GCSE Computer Science
Binary and hexadecimal — GCSE Computer Science
Why computers use binary
Computers store everything as binary — sequences of 1s and 0s. Not because it's elegant, but because it maps directly to physical reality: a switch is either on or off, a transistor is either conducting or not. Binary isn't a convention. It's a consequence of how the hardware works.
GCSE Computer Science expects you to convert between binary, denary, and hexadecimal — and to understand why each one exists.
Binary — base 2
Each binary digit is a bit. Eight bits make a byte. Each bit has a place value — 128, 64, 32, 16, 8, 4, 2, 1 — and the value of the number is the sum of all the place values where the bit is 1.
128 64 32 16 8 4 2 1
0 1 0 0 1 1 0 1 = 7764 + 8 + 4 + 1 = 77. That's all binary conversion is — adding up the place values of the bits that are switched on.
Hexadecimal — base 16
Hexadecimal uses 16 digits: 0–9, then A–F. A is 10, B is 11, up to F which is 15. Each hex digit represents exactly four binary bits — which is why hex is used as a shorthand for binary. Two hex digits represent one byte.
Binary: 0100 1101
Hex: 4 D = 4DConverting between them
Denary to binary: find the largest place value that fits, subtract it, repeat.
Binary to hex: split into groups of four bits, convert each group.
Hex to denary: multiply each digit by its place value (16¹, 16⁰) and add.
The interactive tool below lets you type any value and watch the conversion happen in real time. The relationship between the columns becomes intuitive faster than any written explanation can make it.
Confusing the number of bits with the highest value they can represent. 8 bits can represent 256 values (0–255), not 0–256. The distinction between “how many values” and “highest value” appears on mark schemes.
What examiners actually test
Conversion questions are almost always worth straightforward marks — if you know the method, you get the marks. The most common mistakes are getting the place values wrong, forgetting that hex goes A–F, and losing track of which direction the conversion is going. Practice with the tool until the place values are automatic.
Binary and hex conversion is one of the few GCSE topics where the marks are almost guaranteed once the method's automatic — which takes more reps than one worked example gives. Python Coach's 195 challenges across 27 lessons build that automaticity, with progress tracking for every student in your class. Sixty teaching days free, no payment details required to set your school up.
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