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")

User presses A on keyboard
Keyboard sends electronic signal
Signal enters system unit
Signal temporarily stores in RAM
CPU processes the signal
Display adapter sends data to monitor
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

Why do computers use binary?
Convert 25₁₀ to binary
What is the hex equivalent of decimal 15?
How many bits in a byte?
Explain RGB colour model
Convert 10110111₂ to hex
What does Unicode support that ASCII doesn't?
Find MSB & LSB of 1100101₂
Why is hexadecimal useful?
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.

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Monday, June 1, 2026