Form Three Computer Science Notes

All Form Three Computer Science Chapters

1. Chapter 1Data RepresentationRead below · Free
2. Chapter 2Computer ProgrammingContinue in the app
3. Chapter 3Computer NetworksContinue in the app
4. Chapter 4Database and Database Management SystemContinue in the app

Learning Outcomes

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

• explain the concept of data representation and the difference between data and information;
• describe bits, bytes and larger storage units;
• identify the four main number systems (decimal, binary, octal, hexadecimal) and convert between them;
• perform binary addition and subtraction;
• explain ASCII and Unicode and why Unicode matters for Kiswahili and other languages;
• apply knowledge of data representation to everyday digital technology.

Key Terms and Concepts

1. Concept of Data Representation

Data are the raw materials of computing – numbers, letters, symbols, images, sounds and video that a computer receives. On their own they have little meaning.

Data representation is the way these raw materials are turned into a form that the computer’s electronic circuits can understand and process. All modern computers use digital (binary) representation.

Difference Between Data and Information

Why Computers Represent Data Digitally

• Electronic circuits are reliable when they only have two clear states: ON (1) and OFF (0).
• Binary signals are less affected by noise and interference than continuous (analogue) signals.
• Digital data can be copied, stored and transmitted without loss of quality.
• It is easy to design hardware and software that work with only two symbols.

Bits, Nibbles, Bytes and Larger Units

A bit is the smallest piece of digital data. It can hold only one of two values: 0 (OFF / false / low voltage) or 1 (ON / true / high voltage). All data inside a computer is ultimately stored as long strings of bits.

Types of Digital Data and Data Types

• Numbers – integers and real numbers used in calculations.
• Text – letters, digits and symbols that form words and sentences.
• Images – still pictures made of coloured dots (pixels).
• Audio – sound waves sampled and stored as numbers.
• Video – sequences of images plus audio played at high speed.

Programming languages classify data so the computer knows how to treat them: Integer, Real/Decimal, Character, String, Boolean (True/False).

2. Number Systems and Their Representation

A number system is a method of writing numbers using a limited set of symbols (digits) and rules. The most important property is its base (also called radix). In positional notation the value of a digit depends on its position; moving one place to the left multiplies the value by the base.

The Four Number Systems You Must Know

Decimal Number System (Base 10)

• Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
• Used by humans in everyday life
• Each place is a power of 10

Binary Number System (Base 2)

• Digits: 0 and 1 only
• The native language of computers
• Each place is a power of 2: … 16, 8, 4, 2, 1

Octal Number System (Base 8)

• Digits: 0–7
• Sometimes used as a shorter way to write binary
• Each place is a power of 8

Hexadecimal Number System (Base 16)

• Digits: 0–9 and A, B, C, D, E, F (where A=10, B=11 … F=15)
• Very common in computing (memory addresses, colour codes, MAC addresses)
• Each place is a power of 16

3. Conversion Between Number Systems

Binary → Decimal

Write the place values (powers of 2) under each bit and add the values where the bit is 1.

Decimal → Binary (Repeated Division)

Divide the decimal number by 2 repeatedly and record the remainders. Read the remainders from bottom to top.

Hexadecimal → Decimal

Decimal → Hexadecimal

Use repeated division by 16. Remainders 10–15 are written as A–F.

Binary ↔ Hexadecimal (Shortcut)

Group binary digits in sets of four (starting from the right). Convert each group to its hex equivalent.

4. Binary Arithmetic

Rules of Binary Addition

• 0 + 0 = 0
• 0 + 1 = 1
• 1 + 0 = 1
• 1 + 1 = 0 and carry 1 to the next column
• 1 + 1 + 1 = 1 and carry 1

Rules of Binary Subtraction

• 0 – 0 = 0
• 1 – 0 = 1
• 1 – 1 = 0
• 0 – 1 → borrow 1 from the left (the 0 becomes 10₂ which is 2₁₀), so 10₂ – 1 = 1

Always convert the binary numbers and the answer back to decimal and verify that the arithmetic is correct. This catches most common errors.

5. Character Coding: ASCII and Unicode

Computers only understand numbers. To store letters, digits and symbols we must give each character a unique numeric code. This process is called character coding (or character encoding).

ASCII

• American Standard Code for Information Interchange
• Uses 7 bits → 128 possible characters (0–127)
• Covers English uppercase & lowercase letters, digits 0–9, punctuation and control codes

Unicode

• Designed to support every writing system in the world
• Can represent over 1 million characters
• Includes Latin, Arabic, Chinese, Kiswahili letters, emojis, mathematical symbols, etc.
• Common encodings: UTF-8 (most popular on the web) and UTF-16

Differences Between ASCII and Unicode

Chapter Summary

• Data are raw facts; information is processed, meaningful data.
• Computers represent all data digitally using bits (0 and 1) because two-state electronics are reliable and noise-resistant.
• Storage units: bit → nibble (4 bits) → byte (8 bits) → KB → MB → GB → TB (powers of 1024).
• Main digital data types: numbers, text, images, audio, video. Programming data types include integer, real, character, string and Boolean.
• Number systems: Decimal (base 10), Binary (base 2), Octal (base 8), Hexadecimal (base 16). Each uses positional (place-value) notation.
• Conversion methods: place-value addition (to decimal) and repeated division (from decimal). Binary ↔ Hex is done by grouping bits in fours.
• Binary addition and subtraction follow simple rules with carry and borrow; always verify by converting to decimal.
• ASCII encodes 128 English characters with 7 bits. Unicode encodes virtually every character in the world (including Kiswahili) and is the modern standard.
• Understanding data representation is essential for everything digital – from phone storage to AI systems.