Base Camp
Decimal, binary, hex. Meet the three number bases, learn their digit sets, and nail the grade-9 "why hex?" answer.
Work it through together, step by step
A free interactive activity that works the method through with a class, step by step.
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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.
The three bases
You need three number bases for this topic. Each has its own fixed set of digits:
Why binary?
A computer is built from millions of tiny switches, each either **off** or **on**. Two states means two digits, so at the lowest level every piece of data and every instruction is stored in **base 2**.
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
Rank the hex digits
Hex borrows letters once it runs past 9: A is 10, B is 11, C is 12, and so on up to F. Put these four hex digits in order, **smallest value first**.
- 9
- A
- C
- F
Match the digit sets
- Decimal, base 10
- Binary, base 2
- Hexadecimal, base 16
- Digits 0 to 9
- Only 0 and 1
- Digits 0 to 9, then A to F
Why bother with hex?
Computers work in binary, so why do programmers write hex? Two reasons, and top answers give **both**:
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.
What is C worth?
Hex counts 0 to 9, then the letters take over: A is 10, B is 11, and so on. What decimal value does the hex digit **C** represent?
Hex in the wild
You meet hex wherever binary needs to be human-friendly. A web colour like **#FF8800**, a memory address, and a device's MAC address are all written in hexadecimal, because it stays short and converts straight back to the bits underneath.
Spot the base
A web colour is written as `#1A2B`. Which base is that?
- Hexadecimal
- Binary
- Decimal
Explain it yourself
In your own words, explain why programmers use hexadecimal instead of writing raw binary. A grade-9 answer covers BOTH reasons.
- First reason: it is easier for humans to read and write
- Second reason: it converts easily to and from binary (one hex digit = 4 bits)
- Write in full sentences