Worksheet

A7.7 Analogue, digital and graphics

Data representation · A level · AQA 7517 4.5.6.1, Eduqas A500QS 2.3 · about 30 min

What this lesson is about

Analogue and digital signals, ADCs and DACs, bitmapped and vector graphics and when to use each.

• Bit patterns
• Analogue and digital
• ADC and DAC
• Bitmapped graphics
• Vector graphics
• Vector or bitmap?

Questions 6 marks in all

1. [1 mark]How many bytes does an 800 x 600 bitmap with a colour depth of 24 bits take, ignoring metadata?

2. [1 mark]How many different levels can a 10-bit ADC output?

3. [1 mark]A company logo must look sharp on a business card and on a large banner. Which is better, and why?

   1. AA vector graphic, because the shapes are recalculated at any size with no loss
   2. BA bitmap, because it stores every pixel
   3. CA bitmap, because it has a colour depth
   4. DA vector graphic, because it is always a smaller file

4. [1 mark]Which of these would a vector graphic store for a circle?

   Tick every answer that is true.

   1. AThe centre coordinates
   2. BThe radius
   3. CThe fill colour
   4. DThe colour of every pixel inside it

5. [1 mark]Where would a DAC be used?

   1. ABetween a computer's digital audio and a loudspeaker
   2. BBetween a microphone and a computer
   3. CBetween a light sensor and a microcontroller
   4. DInside a hard disk to store bits

6. [1 mark]The byte 01000001 is stored in memory. What does it represent?

   1. AIt depends on how the program interprets it
   2. BThe letter A
   3. CThe number 65
   4. DA machine code instruction

The task: vector to bitmap

shapes is a vector drawing of two objects. A rectangle has x and y (its top-left corner) and w and h; a circle has a centre cx, cy and a radius r. All are in pixels. Rasterise it onto a bitmap WIDTH 32 pixels wide and HEIGHT 16 pixels tall, 1 bit per pixel. 1. The pixel in column col (0 to 31) and row row (0 to 15) has its centre at (col + 0.5, row + 0.5). It is on when that centre is inside any shape: for a rectangle, x <= px < x + w and y <= py < y + h; for a circle, the squared distance from the centre is no more than r squared. 2. Print the 16 rows, top row first, each as 32 characters: # for on and . for off. 3. Then print, calculating each number from WIDTH and HEIGHT: 1-bit bitmap: <n> bits, 24-bit bitmap: <n> bits, and 1-bit bitmap at 4 times the size: <n> bits (4 times the width and 4 times the height, still 1 bit per pixel).

# the two lines every program starts with: the commands, then the robot
from bugbot import *
connect()

WIDTH = 32
HEIGHT = 16
shapes = [
    {"type": "rect", "x": 2, "y": 2, "w": 10, "h": 6},
    {"type": "circle", "cx": 22, "cy": 8, "r": 5},
]

def inside(shape, px, py):
    return False

Plan your program here, then type it in and press Run.

Do it on the robot
www.bugbotlab.com/learn/a7-7-analogue-digital-and-graphics/
The simulator checks it and tells you when it passes. Nothing to install, no account.

Challenges

1. Rasterise the drawing at 4 times the size by scaling the shapes, not the bitmap. Compare it with scaling the 32 × 16 bitmap up.
2. Add a line shape with two end points and a thickness.
3. Estimate how many bytes the vector drawing takes as text, and compare it with the 24-bit bitmap.