Programming, problem solving, and algorithms

CPSC 203, 2026 W1

September 17, 2026

Announcements

• POTW1 and Lab1 are due Sunday at 8pm.
  • POTW2 and Lab2 will become available after that.
• Enroll in CPSC203 on PrairieTest.
  • Book your slot for examlet 1 (Thur Oct 1 - Mon Oct 5).
  • Students with accommodations: If you cannot see your accommodation when you try to book a slot, email me.
• First practice examlet will become available on Monday.
  • Covers same material as examlet 1.

Today’s Plan

• Data vs Information
  • Symbols can have multiple meanings
• Representation in computers
  • Computer hardware interprets electrical signals as binary digits (“bits”).
  • We can use bits to represent numbers, and numbers to represent virtually anything.

Summary

Today we explore the concept of representation in two important senses. First, we examine how computers represent rich, culturally complex concepts like colour using simple numbers. Second, we use colour representation as a metaphor for diversity and inclusion in computer science - just as removing a colour channel limits the colours we can create, limiting diversity of experience limits the ideas we can explore. We conclude by seeing this representation in action through image manipulation code.

Data vs Information

Data vs Information

• You care about information.
• Programs can process data

The definition of “information” and “data” are a bit slippery, because what is information in one context might be data in another. For a particular problem, the data is what the program can process while the information is what the human cares about. Note that the representation / interpretation might be trivial: If the information is numbers, then the data is probably the same number (forboding…).

Also: Humans will still have to transform information into knowledge and/or action…

Multiple Interpretations

• What do the following English words mean?
  • produce
  • contest
  • object
  • console
• What does this colour mean?

• With interpretation (noun or verb), the word meaning becomes clear.

• Red can mean many things

  • emotion: anger, joy, love, mourning (depends on your cultural background)
  • politics: communism, socialism (but: Republicans???)
  • safety: danger, stop
  • finance: loss or debt

Multiple Representations

• How can we represent this colour?

• Words

  • red (english)
  • rouge (french)
  • ckʷim (hən̓q̓əmin̓əm̓)
  • pula (tagalog)
  • 红色 (simplified Chinese)

• Numbers

  • (255, 0, 0)
  • #FF0000

• light of a certain wavelength
• an object which reflects those wavelengths, such as a fabric swatch
• blood(?)
• hən̓q̓əmin̓əm̓ is the language of the Musqueam people.

How to Design Data / Functions / Programs

• Let’s review HtDD / HtDF / HtDF recipes

Computer Representation

Representation

Today we’re exploring a fundamental question: How do we represent the world as data?

Note that “representation” has (at least) two meanings:

• Technical: How computers encode rich concepts (like colour) as numbers
• Social: Who is represented in this discipline, and why it matters

Course content will focus on the former.

As a field, computer science continues to struggle with the latter. I encourage you all, both in the course and beyond, to stamp your own interpretations and ideas on the field even if the incumbents might not agree. While the demographics of computing have been historically narrow, the field also has an unmatched enthusiasm for innovation and “breaking things”.

Computer Data

What does data look like to a computer?

• Detect voltage levels (actually the presence of electrical charges in tiny capacitors).

• Analog vs digital: What’s the difference?

• Binary digits –> “bits”

• Picture the capacitors as little cups containing water.
  • Discuss analog vs digital interpretation of the amount of water.
• Positive and negative charges interpreted as 1 and 0, which leads us to “binary”
  • Discuss why we decided to go with binary, as opposed to decimal or something else. (Actually, in some systems they use other powers of 2.)

But Humans use Decimal Numbers

• Most common approach to representing numbers for humans is the Hindu-Arabic numeral system.
  • It is a positional system using 10 as the radix.
  • Often called base-10 or decimal.

3	1	5	7
103 = 1000	102 = 100	101 = 10	100 = 1

Write out full english version of the decimal number.

Converting between Bases

• We can use other bases.
  • The Babylonians used base-60.
  • Computers use base-2 or binary.

1	1	0	1
[2]3 = 8	[2]2 = 4	[2]1 = 2	[2]0 = 1

Convert the binary number to decimal.

Your turn: Thinking about bits

• What’s the largest number you can represent with 4 bits?
• How many bits do you need to represent 120?
• If I give you one more bit, what happens to how many numbers you can represent?
• How high can you count on your fingers? and toes?
• As the number \(k\) grows, how does the number of digits grow?

• Largest with 4 bits: 15 (1111).
• Bits for 120: 7 bits (120 < 128 = 2^7).
• One more bit: DOUBLES the numbers you can represent!
• Remember 2¹⁰ about 1000, 2²⁰ = 10⁶.
• Complexity (number of digits) grows as \(\log k\).
• What about non-positional number systems?
  • Tally or roman numerals grow as \(k\) (even for Roman numerals, since the largest single digit is “M” = one thousand).

From bits to… everything?

We can represent integers, so we can assign integers to any other (discrete) data

• Text: ASCII or Unicode (aka UTF-8, UTF-16, UTF-32)
• Sound (amplitude samples)
• Images (pixel colours)
• Video (sequences of images)
• Humans (UBC student numbers, social insurance numbers, national identification number, …)

Let’s see how this works with colour.

How many different characters can we represent with UTF-32? Just 1,112,064 (even though 2³² = 4 billion).

Colour

Colour Interpretation

How does light wavelength become colour? Biological interpretation

What’s your favorite colour? Psychological interpretation

Does that colour influence your dress/decor/purchases? Cultural interpretation

Normal computer images do none of these three things (although it does take advantage of how human biology detects light).

Human Colour Perception

• Human color vision has three channels
  • Our brain experiences color based on the intensity of light detected by “red”, “green” and “blue” cone cells in our retinas

• If we are shown a yellow wavelength
  • L cones will respond strongly
  • M cones will respond almost as strongly
  • S cones will respond weakly
• To fake a yellow wavelength (for a human)
  • Show a lot of a red wavelength
  • Show a little less of a green wavelength
  • Show little or no blue wavelength

Colour Representation

• So we only need to figure out how to manage blends of three colors!

• Can we use integers to represent colours?

  • One way: RGB or (red, green, blue), where each “component” is integer in the range 0 through 255.
  • For example: (255, 0, 127) == ?
  • Fun calculator for colour values: https://colorizer.org

• Why 256 possible values?

• Early computer colour might only use 5 bits / channel (so slightly less than 16 bits).
  • 8 bits / channel is convenient as (1) computers actually work with data on a byte (or even word = 32 or 64 bit) level and (2) it is sufficient that humans don’t notice the gradations.

Aside: Other Colour Representations

• There are alternative ways to represent colour.
  • HSV (hue, saturation, value) is closer to how humans usually pick colours.
  • CMY (cyan, magenta, yellow) for reflective colour.
  • Sometimes you want more than three channels:
    • “Alpha” for controlling transparency.
    • CMYK to allow for proper black.
    • Additional wavelengths for sensors operating outside human capability.

• HSV:
  • Hue (H): The color family, measured in degrees from 0° to 360° on a color wheel (0° is red, 120° is green, and 240° is blue).
  • Saturation (S): The purity or intensity of the color, ranging from 0% (gray) to 100% (vivid, pure color).
  • Value (V): The brightness or lightness of the color, ranging from 0% (absolute black) to 100% (full brightness).
• CMYK is used for printers.
• “Multi-spectral” images are used widely in geosensing and astronomy.

Colour Representation Example

0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1

• What colour is this?

• Easier to read if we use hexadecimal (base-16) representation:

  • A hex “digit” is one of 0123456789abcdef
  • One hex digit can represent the same as four binary digits

0 1 0 1 | 1 0 1 1 | 0 1 0 1 | 1 0 1 1 | 0 1 0 1 | 1 0 1 1

5 | b | 5 | b | 5 | b

None of these colours: This is a shade of grey.

Practice

What colour is this 24-bit number?

0110 0111 0100 1110 1010 0111

• First: convert to hex using digits 0123456789abcdef

Walk through conversion on board: - First 8 bits (0110 0111) = Red channel - Next 8 bits (0100 1110) = Green channel - Last 8 bits (1010 0111) = Blue channel - Convert each 4-bit group to hex digit - Result: #674ea7