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
- Octal
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