1.1 - Binary and Hexadecimal (Data Representation) | IGCSE Computer Science (0478)

In this IGCSE Computer Science lesson (0478), we explain binary and hexadecimal number systems. Understand how computers use binary, why hexadecimal is needed, and how to convert between number systems with simple examples. 📘 Based on the Cambridge IGCSE syllabus 🎓 Perfect for revision and learning basics of digital data 🔢 Lesson 1.1: Binary and Hexadecimal | IGCSE Computer Science (0478) Computers operate using only two digits: 0 and 1. This is known as the binary number system. However, binary numbers can become long and difficult for humans to read, so we often use a simpler representation: the hexadecimal system. In this lesson, we’ll break down both systems, how to convert between them, and why they are essential for computing. 🔹 Binary Number System (Base 2) Uses only two digits: 0 and 1 Each digit is called a bit A group of 8 bits is a byte Binary represents on/off, true/false, or high/low voltage in computers 📌 Example: Binary number: 1101 Decimal equivalent: 8 + 4 + 0 + 1 = 13 📊 Positional values in binary (from right to left): Bit Value 1 2⁰ = 1 0 2¹ = 2 1 2² = 4 1 2³ = 8 So, 1101₂ = 13₁₀ 🔹 Hexadecimal Number System (Base 16) Uses 16 digits: 0 to 9 and A to F A = 10, B = 11, ..., F = 15 Often used in memory addresses, colour codes, and machine code 📌 Example: Hex 1A = (1 × 16) + 10 = 26 🔄 Why Use Hexadecimal in Computing? Shorter and easier to read than long binary numbers Compact format for memory values (1 byte = 2 hex digits) Common in low-level programming, debugging, and HTML colours (e.g., #FF5733) 🔁 Converting Between Binary and Hexadecimal Binary → Hexadecimal Break binary into groups of 4 bits (from right to left) Convert each group to a hex digit 📘 Example: Binary: 11110011 → 1111 0011 → F3 (F = 15, 3 = 3) Hexadecimal → Binary Convert each hex digit to 4-bit binary 📘 Example: Hex: A7 → A = 1010, 7 = 0111 → Binary = 10100111 🧠 Real-World Applications Memory locations in RAM and ROM are often displayed in hex Web design: Colour codes use hex (e.g., #00FF00) Assembly/machine code: Instruction sets are written in hex MAC addresses: Hex is used in hardware IDs 🧪 Practice Exercises Convert 10110101 to hexadecimal Convert 3F to binary Convert 10011010 to decimal What is the binary equivalent of B4? 🎓 IGCSE Syllabus Requirements You must be able to: Convert between binary, decimal, and hexadecimal Add binary numbers Understand practical uses of binary and hex Know why hexadecimal is used instead of binary in many applications 🧾 Important Keywords Bit, Byte Base 2, Base 16 Nibble (4 bits) Hexadecimal representation Binary addition Overflow errors 🏁 Conclusion Understanding binary and hexadecimal is foundational to computer science. Every program, image, or video is just a long sequence of 0s and 1s — and hexadecimal helps us manage and understand it better. 🏷 Hashtags & Keywords #BinaryNumbers #Hexadecimal #IGCSEComputerScience #0478 #BinaryToHex #HexToBinary #DataRepresentation #CambridgeIGCSE #BooleanLogic #ComputerScienceBasics