GRADE 10 ICT UNIT 3 Data Representation in Computer Systems English Medium Online Classes

What is Data Representation?

Computers cannot understand human languages directly. They only understand electrical signals with two states:

State	Binary Value
OFF	0
ON	1

Everything inside a computer is represented using combinations of 0 and 1:

• 🔤 Letters & Text
• 🔢 Numbers
• 🖼️ Images & Videos
• 🎵 Music & Audio
• 📄 Documents

🔄 How a Letter Appears on Screen (Example: "A")

1. User presses A on keyboard
2. Keyboard sends electronic signal
3. Signal enters system unit
4. Signal temporarily stores in RAM
5. CPU processes the signal
6. Display adapter sends data to monitor
7. Letter A appears on screen ✨

💡 Why Binary?
Electronic circuits easily identify only two conditions:
• High Voltage = 1
• Low Voltage = 0
→ Binary is the most reliable system for computers!

Definition

A Number System is a method of representing numbers using symbols.

Key Components:

• Unit: A single object (e.g., one mango, one book)
• Number: A symbol representing quantity (e.g., 1, 25, 100)
• Base (Radix): Number of symbols available in the system

📊 Main Number Systems in Computing

System	Base	Symbols Used	Badge
Binary	2	0, 1	Base-2
Octal	8	0–7	Base-8
Decimal	10	0–9	Base-10
Hexadecimal	16	0–9, A–F	Base-16

🎯 Exam Tip: Memorize the bases! Binary=2, Octal=8, Decimal=10, Hex=16

Binary Digits (Bits)

Only two values: 0 and 1

Binary	Circuit State
0	OFF
1	ON

🎨 Binary in Colour: RGB Model

Computers create colours using three channels:

• 🔴 Red
• 🟢 Green
• 🔵 Blue

Each channel ranges from 0 to 255 (8 bits = 2⁸ = 256 values)

Example: Dark Purple
R = 135, G = 31, B = 120
Written as: (135, 31, 120)

Why 255? → 11111111₂ = 255₁₀ (max value for 8 bits)

💡 Real-World Use: Hex Colour Codes

Hex Code	Colour	RGB Equivalent
#FF0000	🔴 Red	(255,0,0)
#00FF00	🟢 Green	(0,255,0)
#0000FF	🔵 Blue	(0,0,255)
#871F78	🟣 Dark Purple	(135,31,120)

Decimal Basics

• Base: 10
• Digits: 0,1,2,3,4,5,6,7,8,9

📐 Positional Value Concept

25₁₀ = (2 × 10¹) + (5 × 10⁰) = 20 + 5 = 25

Weighting Factors Table

Position	Value	Name
10⁰	1	Ones
10¹	10	Tens
10²	100	Hundreds
10³	1000	Thousands

Example with Decimals

302.75₁₀ = 3×10² + 0×10¹ + 2×10⁰ + 7×10⁻¹ + 5×10⁻²
= 300 + 0 + 2 + 0.7 + 0.05
= 302.75

Binary Basics

• Base: 2
• Digits: 0, 1
• Bit: Smallest unit = 1 Binary Digit

Binary Weighting Factors

Position	2ⁿ	Value
2⁰	1	1
2¹	2	2
2²	4	4
2³	8	8
2⁴	16	16
2⁵	32	32
2⁶	64	64
2⁷	128	128

✅ Conversion Example

11101101₂ = 1×128 + 1×64 + 1×32 + 0×16 + 1×8 + 1×4 + 0×2 + 1×1
= 128 + 64 + 32 + 0 + 8 + 4 + 0 + 1
= 237₁₀

🔷 Octal Number System (Base-8)

• Digits: 0,1,2,3,4,5,6,7
• Weighting: 8⁰=1, 8¹=8, 8²=64, 8³=512

236₈ = (2×64) + (3×8) + (6×1) = 128 + 24 + 6 = 158₁₀

🔶 Hexadecimal Number System (Base-16)

• Digits: 0–9 and A–F
• Hex → Decimal: A=10, B=11, C=12, D=13, E=14, F=15

Position	16ⁿ	Value
16⁰	1	1
16¹	16	16
16²	256	256
16³	4096	4096

15E₁₆ = (1×256) + (5×16) + (14×1) = 256 + 80 + 14 = 350₁₀

✨ Why Hexadecimal Matters

Binary numbers get very long! Hex provides a compact shorthand:

1111111111111111₂ → FFFF₁₆ (much easier to read & write!)

🛠️ Real Uses of Hex

• 📍 Memory addresses: 0x7A4F
• 🎨 Web colour codes: #FF5733
• 🐛 Error/debug codes in programming
• 🌐 URL encoding & web design

📌 Decimal Numbers

Term	Definition	Example: 329
MSD Most Significant Digit	First non-zero digit from the left	3
LSD Least Significant Digit	Last non-zero digit from the right	9

More Examples

Number	MSD	LSD
1237	1	7
58.32	5	2
0.0975	9	5

💻 Binary Numbers: MSB & LSB

Binary: 1001₂
• MSB (Most Significant Bit) = Leftmost 1 → 1
• LSB (Least Significant Bit) = Rightmost bit → 1

💡 MSB has the highest weight; LSB has the lowest weight in binary calculations.

🔁 Decimal → Binary (Divide by 2)

Convert 12₁₀ to Binary:

12 ÷ 2 = 6 → remainder 0
6 ÷ 2 = 3 → remainder 0
3 ÷ 2 = 1 → remainder 1
1 ÷ 2 = 0 → remainder 1

Read remainders bottom → top: 1100₂ ✅

🔁 Decimal → Octal (Divide by 8)

158₁₀ → Octal:
158÷8=19 r6 | 19÷8=2 r3 | 2÷8=0 r2
Answer: 236₈

🔁 Decimal → Hex (Divide by 16)

47₁₀ → Hex:
47÷16=2 r15 → 15 = F
Answer: 2F₁₆

---

⚡ Shortcut: Binary → Octal (Group by 3)

Binary	Octal
000	0
001	1
010	2
011	3
100	4
101	5
110	6
111	7

1011101₂ → Group: 001 011 101 → 1 3 5 → 135₈

⚡ Shortcut: Binary → Hex (Group by 4)

Binary	Hex	Binary	Hex
0000	0	1000	8
0001	1	1001	9
0010	2	1010	A
0011	3	1011	B
0100	4	1100	C
0101	5	1101	D
0110	6	1110	E
0111	7	1111	F

10110₂ → Pad: 0001 0110 → 1 6 → 16₁₆

🎯 Pro Tip: Always pad with leading zeros to make complete groups of 3 (octal) or 4 (hex)!

📦 Data Storage Hierarchy (Exam Critical!)

Unit	Equivalent	Real-World Example
1 Bit	0 or 1	Single switch state
1 Nibble	4 Bits	Half a byte
1 Byte	8 Bits	One character (e.g., 'A')
1 KB	1024 Bytes	Short text paragraph
1 MB	1024 KB	1 MP3 song (~3-5 MB)
1 GB	1024 MB	~250 photos or 1 HD movie
1 TB	1024 GB	~250,000 photos
1 PB	1024 TB	Large data centre storage

🔤 Character Coding Systems

📜 ASCII (American Standard Code for Information Interchange)

• Represents English letters, numbers, basic symbols
• 7-bit or 8-bit encoding
• Examples: A=65, B=66, a=97

🌍 Unicode (Universal Character Encoding)

• Supports all world languages: Sinhala, Tamil, Arabic, Chinese, Emoji 😊
• Backward compatible with ASCII
• Modern standard for web & software

⚠️ Exam Alert: Know the difference! ASCII = English only; Unicode = Global languages.

🔑 Key Facts to Memorize

BASES: • Binary = 2 • Octal = 8 • Decimal = 10 • Hex = 16 DIGITS: • Binary → 0,1 • Octal → 0–7 • Decimal → 0–9 • Hex → 0–9, A–F STORAGE: • 1 Bit = smallest unit • 1 Byte = 8 Bits • 1 KB = 1024 Bytes (NOT 1000!) COLOUR: • RGB range = 0–255 per channel • 8 bits = 1 byte = 256 values CONVERSION SHORTCUTS: • Binary→Octal: group by 3 bits • Binary→Hex: group by 4 bits SIGNIFICANCE: • MSD/MSB = Leftmost (highest weight) • LSD/LSB = Rightmost (lowest weight)

🎯 Top 10 Exam Questions

1. Why do computers use binary?
2. Convert 25₁₀ to binary
3. What is the hex equivalent of decimal 15?
4. How many bits in a byte?
5. Explain RGB colour model
6. Convert 10110111₂ to hex
7. What does Unicode support that ASCII doesn't?
8. Find MSB & LSB of 1100101₂
9. Why is hexadecimal useful?
10. Calculate storage: How many KB in 2 MB?

🔘 Part A: Multiple Choice (MCQ)

Q1. Which number system is directly used by computers? A. Decimal   B. Octal   C. Binary   D. Hexadecimal

✅ Answer: C. Binary
Computers use electronic circuits with two states: ON(1) and OFF(0).

Q2. What is the base of the Binary Number System? A. 8   B. 10   C. 16   D. 2

✅ Answer: D. 2
Binary uses only two digits: 0 and 1.

Q3. Which symbol is NOT used in Octal? A. 5   B. 6   C. 7   D. 8

✅ Answer: D. 8
Octal digits: 0,1,2,3,4,5,6,7 only.

Q4. Hex equivalent of decimal 15? A. E   B. F   C. G   D. H

✅ Answer: B. F
Decimal 10=A, 11=B, 12=C, 13=D, 14=E, 15=F

Q5. Smallest unit of data? A. Byte   B. Bit   C. KB   D. Nibble

✅ Answer: B. Bit
Bit = Binary Digit (0 or 1)

🕳️ Part B: Fill in the Blanks

Question	Answer
Base of decimal system	10
Smallest data unit	Bit
A nibble contains ___ bits	4
1 Byte = ___ bits	8
Hexadecimal base	16
Binary digits	0 and 1
Hex after E	F
MSD is on the ___ side	Left
LSD is on the ___ side	Right
RGB = Red, Green, ___	Blue

✍️ Part C: Short Answer Samples

Q: Why do computers use Binary?

Electronic circuits easily represent two stable states: ON and OFF. These map perfectly to binary digits 1 and 0, making processing reliable, fast, and simple to implement in hardware.

Q: What is Unicode?

Unicode is a universal character encoding standard that represents text in virtually all writing systems worldwide (Sinhala, Tamil, Arabic, Chinese, Emoji, etc.), unlike ASCII which is English-only.

🔁 Part E: Conversion Practice (Answers Only)

Question	Answer
25₁₀ → Binary	11001₂
50₁₀ → Binary	110010₂
158₁₀ → Octal	236₈
47₁₀ → Hex	2F₁₆
1011₂ → Decimal	11₁₀
11111111₂ → Decimal	255₁₀
236₈ → Decimal	158₁₀
2F₁₆ → Decimal	47₁₀
1011101₂ → Octal	135₈
10110111₂ → Hex	B7₁₆

🎓 Final Tip: Practice conversions daily! Write out the steps until they become automatic. Focus on Binary↔Decimal and Binary↔Hex – these appear in 90% of Unit 3 exams.