Topic 2 - Computer Architecture

IB Computer Science

Data Representation

Bits and Bytes

Binary

• Language of the CPU and modern computing
• 1, 0
• Base 2

Binary→Denary

Examples

• 11101001→
• 10001101→

Examples

• 11101001→233
• 10001101→141

Denary→Binary

Examples

• 168→
• 83→

Examples

• 168→10101000
• 83→01010011

Hexadecimal

• More efficiently represents large binary values
• Colors
• Memory addresses (esp. in assembly)
• MAC Addresses
• Base 16

Hexadecimal→Denary

Hexadecimal→Denary

Examples

• 3B →
• 18E →

Examples

• 3B → 59
• 18E → 398

Denary→Hexadecimal

Examples

• 480 → 1E0
• 232 → E8

Hexadecimal ↔ Binary

• Each hexadecimal digit represents 4 binary bits
• 111011 → 3B
• 11010110 → D6
• 92 → 10010010

How is text displayed?

• Strings are made up of characters
• Each character is represented by a certain number of bytes
• Two formats: ASCII and Unicode

ASCII

• Use 8 bits for each character
• 7 bits used for each character, 1 bit is parity bit
• 2^7 or 128 possible characters
• Lower case, capitals, numbers, symbols, spaces, punctuation included

Unicode

• Used to represent multiple languages
• More bits, so more characters can be represented
• UTF-8 → 8 bits

UTF-16 → 16 bits

UTF-32→32 bits

How are images displayed?

• Each display (monitor, phone screen, etc.) is divided into pixels
• pixel = “little square” in grid
• pixel = smallest controllable element in display
• Each pixel has a different color
• Each pixel has one color at one moment
• The color is combination of red, blue and green
• Pixels together display image
• 1024x764 screen resolution →1024 pixels high, 764 wide
• 1080p, HD, 4K refers to number of pixels in screen

Pixels

• Each color in each pixel represented by 6 digit hexadecimal value( Ex: 70EF5A)
• First two values represent red, second two represent green and last two represent blue (Ex:70EF5A)
• 16^2*16^2*16^2 = 256*256*256 possible color combinations

IB Questions

Answers

https://drive.google.com/file/d/1SzuKvNN7ybuq7jsR4C9pBF4i6xHxUiOq/view?usp=sharing

​