Base Camp

Base Camp 🏔️

The same value can be written in different **number bases** — and for this topic you need three of them: **decimal**, **binary** and **hexadecimal**. By the end you'll know each base's digit set, why computers live in binary, and the grade-9 answer to *"why do programmers use hex?"* — the bit examiners love to mark.

Decimal — base 10

**Decimal** is the everyday system you already count in. It is **base 10**: it uses **ten** digits, `0` to `9`. When you run out of digits you carry into the next column — that is why `9 + 1` rolls over to `10`.

Binary — base 2

A computer is built from millions of tiny switches, each either **off** or **on**. So at the lowest level every piece of data and every instruction is stored in **binary**. **Binary** is **base 2**: it uses just **two** digits, `0` and `1`. That is the whole alphabet a computer really has.

Binary's alphabet

Which digits can appear in a binary number?

• Only 0 and 1
• 0 to 9
• 0 to 7
• 0 to 9 and A to F

Hexadecimal — base 16

**Hexadecimal** (hex for short) is **base 16**, so it needs **sixteen** digits. The digits `0`–`9` aren't enough, so hex borrows letters: • `A` = 10 · `B` = 11 · `C` = 12 • `D` = 13 · `E` = 14 · `F` = 15 So the hex digits run `0 1 2 3 4 5 6 7 8 9 A B C D E F`.

Letters as digits

In hexadecimal, what value does the digit `F` stand for?

• 15
• 16
• 6
• 14

Match the digit sets

Why bother with hex? 💡

Computers work in binary, so why do programmers write hex? Two reasons — and top answers give **both**: 1. **Easier for humans** to read and write — one hex digit replaces four binary digits, so hex is far shorter and you make fewer copying mistakes. 2. **Simple to convert to/from binary** — each hex digit maps to exactly **4 bits** (a *nibble*), so swapping between them is quick and reliable.

The grade-9 answer

Pick the TWO reasons programmers use hexadecimal.

• It is shorter and easier for humans to read and write
• It converts easily to and from binary
• Computers actually store data in hex
• Hex needs fewer wires inside the CPU

One digit, four bits

Each hexadecimal digit represents exactly _____ binary bits, which makes hex a _____ way to write out long binary numbers.

Where you'll meet them

Each base has its place: • **Decimal** — how humans do everyday maths. • **Binary** — how the computer really stores everything, deep down. • **Hex** — a human-friendly shorthand for binary: colour codes like `#FF8800`, memory addresses and MAC addresses are all written in hex.

Spot the base

A web colour is written as `#1A2B`. Which base is that?

• Hexadecimal
• Binary
• Decimal

In the exam 🎯

Camp packed. Grade-9 habits for number bases: • Know the digit sets cold: decimal `0–9`, binary `0–1`, hex `0–9` then `A–F`. • *"Why hex?"* needs **both** halves — easier for humans to read/write **and** simple to convert to/from binary. • Remember one hex digit = **4 bits**, and computers store everything in **binary** because their switches are two-state.