Cambridge Syllabus Notes

📚 Data Representation

Computers store everything as numbers. The simplest numbers are 0 and 1, called bits. A group of 8 bits is called a byte and can represent 256 different values (from 0 to 255). All data—text, images, audio, video—gets broken down into these tiny on/off signals.

💡 Why Binary?

Think of a light switch: it’s either off (0) or on (1). Binary uses the same idea. It’s simple, reliable, and fits perfectly with electronic circuits that can easily detect two distinct voltage levels.

🔢 Binary Numbers

Each bit can be 0 or 1. The value of a binary number is calculated by adding powers of 2 for each bit that is 1. For example:

Binary	Decimal
0000	0
0001	1
0010	2
0011	3
0100	4
0101	5
0110	6
0111	7
1000	8
1001	9

📝 Representing Text: ASCII

ASCII (American Standard Code for Information Interchange) assigns a decimal number to each character. For example, 'A' = 65, 'a' = 97. Here’s a quick reference:

Character	Decimal	Binary
A	65	01000001
a	97	01100001
0	48	00110000
9	57	00111001
Space	32	00100000

📷 Images, Audio & Video

All media is stored as numbers too:

📷 Images – a grid of pixels. Each pixel can be 8‑bit grayscale (0–255) or 24‑bit colour (8 bits each for Red, Green, Blue).
🎧 Audio – a sequence of samples. CD audio uses 16‑bit samples at 44.1 kHz.
📹 Video – frames of images plus audio, all encoded as binary data.

📝 Exam Tips

Tip 1: 1 bit = 2 states, 8 bits = 256 values. Use $2^n$ to find the range for any number of bits.

Tip 2: When converting decimal to binary, repeatedly divide by 2 and write down the remainders (bottom‑up).

Tip 3: For ASCII, remember common ranges: 65–90 for A–Z, 97–122 for a–z, 48–57 for 0–9, 32 for space.

Tip 4: Show step‑by‑step conversions in exam answers; this demonstrates understanding.

Tip 5: Practice converting between binary, decimal, and hexadecimal (base‑16) – many questions involve hex.

Understand how and why computers use binary to represent all forms of data