Hello Class! 

Please read this article on topic A1.2.2

Please email me your answers by 9:30

No. You may not use a calculator. 

I love these questions because they get to the "why" of binary.

By the end of this lesson, you should be able to:

1. Describe how integers are represented using binary and hexadecimal (A1.2.1).

2. Convert between decimal, binary, and hexadecimal (A1.2.1).

3. Explain how binary encodes different types of data such as text, images, audio, and video (A1.2.2).

Part 1: 

1. Binary and Hexadecimal Represent Numbers

All data in computers is represented using bits (0s and 1s).
Examples:

• Decimal (base 10): digits 0–9

• Binary (base 2): digits 0–1

• Hexadecimal (base 16): digits 0–9 + A–F (A=10 … F=15)

Binary is efficient for machines, while hexadecimal is convenient for humans because 1 hex digit = 4 bits.

2. Conversion Rules

• Binary → Decimal: Expand using powers of 2
  Example: 101012=1⋅24+0⋅23+1⋅22+0⋅21+1⋅2010101_2 = 1·2^4 + 0·2^3 + 1·2^2 + 0·2^1 + 1·2^0101012​=1⋅24+0⋅23+1⋅22+0⋅21+1⋅20

• Hex → Decimal: Expand using powers of 16
  Example: 2F16=2⋅161+15⋅160=32+15=472F_{16} = 2·16^1 + 15·16^0 = 32 + 15 = 472F16​=2⋅161+15⋅160=32+15=47

• Binary ↔ Hex (Fast Method)
  Group into 4-bit chunks and translate.

3. Binary Stores All Types of Data

Everything becomes bits. Examples:

• Integers stored directly as binary numbers.

• Characters use encoding (ASCII or Unicode) where each character maps to a number.

• Images store pixels as binary numbers representing colour values.

• Audio stores sample amplitude as binary numbers taken many times per second.

• Video combines binary image frames + binary audio.

Part 2

Task A: Conversions

Convert the following:

1. 110101121101011_211010112​ → decimal

2. 10110010210110010_2101100102​ → hexadecimal

3. 3F163F_{16}3F16​ → binary

4. A716A7_{16}A716​ → decimal

5. Convert 2025102025_{10}202510​ into:

   • binary

   • hexadecimal

Task B: Short Answer Questions

Write clear explanations using complete sentences.

1. Explain why binary is used inside computers instead of decimal.

2. Describe how characters are stored using binary encoding.

3. Explain how a computer stores colour in an image. Your answer should mention numbers and binary.

4. Explain why hexadecimal is used by programmers even though computers use binary.

Task C: Application Question

A phone is recording video at 30 frames per second.
Each frame stores 1,000,000 pixels, and each pixel uses 24 bits.

1. Explain how binary is being used to store this video.

2. Calculate how many bits are needed to store 1 second of video.

3. Convert your answer from bits into bytes (divide by 8).

Optional Extension (For Early Finishers)

Research Unicode. Explain:

• Why ASCII is insufficient today.

• How Unicode solves this problem using binary encoding.

Write 1 short paragraph.