QTM 350 - Data Science Computing
Lecture 02: Computational Literacy
22 January, 2025
Course information
- Instructor: Danilo Freire
- Lectures: Mondays and Wednesdays, 2:30-3:45pm
- Office hours: At any time, just send me an email in advance
- Please remember to check the course repository regularly for updates and announcements 😉
The first computers
- Historically, a computer was a person who makes calculations, especially with a calculating machine
- To do calculations we use numbers. How to represent them?
- Fingers
- Pebbles
- Strings (Inca Khipu)
- Abacus
Video: How to use an abacus
Four-species mechanical calculators
The first mechanical calculator capable of performing all four basic arithmetic operations (addition, subtraction, multiplication, and division)
Invented by Gottfried Wilhelm Leibniz in 1694
If you took a statistics course before the late 1970s, you likely used this type of mechanical calculator for your computations
Silicon-based computers
The 1970s marked the transition from mechanical to electronic:
- Transistors act as switches for electronic signals
- Integrated circuits combine multiple transistors on a single chip
- Microprocessors are integrated circuits that contain the functions of a computer’s central processing unit (CPU)
- They follow the Von Neumann architecture
Von Neumann Architecture
- The Von Neumann Architecture stores both program instructions and data together in a slow storage medium, such as a hard disk, and transfers them to faster RAM for execution by the CPU
- This is the basis for almost all modern computers
- When proposed in 1945, this architecture was revolutionary, as programs were previously seen as part of the machine, distinct from the data they operated on
Von Neumann Architecture
- Advantages:
- Efficient memory use, with less need for separate areas
- Flexibility in data storage and manipulation
- Simplicity in design and operation
- Disadvantages:
- Von Neumann bottleneck: Limits computing performance due to sequential processing of instructions and data through a single bus
- The CPU often waits for data due to its faster processing speed compared to memory transfer rates
- Harvard architecture is an alternative that separates data and instruction memory
Computers run on 0s and 1s
- Computers represent everything by using 0s and 1s
- Transistors act as switches, with 1 for high voltage level and 0 for low voltage level
- Computers use binary because transistors are easy to fabricate in silicon and can be densely packed on a chip
- But how does this work?
- How can we represent text, images, and videos using only 0s and 1s?
- This leads us to abstraction: representing ideas at different levels of detail by identifying what is essential
- We will use abstraction to translate 0s and 1s to decimal numbers, then translate those numbers to other types
Converting coins to dollars
- We can convert between number systems by translating a value from one system to the other
- For example, the coins on the left represent the same value as $0.87
- Using pictures is clunky. Let’s make a new representation system for coins
Converting coins to dollars
- To represent coins, we will make a number with four digits
- The first represents quarters, the second dimes, the third nickels, and the fourth pennies
- c3102 =
- 3 x $0.25 + 1 x $0.10 + 0 x $0.05 + 2 x $0.01 =
- $0.87
Converting dollars to coins
How do we convert money from dollars to coins? Assume we want to minimise the number of coins used
For example, what is $0.59 in coin representation? Use the same four-digit system: quarters, dimes, nickels, and pennies
$0.59 = 2 x $0.25 + 0 x $0.10 + 1 x $0.05 + 4 x $0.01 = c2014
Images as collections of colours
- What if we want to represent an image? How can we convert that to numbers?
- First, break the image down into a grid of colours, where each dot of color has a distinct hue
- A dot of color in this context is called a pixel
- Now we just need to represent a single color (a pixel) as a number!
Images as collections of colours
RGB colour model
- The RGB colour model is widely used in digital displays
- Each pixel is represented by three numbers, each ranging from 0 to 255
- The first number represents the amount of red, the second the amount of green, and the third the amount of blue
- 00000000 is no r/g/b and 11111111 is very r/g/b!
- You can try different colours here
Number systems – Hexadecimal
What is hexadecimal?
- When we represent values with multiple bytes, it can be hard to distinguish where numbers begin and end
- Hexadecimal is a number system with 16 digits: 0123456789ABCDEF
- It is used to represent binary numbers in a more compact way
- Each hex digit corresponds to 4 binary bits, making it a shorthand for binary:
- 0000 = 0
- 0001 = 1
- 0010 = 2
- …
- 1110 = E
- 1111 = F
Represent text as individual characters
Characters and glyphs
- Next, how do we represent text?
- First, we break it down into smaller parts, like with images. In this case, we can break text down into individual characters
- A character is the smallest component of text, like A, B, or /.
- A glyph is the graphical representation of a character.
- In programming, the display of glyphs is typically handled by GUI (Graphical User Interface) toolkits or font renderers
Represent text as individual characters
Lookup tables
- For example, the text “Hello World” becomes
H, e, l, l, o, space, W, o, r, l, d - Unlike colours, characters do not have a logical connection to numbers
- To represent characters as numbers, we use a lookup table called ASCII
- ASCII stands for American Standard Code for Information Interchange
- As long as every computer uses the same lookup table, computers can always translate a set of numbers into the same set of characters
ASCII is nothing but a simple lookup table
Yes, really!
For basic characters, we can use the encoding system called ASCII. This maps the numbers 0 to 255 to characters. Therefore, one character is represented by one byte
Check it out here: ASCII Table
ASCII is nothing but a simple lookup table
Translation
“Hello World” =
01001000 01100101 01101100 01101100 01101111 00100000 01010111 01101111 01110010 01101100 01100100
Your turn!
Practice Exercise 03
- Translate the following binary into ASCII text:
01011001 01100001 01111001
The genesis of programming
Zuse’s computers
- Konrad Zuse was a German engineer and computer pioneer
- He created the first programmable computer, the Z3, in 1941
- The Z3 was the first computer to use binary arithmetic and read binary instructions from punch tape
- Example: Z4 had 512 bytes of memory
- Zuse also created the first high-level programming language, Plankalkül
What is Assembly language?
- Assembly language is a low-level programming language that allows writing machine code in human-readable text
- Each instruction corresponds to a single machine code instruction
- The first assemblers were human!
- Programmers wrote assembly code, which secretaries transcribed to binary for machine processing
Some curious facts about Assembly!
The Apollo 11 mission to the moon was programmed in assembly language
The code is available here: https://github.com/chrislgarry/Apollo-11 (good luck reading it! 😅)
One of the files is the
BURN_BABY_BURN--MASTER_IGNITION_ROUTINE.agc🔥 🚀But if Assembly is so fast and efficient, why don’t we use it all the time?
Low-level vs high-level languages
- Low-level languages are closer to machine code and are harder to read and write
- High-level languages abstract from hardware details and are portable across different systems
- Compiled Languages: Convert code to binary instructions before execution (e.g.,
C++,Fortran,Go). - Interpreted Languages: Run inside a program that interprets and executes commands immediately (e.g.,
R,Python).
