million km away from NASA’s Control Centre (on planet Earth!), the radio transmissions needs to be optimised by reducing the quantity of data that needs to be transmitted to the rover.

NASA would hence like you to review the code you produced to complete mission 1 to see if it would be possible to provide a shorter algorithm (in other words to reduce the number of lines in the code needed to direct the rover around the perimeter).

mars-path-1

To do so you will need to use a for loop which will enable you to reduce the number of repeating instructions in your code.

For instance, you can try the following code to get you started:

for i in range(3):
   rover.forward(200)
   rover.left(120)

You will need to adapt your code from mission to make effective use of a for loop, and hence reduce the amount of data to be transmitted from planet Earth to planet Mars.

Mars Perseverance Simulator Environment (MPSE):

Mission 3: Exploring the whole area

NASA would like to create a detailed surface map of the delimited area. To do so, it needs the rover to circulate through the whole area. The path to follow has been highlighted in white in the simulator environment. Write an algorithm to direct the rover alongside this path. Make sure your code is optimised to limit the amount of data to transfer across to the rover.

mars-path-2

Mars Perseverance Simulator Environment (MPSE):

Mission 4: Alternative Path

NASA would like to investigate an alternative path to cover the whole area. The path to follow has been highlighted in white in the simulator environment. Once again, your mission is to write an algorithm to direct the rover alongside this path. Make sure your code is optimised to limit the amount of data to transfer across to the rover.

mars-path-3

Mars Perseverance Simulator Environment (MPSE):

Mission 5: Finding Craters

While completing the full map of the area, the rover identified three small craters. NASA would like you to write an algorithm to visit these three craters one at a time using the information provided on the highlighted path.

mars-path-4

Mars Perseverance Simulator Environment (MPSE):

Mission 6: Finding Craters near a rift!

NASA would like the rover to explore three additional craters. However these are located next to a rift. NASA would like you to write an algorithm to visit these three craters one at a time. You will have to do so making sure the rover does not fall into the rift!

mars-path-6

Mars Perseverance Simulator Environment (MPSE):

Mission 6: Giant Crater Exploration

Finally, NASA would like to explore one giant crater by taking the rover all around the crater. You will need to write an optimised algorithm to go around the crater using the information provided on the highlighted path.

mars-path-5

Remember: To optimise your algorithm, you should make use of a for loop. e.g.

for i in range(3):
   rover.forward(200)
   rover.left(120)

Mars Perseverance Simulator Environment (MPSE):

Solution...

The solution for this challenge is available to full members!
Find out how to become a member:
➤ Members' Area

Tagged with: Python Turtle

Wanted Poster (CSS Task)

Posted on March 10, 2021 by Administrator Posted in Computer Science, HTML, CSS & JavaScript, Solved Challenges

For this challenge we will create a Wanted Poster using a range of HTML and CSS skills.

CSS Selectors & CSS Properties

In order to complete this challenge, you need a good understanding of how CSS selectors work. You can learn about CSS selectors on w3schools.com.

To customise the look & feel of your poster using CSS code, you will use different types of selectors such as:

TAG
.class
#id
element child-element
element child-element:first-child

In this challenge we will use various CSS properties such as:

font-family:
font-size:
color:
font-weight:
font-style:
text-align:
padding:
margin:
background-image:
etc.

You can learn more about all these CSS properties on w3schools.com.

CSS Box Model

To understand how margin, borders and padding works you need to understand the CSS Box Model. Click on this picture to find out more:

HTML & CSS Code

To complete this challenge, you will need to edit the code below by clicking on the top-right button “Edit on Codepen”.

See the Pen
WANTED Poster by 101 Computing (@101Computing)
on CodePen.

Note that this script will the following three pictures:

Mugshot Image: https://www.101computing.net/wp/wp-content/uploads/mugshot.png
Wood Texture: https://www.101computing.net/wp/wp-content/uploads/wood.jpg
Parchment Texture: https://www.101computing.net/wp/wp-content/uploads/parchment.jpg

Instructions

Final Poster Preview

This is what your poster should look like at the end of this task:

Solution...

The solution for this challenge is available to full members!
Find out how to become a member:
➤ Members' Area

Tagged with: CSS

Binary Search Tree Implementation

Posted on March 4, 2021 by Administrator Posted in Algorithms, Computer Science, Computing Concepts, OOP Concepts, Python - Advanced, Python Challenges

Binary Search Trees are an effective solution to store data in a computer program and perform a binary search.

The benefits of using a BST (Binary Search Tree) data structure is that data can be added to the tree as it is received and the BST structure will store it effectively so that:

A sorted list of the data can be generated using an in-order traversal of the tree.
A binary search can be easily implemented making this data structure very effective to access/search through. A binary search has an O(log(n)) notation for time complexity.
Data/Nodes can easily be added or removed from the tree without having to rearrange the whole data structure

The characteristics of a Binary Search Tree are as follows:

Being a type of tree data structure, it consists of nodes and branches with a parent/child relationship between nodes,
Each node can have a maximum of two children node: The left child and the right child,
The left subtree of a node contains only nodes with values lesser than the node’s value.
The right subtree of a node contains only nodes with values greater than the node’s value.

When a new node is added to the tree, if added in a way that do not conflict with the 4 characteristics listed above.

Capital Cities BSTRandom Numbers BST

Can you add the following cities to this Binary Search Tree:

Cape Town

Seoul

How would you then remove New-York from this BST tree?

Can you add the following numbers to this Binary Search Tree:

How would you then remove number 28 from this BST tree?

Depth-first Traversal Of Binary Search Tree

The three depth-first traversal methods to read through all the nodes of a BST are:

Pre-order Traversal
In-order Traversal
Post-order Traversal

The in-order traversal is frequently used as it retrieves the nodes in order: alphabetical order or numerical order depending on the data types of the nodes’ values. This remains the case even if the nodes were added to the tree in a completely different order.

You can read more and practise your understanding of the different breadth-first and depth-first traversals of tree on this blog post as well as investigate their algorithms (in pseudocode).

Python Implementation

Different approaches can be used to implement a Binary Search Tree in Pythons. It can be achieved by combining different data structures (e.g. hash tables and lists). However in this blog post we will implement our BST data structure using Object Oriented concepts (OOP Programming).

First we will create a Node class to store the following 3 values:

The value of the node,
A pointer to the left node,
A pointer to the right node.

Here is the Python code for the Node class:

class Node:
  def __init__(self, value, left=None, right=None):
    self.value = value
    self.left = left
    self.right = right

We will then create a Tree class.
The main property of our Tree class will be its root Node. We will then implement a range of methods as follows:

insert() – Insert a new value/node in the correct position within the BST,
delete() – Find a node based on its value and remove it from the tree,
find() – Perform a Binary Search on the tree to find a specific Node based on its value,
preorder_traversal() – Perform and output the result of a pre-order traversal of the tree,
inorder_traversal() – Perform and output the result of an in-order traversal of the tree,
postorder_traversal() – Perform and output the result of a post-order traversal of the tree,
draw() – Perform and output the result of a post-order traversal of the tree.

You can investigate the Python code used to implement all of the above 7 methods in the trinket below.

Python Code

Use the following Python code to build your own BST, adding one value at a time. You will be able to visualise your tree on screen and view the outputs of the three depth-first traversal methods:

Python Challenge

Add two methods to the Tree class as follows:

saveToFile() – Save the whole content of the binary tree in a text file. You will have to investigate the best format to do so. For instance you could save the BST data structure as a JSON file or an XML file.

loadFromFile() – Load the whole content of the binary tree from a text file (using the JSON or XML formats).

Tagged with: Binary Tree

Lossless Compression: Huffman Coding Algorithm

Posted on March 4, 2021 by Administrator Posted in A Level Concepts, Algorithms, Computer Science, Computing Concepts, Python - Advanced, Python Challenges, Solved Challenges

The Huffman Coding algorithm is used to implement lossless compression. For the purpose of this blog post, we will investigate how this algorithm can be implemented to encode/compress textual information.

The principle of this algorithm is to replace each character (symbols) of a piece of text with a unique binary code. However the codes generated may have different lengths. In order to optimise the compression process, the idea behind the Huffman Coding approach is to associate shorter codes to the most frequently used symbols and longer codes to the less frequently used symbols.

So let’s consider the following message which consists of 20 characters:

Note that the Huffman coding algorithm is normally used to compress larger amount of data and would not really be used to compress such a small message!

Step 1: Frequency Analysis

The first step of the Huffman Coding algorithm is to complete a frequency analysis of this message by:

Identifying all the symbols used in the message,
Identifying their weights (or frequencies) by counting their occurrences (the number of times they appear) within the message,
Sorting this list of symbols in ascending order of their weights.

Step 2: Organising Symbols as a Binary Tree

To do so each symbol becomes a node storing the symbol itself and its weight.
Then the tree is constructed through the following iterative process:

Step 3: Generating the Huffman Codes

Using the above tree, we can now identify the Huffman code for each symbol (leaves of the tree. This is done by highlighting the path from the Root node of the tree to the required leave/symbol. The labels of each branch are concatenated to form the Huffman code for the symbol.

As you can see, most frequent symbols are closer to the root node of the tree, resulting in shorter Huffman codes.

The resulting Huffman Codes for our message are:

Encoding the message

We can now encode the message by replacing each symbol with its matching Huffman code.

Encoded/compressed message:

010100111101000011111011010111100001101111010000111100101000110

Python Implementation

Here is a Python implementation of the Huffman Coding algorithm:

Python Task

To complete the above code, we need an extra method to our HuffmanEncoder class called decode().

This method should take two parameters:

An encoded message (Binary string)
the Huffman codes used to encode the message (Using a python dictionary)

Using the above information, the decode() method would then decode the message one character at a time.

Solution...

The solution for this challenge is available to full members!
Find out how to become a member:
➤ Members' Area

Tagged with: Binary Tree

Average night’s sleep survey

Posted on March 2, 2021 by Administrator Posted in Computer Science, Python - Intermediate, Python Challenges

For her PSHE homework on the importance of sleep, Clarisse has decided to collect data from pupils of different year groups from her school. She will do so using a short survey.

The aim of the survey will be to find out, on average, how many hours of sleep students have per night and to compare these findings with the recommended number of hours for high school students.

According to the National Sleep Foundation, the recommended numbers of hours of sleep per night are as follows:

Age Group	Recommended Sleep
School-aged Children 6-13 years	9 to 11 hours
Teenagers 14-17 years	8 to 10 hours
Young Adults 18-25 years	7 to 9 hours

Clarisse’s survey will only have one question: How many hours do you sleep each night?

To help her calculate the resulting average number of hours of sleep per night she would like you to write a Python program based on the following flowchart:

This algorithm is based on:

Algorithm Trace Table

To gain a better understanding of how this algorithm works you will need to complete the following trace table considering the following user inputs:

8 , y , 10 , y , 12 , n

Line Number	carryOn	totalHours	numberOfStudents	carryOn ==”y”	hours	average	OUTPUT
1	“y”
2		0
3			0
4				True
5					8
6		8
7			1
8						8
9							8
10	“y”
4				True
5					10
6		18
…

Python Code

Use the above flowchart to complete the Python code for this program:

Extension Task

Write a new program to make suitable recommendations to school children on whether or not they are spending enough time sleeping per night. Your program should:

Ask for the name and the age of the end-user,
Ask for the number of hours they spend sleeping each night (on average),
Compare this number of hours with the recommended hours for their age category,
Display an approriate message to say whether:
- They are not spending enough time sleeping per night,
- They are spending the recommended amount of time sleeping per night,
- They are spending more than the recommended amount of time sleeping per night!

Your algorithm will be based on:

As a reminder, the recommended numbers of hours of sleep per night are as follows:

Age Group	Recommended Sleep
School-aged Children 6-13 years	9 to 11 hours
Teenagers 14-17 years	8 to 10 hours
Young Adults 18-25 years	7 to 9 hours

Testing

Create a test plan to test your program. Make sure to include valid, boundary, invalid and erroneous test data in your test plan: (click on the … to add your own data)

Test #	Input Values:	Type of test	Expected Output	Actual Output
#1	Age: 12 Number of Hours: 10	Valid Test	You are spending the recommended amount of time sleeping per night.
#2	Age: … Number of Hours: …	Valid Test	…
#3	Age: … Number of Hours: …	Invalid Test	…
#4	Age: … Number of Hours: …	Invalid Test	…
#5	Age: … Number of Hours: …	Boundary Test	…
#6	Age: … Number of Hours: …	Boundary Test	…
#7	Age: … Number of Hours: …	Erroneous Test	…
#8	Age: … Number of Hours: …	Erroneous Test	…

Tagged with: Flowchart, iteration, Trace Table

Reverse Polish Notation Parser

Posted on March 1, 2021 by Administrator Posted in A Level Concepts, Computer Science, Computing Concepts, Python - Advanced, Python Challenges

Reverse Polish notation (RPN), also known as Polish postfix notation or simply postfix notation, is a mathematical notation in which operators follow their operands. This notation is an alternative notation to the standard infix notation in which operators are located between their operands or to the prefix Polish notation (PN), in which operators precede their operands.

Note that the description “Polish” refers to the nationality of logician Jan Łukasiewicz, who invented Polish notation in 1924

Prefix Notation (a.k.a. Polish Notation)	Infix Notation	Postfix Notation (a.k.a. Reverse Polish Notation)
+ 2 5	2 + 5	2 5 +

Binary Expression Trees

The Polish Notations (prefix or postfix) are used by programming language interpreters where Boolean and arithmetic expressions are parsed into abstract syntax trees. You can find out more about the use of binary trees to store Boolean and arithmetic expressions and about the pre-order, in-order and post-order depth-first traversals of a binary tree.

The use of binary expression trees can be used to facilitate the conversion of an expression from a more intuitive infix notation to either a prefix (RPN) notation or postfix (PN) notation.

The Shunting-Yard Algorithm

Edsger W. Dijkstra invented the shunting-yard algorithm to convert infix expressions to postfix expressions (RPN). The name comes from the fact that the algorithm’s operation resembles that of a railroad shunting yard.

Why use the prefix notation or postfix notations?

The main benefit of both the Polish Notation and of the Reverse Polish Notation over the infix notation is that they do not require the use of parentheses as long as each operator has a fixed number of operands.

For instance:

Prefix Notation (a.k.a. Polish Notation)	Infix Notation	Postfix Notation (a.k.a. Reverse Polish Notation)
x + 3 4 5	(3 + 4) x 5	3 4 + 5 x

As a result, entering an expression using the Polish Notations (PN or RPN) is quicker and would lead to less errors even though it may appear less intuitive to start with than the infix notation.

The reverse Polish scheme was first introduced in 1954 by Arthur Burks, Don Warren, and Jesse Wright and was later on reinvented by Friedrich L. Bauer and Edsger W. Dijkstra in the early 1960s in order to reduce computer memory access by using a stack to evaluate a RPN expression.

Using a Stack to evaluate a RPN expression

The following Python code demonstrated the use of a Stack data structure to evaluate/parse an expression using the Reverse Polish Notation.

You can retrace the steps from this algorithm using the following arithmetic expressions:

Expression #1Expression #2Expression #3Expression #4Expression #5

Operand Stack:

Expression:

Operand 1:
Operand 2:
Operator:
Result:

Operand Stack:

Expression:

Operand 1:
Operand 2:
Operator:
Result:

Operand Stack:

Expression:

Operand 1:
Operand 2:
Operator:
Result:

Operand Stack:

Expression:

Operand 1:
Operand 2:
Operator:
Result:

Operand Stack:

Expression:

Operand 1:
Operand 2:
Operator:
Result:

Truth Table Generator (Using Python)

Posted on March 1, 2021 by Administrator Posted in Computer Science, Computing Concepts, Python - Intermediate, Python Challenges

The purpose of this blog post is to write a Python script that will interpret a Boolean expression and output its full Truth Table.

Boolean Expressions & Truth Tables

Before attempting this challenge, you should test your understanding of Boolean expressions, logic gates diagrams and truth tables by competing this online quiz:
Online QuizBoolean Expressions, Logic Gates Diagrams and Truth Tables

Python Bitwise Operators

To implement a Python script than can interpret a Boolean expression we will the following bitwise operators:

Bitwise Operator	Example	Meaning
&	a & b	Bitwise AND
\|	a \| b	Bitwise OR
^	a ^ b	Bitwise XOR
~	~a	Bitwise NOT

Note that in Python, the following two bitwise operators can also be used to perform a bitwise left shift or right shift:

Bitwise Operator	Example	Meaning
<<	a << n	Bitwise left shift by n places
>>	a >> n	Bitwise right shift by n places

Python Code (Solution)

Here is the Python code for our Truth Table Generator function truthTable() which takes two parameters:

A Boolean expression: e.g. A AND NOT (B OR C)
The number of inputs: either 2, 3 or 4: A, B, C and D

Your Task

Write an additional function to perform a bitwise left shift or a bitwise right shift using the bitwise operators << and >>.

Check that performing a left shift by n place(s) is equivalent to multiplying a number by 2ⁿ.

For instance 5 << 3 is the same as 5×2³ = 40.

Check that performing a right shift by n place(s) is equivalent to dividing a number by 2ⁿ (whole division).

For instance 40 >> 3 is the same as 40/2³ = 5.

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Books Corner

Positional Notation (a.k.a Place Value Notation)

Additive Notation

Online conversions

Roman Numerals: Additive and Subtractive Notation

Online conversions

UPC Encoding

Decoding a barcode

Barcode Generator

Check digits

Online Encoder

Decoding Tasks

Solution...

Mission 1: Delimiting the area

Mission 2: Code Optimisation

Mission 3: Exploring the whole area

Mission 4: Alternative Path

Mission 5: Finding Craters

Mission 6: Finding Craters near a rift!

Mission 6: Giant Crater Exploration

Solution...

CSS Selectors & CSS Properties

CSS Box Model

HTML & CSS Code

Instructions

Final Poster Preview

Solution...

Depth-first Traversal Of Binary Search Tree

Python Implementation

Python Code

Python Challenge

Step 1: Frequency Analysis

Step 2: Organising Symbols as a Binary Tree

Step 3: Generating the Huffman Codes

Encoding the message

Python Implementation

Python Task

Solution...

Algorithm Trace Table

Python Code

Extension Task

Testing

Binary Expression Trees

The Shunting-Yard Algorithm

Why use the prefix notation or postfix notations?

Using a Stack to evaluate a RPN expression

Boolean Expressions & Truth Tables

Python Bitwise Operators

Python Code (Solution)

Your Task

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