Programming, problem solving, and algorithms

CPSC 203, 2025 W2

January 14, 2026

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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.

Learning outcomes

1. Computers interpret electrical signals as bits, and bits can be used to represent numbers, and numbers can be used to represent colours, which suggests that we can represent virtually anything!

Representation

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

We’ll look at “representation” in two important senses:

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

Let’s start with something personal and familiar: colour.

Annotate as you go - don’t read the bullets verbatim. Let the dual meaning emerge through the lesson.

Colour interpretation

What’s your favorite colour? Do you have a sense for why it’s your favorite? Does that colour influence your dress/decor/purchases?

Psychological: https://www.buzzfeed.com/mermaidbarbie/which-color-truly-matches-your-personality-24h9koy69s

Cultural: https://en.wikipedia.org/wiki/Color_symbolism

Your turn: Colour—cultural interpretations

Activity—In pairs, choose a colour (primary or secondary) and find something in its cultural symbolism that surprises you. Contradictions are especially interesting. Report your findings to the class (briefly).

05:00

Big design implications for data visualization

Colour—representation

First, some general questions…

What does data look like to a computer?

Is that enough?

1. Positive and negative charges interpreted as 1 and 0.
2. Binary digits = bits

Colour—representation

Can we use bits to represent integers?

3	1	5	7
103	102	101	100

103	102	101	100
23	22	21	20

Talk about the BASE of the number.

Your turn: Binary to decimal

Convert these binary numbers to decimal:

Binary	Decimal
1010	_______
1101	_______
0111	_______

03:00

Answers: 10, 13, 7

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?

03:00

• Largest with 4 bits: 15 (1111)
• Bits for 120: 7 bits (120 < 128 = 2^7)
• One more bit: DOUBLES the numbers you can represent!

Can we represent any integer this way? YES! Until we run out of memory. But we have more memory than we can even conceive of.

From bits to… everything?

We’ve seen that bits can represent integers.

But integers are just the beginning!

If we can assign numbers to things, we can represent anything:

• Text (A=65, B=66, …)
• Sound (amplitude samples)
• Images (pixel colours)
• Video (sequences of images)
• Your favorite song, your family photos, this lecture…

Let’s see how this works with colour.

Colour—representation

Can we use integers to represent colours?

One way: RGB (red, green, blue), where each “component” is in range 0 through 255.

ex. (255, 0, 127) ==

Fun calculator for colour values: https://colorizer.org

How many bits for 256 values? 4 5 6 7 8 9 10

Colour—representation

What colour is

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

Easier to read if we use hexadecimal representation:

Each component is represented by 2 hex digits 0123456789abcdef

ex. #674ea7

Hex = base 16

Colour—hexadecimal

What colour is this 24-bit number?

0110 0111 0100 1110 1010 0111

Converting to hexadecimal: #___________

(Use 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

Representation: An aside

What do you observe about the following RGB colours?

Red	Green	Blue
255	0	0
17	0	178
45	0	13
200	0	220
62	0	37
130	0	95

[Your 7-minute narrative with RGB cube prop about missing dimensions and diversity in CS]

Colour and Code

Make the poppies pop!

PC: https://www.epicgardening.com/spring-wildflowers-from-seed/

Examine each pixel. If its red colour channel is high (over 200, say), then leave it as is. Otherwise, change the pixel to grey by setting all 3 colour channels to the average of their original values.

Colour and Code

import numpy as np
from skimage import io
import matplotlib.pyplot as plt

Pixel = tuple[np.uint8, np.uint8, np.uint8]  # (r, g, b)

'''Input: Pixel p
   Output: Pixel
   Function: If the pixel has high red value, then don't change it, otherwise
   fade the pixel to grey.  Note, to grey a pixel, set all colour channels to
   the average of the 3.
'''
def boost_red_pixel(p: Pixel) -> Pixel:
    # setup -- extract the colour channels as ints
    red = int(p[0])
    green = int(p[1])
    blue = int(p[2])
    # compute grey 
    grey = (red + green + blue)//3

    # conditionally change the pixel to grey
    if red < 200:
        red = green = blue = grey

    # return updated pixel
    return (red, green, blue)

def fancify(img: np.ndarray) -> np.ndarray:
    H, W = img.shape[:2] # grab the height and width of the image
    out = img.copy()     # write to a copy

    # traverse every pixel in the image and change it!
    for row in range(H):
        for col in range(W):
            out[row, col] = boost_red_pixel(img[row,col])

    # return image with changed pixels
    return out

def main() -> None:
    
    img = io.imread('https://raw.githubusercontent.com/UBC-CS/cpsc203/refs/heads/main/images/poppyfield.jpg')[..., :3]     # keep first 3 channels (RGB)
    
    out = fancify(img)
  
    plt.imshow(out)
    plt.axis('off')
    plt.show()
  
main()

Your turn: Change image or boost

Experiment with the code! Try one or more of these:

1. Find a different image URL and boost a different colour (green? blue?)
2. Change the threshold value (try 150 instead of 200)
3. Instead of greying, try inverting: red = 255 - red
4. What happens if you boost pixels that are LOW in red instead of high?

12:00

What you learned today

You’ve discovered something profound:

• Computers store everything as bits (0s and 1s)
• Bits can represent integers (using binary, base 2)
• Integers can represent colours (RGB: three numbers 0-255)
• Which means bits can represent images (grids of pixels)
• And you wrote code to manipulate those images!

From electrical signals → to making poppies pop.